CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available" lang="en" dir="ltr"> <head> <meta charset="UTF-8"> <title>Ternary numeral system - Wikipedia</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )enwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy", "wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgRequestId":"fedca3d1-4531-46fd-a831-04152e95cd0e","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Ternary_numeral_system","wgTitle":"Ternary numeral system","wgCurRevisionId":1253065951,"wgRevisionId":1253065951,"wgArticleId":62950,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["CS1 maint: location missing publisher","Articles with short description","Short description is different from Wikidata","Use dmy dates from May 2019","Pages using sidebar with the child parameter","Webarchive template wayback links","Computer arithmetic","Positional numeral systems","Ternary computers"],"wgPageViewLanguage":"en","wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Ternary_numeral_system","wgRelevantArticleId":62950, "wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":false,"wgFlaggedRevsParams":{"tags":{"status":{"levels":1}}},"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{"pageLanguageCode":"en","pageLanguageDir":"ltr","pageVariantFallbacks":"en"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":false,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":20000,"wgRelatedArticlesCompat":[],"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q1056486","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true, "wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.cite.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","jquery.makeCollapsible.styles":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["ext.cite.ux-enhancements","mediawiki.page.media","site","mediawiki.page.ready","jquery.makeCollapsible","mediawiki.toc","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.ReferenceTooltips","ext.gadget.switcher","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap", "ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession","wikibase.sidebar.tracking"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=en&modules=ext.cite.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cjquery.makeCollapsible.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=en&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=en&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.5"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Ternary numeral system - Wikipedia"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//en.m.wikipedia.org/wiki/Ternary_numeral_system"> <link rel="alternate" type="application/x-wiki" title="Edit this page" href="/w/index.php?title=Ternary_numeral_system&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (en)"> <link rel="EditURI" type="application/rsd+xml" href="//en.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://en.wikipedia.org/wiki/Ternary_numeral_system"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en"> <link rel="alternate" type="application/atom+xml" title="Wikipedia Atom feed" href="/w/index.php?title=Special:RecentChanges&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Ternary_numeral_system rootpage-Ternary_numeral_system skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Jump to content</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Main menu" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Main menu</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Main menu</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">hide</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigation </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z"><span>Main page</span></a></li><li id="n-contents" class="mw-list-item"><a href="/wiki/Wikipedia:Contents" title="Guides to browsing Wikipedia"><span>Contents</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:Current_events" title="Articles related to current events"><span>Current events</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:Random" title="Visit a randomly selected article [x]" accesskey="x"><span>Random article</span></a></li><li id="n-aboutsite" class="mw-list-item"><a href="/wiki/Wikipedia:About" title="Learn about Wikipedia and how it works"><span>About Wikipedia</span></a></li><li id="n-contactpage" class="mw-list-item"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us" title="How to contact Wikipedia"><span>Contact us</span></a></li> </ul> </div> </div> <div id="p-interaction" class="vector-menu mw-portlet mw-portlet-interaction" > <div class="vector-menu-heading"> Contribute </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:Contents" title="Guidance on how to use and edit Wikipedia"><span>Help</span></a></li><li id="n-introduction" class="mw-list-item"><a href="/wiki/Help:Introduction" title="Learn how to edit Wikipedia"><span>Learn to edit</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Community_portal" title="The hub for editors"><span>Community portal</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:RecentChanges" title="A list of recent changes to Wikipedia [r]" accesskey="r"><span>Recent changes</span></a></li><li id="n-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_upload_wizard" title="Add images or other media for use on Wikipedia"><span>Upload file</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Main_Page" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="The Free Encyclopedia" src="/static/images/mobile/copyright/wikipedia-tagline-en.svg" width="117" height="13" style="width: 7.3125em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Special:Search" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Search Wikipedia [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Search</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Search Wikipedia" aria-label="Search Wikipedia" autocapitalize="sentences" title="Search Wikipedia [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Search</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personal tools"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Appearance" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Appearance</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_en.wikipedia.org&uselang=en" class=""><span>Donate</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:CreateAccount&returnto=Ternary+numeral+system" title="You are encouraged to create an account and log in; however, it is not mandatory" class=""><span>Create account</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:UserLogin&returnto=Ternary+numeral+system" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o" class=""><span>Log in</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Log in and more options" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Personal tools" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Personal tools</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_en.wikipedia.org&uselang=en"><span>Donate</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:CreateAccount&returnto=Ternary+numeral+system" title="You are encouraged to create an account and log in; however, it is not mandatory"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Create account</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:UserLogin&returnto=Ternary+numeral+system" title="You're encouraged to log in; however, it's not mandatory. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Log in</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Pages for logged out editors <a href="/wiki/Help:Introduction" aria-label="Learn more about editing"><span>learn more</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:MyContributions" title="A list of edits made from this IP address [y]" accesskey="y"><span>Contributions</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:MyTalk" title="Discussion about edits from this IP address [n]" accesskey="n"><span>Talk</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Site"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Contents" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Contents</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Comparison_to_other_bases" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Comparison_to_other_bases"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Comparison to other bases</span> </div> </a> <button aria-controls="toc-Comparison_to_other_bases-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Comparison to other bases subsection</span> </button> <ul id="toc-Comparison_to_other_bases-sublist" class="vector-toc-list"> <li id="toc-Sum_of_the_digits_in_ternary_as_opposed_to_binary" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sum_of_the_digits_in_ternary_as_opposed_to_binary"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Sum of the digits in ternary as opposed to binary</span> </div> </a> <ul id="toc-Sum_of_the_digits_in_ternary_as_opposed_to_binary-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Compact_ternary_representation:_base_9_and_27" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Compact_ternary_representation:_base_9_and_27"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Compact ternary representation: base 9 and 27</span> </div> </a> <ul id="toc-Compact_ternary_representation:_base_9_and_27-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Practical_usage" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Practical_usage"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Practical usage</span> </div> </a> <button aria-controls="toc-Practical_usage-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Practical usage subsection</span> </button> <ul id="toc-Practical_usage-sublist" class="vector-toc-list"> <li id="toc-Binary-coded_ternary" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Binary-coded_ternary"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Binary-coded ternary</span> </div> </a> <ul id="toc-Binary-coded_ternary-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tryte" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Tryte"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Tryte</span> </div> </a> <ul id="toc-Tryte-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Ternary numeral system</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 33 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-33" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">33 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D8%B8%D8%A7%D9%85_%D8%B9%D8%AF_%D8%AB%D9%84%D8%A7%D8%AB%D9%8A" title="نظام عد ثلاثي – Arabic" lang="ar" hreflang="ar" data-title="نظام عد ثلاثي" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Sam-ch%C3%ACn-hoat" title="Sam-chìn-hoat – Minnan" lang="nan" hreflang="nan" data-title="Sam-chìn-hoat" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Sistema_ternari" title="Sistema ternari – Catalan" lang="ca" hreflang="ca" data-title="Sistema ternari" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Trojkov%C3%A1_soustava" title="Trojková soustava – Czech" lang="cs" hreflang="cs" data-title="Trojková soustava" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Tern%C3%A6rt_talsystem" title="Ternært talsystem – Danish" lang="da" hreflang="da" data-title="Ternært talsystem" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Tern%C3%A4rsystem" title="Ternärsystem – German" lang="de" hreflang="de" data-title="Ternärsystem" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A4%CF%81%CE%B9%CE%B1%CE%B4%CE%B9%CE%BA%CF%8C_%CF%83%CF%8D%CF%83%CF%84%CE%B7%CE%BC%CE%B1_%CE%B1%CF%81%CE%AF%CE%B8%CE%BC%CE%B7%CF%83%CE%B7%CF%82" title="Τριαδικό σύστημα αρίθμησης – Greek" lang="el" hreflang="el" data-title="Τριαδικό σύστημα αρίθμησης" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Sistema_ternario" title="Sistema ternario – Spanish" lang="es" hreflang="es" data-title="Sistema ternario" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Triuma_sistemo" title="Triuma sistemo – Esperanto" lang="eo" hreflang="eo" data-title="Triuma sistemo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Syst%C3%A8me_ternaire" title="Système ternaire – French" lang="fr" hreflang="fr" data-title="Système ternaire" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%82%BC%EC%A7%84%EB%B2%95" title="삼진법 – Korean" lang="ko" hreflang="ko" data-title="삼진법" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Ternara_nombrosistemo" title="Ternara nombrosistemo – Ido" lang="io" hreflang="io" data-title="Ternara nombrosistemo" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Sistema_numerico_ternario" title="Sistema numerico ternario – Italian" lang="it" hreflang="it" data-title="Sistema numerico ternario" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Theluthi" title="Theluthi – Swahili" lang="sw" hreflang="sw" data-title="Theluthi" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Sist%C3%A8m_trin%C3%A8" title="Sistèm trinè – Haitian Creole" lang="ht" hreflang="ht" data-title="Sistèm trinè" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/Sistema_de_numera%C3%A7on_ternairo" title="Sistema de numeraçon ternairo – Mirandese" lang="mwl" hreflang="mwl" data-title="Sistema de numeraçon ternairo" data-language-autonym="Mirandés" data-language-local-name="Mirandese" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E4%B8%89%E9%80%B2%E6%B3%95" title="三進法 – Japanese" lang="ja" hreflang="ja" data-title="三進法" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Tern%C3%A6rt_talsystem" title="Ternært talsystem – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Ternært talsystem" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Uchlik_sanoq_sistemasi" title="Uchlik sanoq sistemasi – Uzbek" lang="uz" hreflang="uz" data-title="Uchlik sanoq sistemasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Tr%C3%B3jkowy_system_liczbowy" title="Trójkowy system liczbowy – Polish" lang="pl" hreflang="pl" data-title="Trójkowy system liczbowy" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Sistema_de_numera%C3%A7%C3%A3o_tern%C3%A1rio" title="Sistema de numeração ternário – Portuguese" lang="pt" hreflang="pt" data-title="Sistema de numeração ternário" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Sistem_ternar" title="Sistem ternar – Romanian" lang="ro" hreflang="ro" data-title="Sistem ternar" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D1%80%D0%BE%D0%B8%D1%87%D0%BD%D0%B0%D1%8F_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0_%D1%81%D1%87%D0%B8%D1%81%D0%BB%D0%B5%D0%BD%D0%B8%D1%8F" title="Троичная система счисления – Russian" lang="ru" hreflang="ru" data-title="Троичная система счисления" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Ternary_numeral_system" title="Ternary numeral system – Simple English" lang="en-simple" hreflang="en-simple" data-title="Ternary numeral system" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Lambar_Tubaxan" title="Lambar Tubaxan – Somali" lang="so" hreflang="so" data-title="Lambar Tubaxan" data-language-autonym="Soomaaliga" data-language-local-name="Somali" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A2%D1%80%D0%BE%D1%81%D1%82%D1%80%D1%83%D0%BA%D0%B8_%D0%BD%D1%83%D0%BC%D0%B5%D1%80%D0%B8%D1%87%D0%BA%D0%B8_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC" title="Троструки нумерички систем – Serbian" lang="sr" hreflang="sr" data-title="Троструки нумерички систем" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Tern%C3%A4ra_talsystemet" title="Ternära talsystemet – Swedish" lang="sv" hreflang="sv" data-title="Ternära talsystemet" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%A5%E0%B8%82%E0%B8%90%E0%B8%B2%E0%B8%99%E0%B8%AA%E0%B8%B2%E0%B8%A1" title="เลขฐานสาม – Thai" lang="th" hreflang="th" data-title="เลขฐานสาม" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C3%9C%C3%A7l%C3%BC_say%C4%B1_sistemi" title="Üçlü sayı sistemi – Turkish" lang="tr" hreflang="tr" data-title="Üçlü sayı sistemi" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D1%80%D1%96%D0%B9%D0%BA%D0%BE%D0%B2%D0%B0_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0_%D1%87%D0%B8%D1%81%D0%BB%D0%B5%D0%BD%D0%BD%D1%8F" title="Трійкова система числення – Ukrainian" lang="uk" hreflang="uk" data-title="Трійкова система числення" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%E1%BB%87_tam_ph%C3%A2n" title="Hệ tam phân – Vietnamese" lang="vi" hreflang="vi" data-title="Hệ tam phân" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E4%B8%89%E9%80%B2%E5%88%B6" title="三進制 – Cantonese" lang="yue" hreflang="yue" data-title="三進制" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%B8%89%E8%BF%9B%E5%88%B6" title="三进制 – Chinese" lang="zh" hreflang="zh" data-title="三进制" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1056486#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Ternary_numeral_system" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:Ternary_numeral_system" rel="discussion" title="Discuss improvements to the content page [t]" accesskey="t"><span>Talk</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Change language variant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">English</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Views"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Ternary_numeral_system"><span>Read</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Ternary_numeral_system&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Ternary_numeral_system&action=history" title="Past revisions of this page [h]" accesskey="h"><span>View history</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Tools" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Tools</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Tools</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">hide</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Actions </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Ternary_numeral_system"><span>Read</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Ternary_numeral_system&action=edit" title="Edit this page [e]" accesskey="e"><span>Edit</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Ternary_numeral_system&action=history"><span>View history</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> General </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:WhatLinksHere/Ternary_numeral_system" title="List of all English Wikipedia pages containing links to this page [j]" accesskey="j"><span>What links here</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:RecentChangesLinked/Ternary_numeral_system" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k"><span>Related changes</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Wikipedia:File_Upload_Wizard" title="Upload files [u]" accesskey="u"><span>Upload file</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:SpecialPages" title="A list of all special pages [q]" accesskey="q"><span>Special pages</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Ternary_numeral_system&oldid=1253065951" title="Permanent link to this revision of this page"><span>Permanent link</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Ternary_numeral_system&action=info" title="More information about this page"><span>Page information</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:CiteThisPage&page=Ternary_numeral_system&id=1253065951&wpFormIdentifier=titleform" title="Information on how to cite this page"><span>Cite this page</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:UrlShortener&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FTernary_numeral_system"><span>Get shortened URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FTernary_numeral_system"><span>Download QR code</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Print/export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=Ternary_numeral_system&action=show-download-screen" title="Download this page as a PDF file"><span>Download as PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Ternary_numeral_system&printable=yes" title="Printable version of this page [p]" accesskey="p"><span>Printable version</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> In other projects </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Ternary_numeral_system" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1056486" title="Structured data on this page hosted by Wikidata [g]" accesskey="g"><span>Wikidata item</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Base-3 numeral system</div> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r1246091330">.mw-parser-output .sidebar{width:22em;float:right;clear:right;margin:0.5em 0 1em 1em;background:var(--background-color-neutral-subtle,#f8f9fa);border:1px solid var(--border-color-base,#a2a9b1);padding:0.2em;text-align:center;line-height:1.4em;font-size:88%;border-collapse:collapse;display:table}body.skin-minerva .mw-parser-output .sidebar{display:table!important;float:right!important;margin:0.5em 0 1em 1em!important}.mw-parser-output .sidebar-subgroup{width:100%;margin:0;border-spacing:0}.mw-parser-output .sidebar-left{float:left;clear:left;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-none{float:none;clear:both;margin:0.5em 1em 1em 0}.mw-parser-output .sidebar-outer-title{padding:0 0.4em 0.2em;font-size:125%;line-height:1.2em;font-weight:bold}.mw-parser-output .sidebar-top-image{padding:0.4em}.mw-parser-output .sidebar-top-caption,.mw-parser-output .sidebar-pretitle-with-top-image,.mw-parser-output .sidebar-caption{padding:0.2em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-pretitle{padding:0.4em 0.4em 0;line-height:1.2em}.mw-parser-output .sidebar-title,.mw-parser-output .sidebar-title-with-pretitle{padding:0.2em 0.8em;font-size:145%;line-height:1.2em}.mw-parser-output .sidebar-title-with-pretitle{padding:0.1em 0.4em}.mw-parser-output .sidebar-image{padding:0.2em 0.4em 0.4em}.mw-parser-output .sidebar-heading{padding:0.1em 0.4em}.mw-parser-output .sidebar-content{padding:0 0.5em 0.4em}.mw-parser-output .sidebar-content-with-subgroup{padding:0.1em 0.4em 0.2em}.mw-parser-output .sidebar-above,.mw-parser-output .sidebar-below{padding:0.3em 0.8em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:115%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><table class="sidebar sidebar-collapse nomobile nowraplinks hlist"><tbody><tr><td class="sidebar-pretitle">Part of <a href="/wiki/Category:Numeral_systems" title="Category:Numeral systems">a series</a> on</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Numeral_system" title="Numeral system">Numeral systems</a></th></tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Positional_notation" title="Positional notation">Place-value notation</a></div></div><div class="sidebar-list-content mw-collapsible-content"><table class="sidebar-subgroup"><tbody><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Hindu%E2%80%93Arabic_numeral_system" title="Hindu–Arabic numeral system">Hindu–Arabic numerals</a></div></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Arabic_numerals" title="Arabic numerals">Western Arabic</a></li> <li><a href="/wiki/Eastern_Arabic_numerals" title="Eastern Arabic numerals">Eastern Arabic</a></li></ul> <hr /> <ul><li><a href="/wiki/Bengali_numerals" title="Bengali numerals">Bengali</a></li> <li><a href="/wiki/Devanagari_numerals" title="Devanagari numerals">Devanagari</a></li> <li><a href="/wiki/Gujarati_numerals" title="Gujarati numerals">Gujarati</a></li> <li><a href="/wiki/Gurmukhi_numerals" class="mw-redirect" title="Gurmukhi numerals">Gurmukhi</a></li> <li><a href="/wiki/Odia_numerals" title="Odia numerals">Odia</a></li> <li><a href="/wiki/Sinhala_numerals" title="Sinhala numerals">Sinhala</a></li> <li><a href="/wiki/Tamil_numerals" title="Tamil numerals">Tamil</a></li> <li><a href="/wiki/Malayalam_numerals" title="Malayalam numerals">Malayalam</a></li> <li><a href="/wiki/Telugu_script#Numerals" title="Telugu script">Telugu</a></li> <li><a href="/wiki/Kannada_script#Numerals" title="Kannada script">Kannada</a></li> <li><a href="/wiki/Dzongkha_numerals" title="Dzongkha numerals">Dzongkha</a></li></ul> <hr /> <ul><li><a href="/wiki/Tibetan_numerals" title="Tibetan numerals">Tibetan</a></li> <li><a href="/wiki/Balinese_numerals" title="Balinese numerals">Balinese</a></li> <li><a href="/wiki/Burmese_numerals" title="Burmese numerals">Burmese</a></li> <li><a href="/wiki/Javanese_numerals" title="Javanese numerals">Javanese</a></li> <li><a href="/wiki/Khmer_numerals" title="Khmer numerals">Khmer</a></li> <li><a href="/wiki/Lao_script#Numerals" title="Lao script">Lao</a></li> <li><a href="/wiki/Mongolian_numerals" title="Mongolian numerals">Mongolian</a></li> <li><a href="/wiki/Sundanese_numerals" title="Sundanese numerals">Sundanese</a></li> <li><a href="/wiki/Thai_numerals" title="Thai numerals">Thai</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c">East Asian systems</div></div><div class="sidebar-list-content mw-collapsible-content"> <dl><dt>Contemporary</dt></dl> <ul><li><a href="/wiki/Chinese_numerals" title="Chinese numerals">Chinese</a> <ul><li><a href="/wiki/Suzhou_numerals" title="Suzhou numerals">Suzhou</a></li></ul></li> <li><a href="/wiki/Hokkien_numerals" title="Hokkien numerals">Hokkien</a></li> <li><a href="/wiki/Japanese_numerals" title="Japanese numerals">Japanese</a></li> <li><a href="/wiki/Korean_numerals" title="Korean numerals">Korean</a></li> <li><a href="/wiki/Vietnamese_numerals" title="Vietnamese numerals">Vietnamese</a></li></ul> <hr /> <dl><dt>Historic</dt></dl> <ul><li><a href="/wiki/Counting_rods" title="Counting rods">Counting rods</a></li> <li><a href="/wiki/Tangut_numerals" title="Tangut numerals">Tangut</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c">Other systems</div></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/History_of_ancient_numeral_systems" title="History of ancient numeral systems">History</a></li></ul> <hr /> <dl><dt><a href="/wiki/Ancient_history" title="Ancient history">Ancient</a></dt></dl> <ul><li><a href="/wiki/Babylonian_cuneiform_numerals" title="Babylonian cuneiform numerals">Babylonian</a></li></ul> <hr /> <dl><dt><a href="/wiki/Post-classical_history" title="Post-classical history">Post-classical</a></dt></dl> <ul><li><a href="/wiki/Cistercian_numerals" title="Cistercian numerals">Cistercian</a></li> <li><a href="/wiki/Maya_numerals" title="Maya numerals">Mayan</a></li> <li><a href="/wiki/Muisca_numerals" title="Muisca numerals">Muisca</a></li> <li><a href="/wiki/Pentadic_numerals" title="Pentadic numerals">Pentadic</a></li> <li><a href="/wiki/Quipu" title="Quipu">Quipu</a></li> <li><a href="/wiki/Rumi_Numeral_Symbols" title="Rumi Numeral Symbols">Rumi</a></li></ul> <hr /> <dl><dt>Contemporary</dt></dl> <ul><li><a href="/wiki/Cherokee_syllabary#Numerals" title="Cherokee syllabary">Cherokee</a></li> <li><a href="/wiki/Kaktovik_numerals" title="Kaktovik numerals">Kaktovik</a> (Iñupiaq)</li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c">By <a href="/wiki/Radix" title="Radix">radix/base</a></div></div><div class="sidebar-list-content mw-collapsible-content"> <dl><dt>Common radices/bases</dt></dl> <ul><li><a href="/wiki/Binary_number" title="Binary number">2</a></li> <li><a class="mw-selflink selflink">3</a></li> <li><a href="/wiki/Quaternary_numeral_system" title="Quaternary numeral system">4</a></li> <li><a href="/wiki/Quinary" title="Quinary">5</a></li> <li><a href="/wiki/Senary" title="Senary">6</a></li> <li><a href="/wiki/Octal" title="Octal">8</a></li> <li><a href="/wiki/Decimal" title="Decimal">10</a></li> <li><a href="/wiki/Duodecimal" title="Duodecimal">12</a></li> <li><a href="/wiki/Hexadecimal" title="Hexadecimal">16</a></li> <li><a href="/wiki/Vigesimal" title="Vigesimal">20</a></li> <li><a href="/wiki/Sexagesimal" title="Sexagesimal">60</a></li></ul> <hr /> <dl><dt><a href="/wiki/Non-standard_positional_numeral_systems" title="Non-standard positional numeral systems">Non-standard radices/bases</a></dt></dl> <ul><li><a href="/wiki/Bijective_numeration" title="Bijective numeration">Bijective</a><span class="nowrap"> </span>(<a href="/wiki/Unary_numeral_system" title="Unary numeral system">1</a>)</li> <li><a href="/wiki/Signed-digit_representation" title="Signed-digit representation">Signed-digit</a><span class="nowrap"> </span>(<a href="/wiki/Balanced_ternary" title="Balanced ternary">balanced ternary</a>)</li> <li><a href="/wiki/Mixed_radix" title="Mixed radix">Mixed</a><span class="nowrap"> </span>(<a href="/wiki/Factorial_number_system" title="Factorial number system">factorial</a>)</li> <li><a href="/wiki/Negative_base" title="Negative base">Negative</a></li> <li><a href="/wiki/Complex-base_system" title="Complex-base system">Complex</a><span class="nowrap"> </span>(<a href="/wiki/Quater-imaginary_base" title="Quater-imaginary base">2<i>i</i></a>)</li> <li><a href="/wiki/Non-integer_base_of_numeration" title="Non-integer base of numeration">Non-integer</a><span class="nowrap"> </span>(<a href="/wiki/Golden_ratio_base" title="Golden ratio base">φ</a>)</li> <li><a href="/wiki/Asymmetric_numeral_systems" title="Asymmetric numeral systems">Asymmetric</a></li></ul></div></div></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="color: var(--color-base)"><div class="sidebar-list-title-c"><a href="/wiki/Sign-value_notation" title="Sign-value notation">Sign-value notation</a></div></div><div class="sidebar-list-content mw-collapsible-content"> <dl><dt>Non-alphabetic</dt></dl> <ul><li><a href="/wiki/Aegean_numerals" title="Aegean numerals">Aegean</a></li> <li><a href="/wiki/Attic_numerals" title="Attic numerals">Attic</a></li> <li><a href="/wiki/Aztec_script#Numerals" title="Aztec script">Aztec</a></li> <li><a href="/wiki/Brahmi_numerals" title="Brahmi numerals">Brahmi</a></li> <li><a href="/wiki/Chuvash_numerals" title="Chuvash numerals">Chuvash</a></li> <li><a href="/wiki/Egyptian_numerals" title="Egyptian numerals">Egyptian</a></li> <li><a href="/wiki/Etruscan_numerals" title="Etruscan numerals">Etruscan</a></li> <li><a href="/wiki/Kharosthi_numerals" class="mw-redirect" title="Kharosthi numerals">Kharosthi</a></li> <li><a href="/wiki/Prehistoric_counting" title="Prehistoric counting">Prehistoric counting</a></li> <li><a href="/wiki/Proto-cuneiform" title="Proto-cuneiform">Proto-cuneiform</a></li> <li><a href="/wiki/Roman_numerals" title="Roman numerals">Roman</a></li> <li><a href="/wiki/Tally_marks" title="Tally marks">Tally marks</a></li></ul> <hr /> <dl><dt><a href="/wiki/Alphabetic_numeral_system" title="Alphabetic numeral system">Alphabetic</a></dt></dl> <ul><li><a href="/wiki/Abjad_numerals" title="Abjad numerals">Abjad</a></li> <li><a href="/wiki/Armenian_numerals" title="Armenian numerals">Armenian</a></li> <li><a href="/wiki/Alphasyllabic_numeral_system" title="Alphasyllabic numeral system">Alphasyllabic</a> <ul><li><a href="/wiki/Aksharapalli" title="Aksharapalli">Akṣarapallī</a></li> <li><a href="/wiki/%C4%80ryabha%E1%B9%ADa_numeration" title="Āryabhaṭa numeration">Āryabhaṭa</a></li> <li><a href="/wiki/Katapayadi_system" title="Katapayadi system">Kaṭapayādi</a></li></ul></li> <li><a href="/wiki/Coptic_numerals" class="mw-redirect" title="Coptic numerals">Coptic</a></li> <li><a href="/wiki/Cyrillic_numerals" title="Cyrillic numerals">Cyrillic</a></li> <li><a href="/wiki/Ge%CA%BDez_script#Numerals" title="Geʽez script">Geʽez</a></li> <li><a href="/wiki/Georgian_numerals" title="Georgian numerals">Georgian</a></li> <li><a href="/wiki/Glagolitic_numerals" title="Glagolitic numerals">Glagolitic</a></li> <li><a href="/wiki/Greek_numerals" title="Greek numerals">Greek</a></li> <li><a href="/wiki/Hebrew_numerals" title="Hebrew numerals">Hebrew</a></li></ul></div></div></td> </tr><tr><td class="sidebar-below" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"> <a href="/wiki/List_of_numeral_systems" title="List of numeral systems">List of numeral systems</a></td></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Numeral_systems" title="Template:Numeral systems"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Numeral_systems" title="Template talk:Numeral systems"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Numeral_systems" title="Special:EditPage/Template:Numeral systems"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>A <b>ternary</b> <span class="rt-commentedText nowrap"><span class="IPA nopopups noexcerpt" lang="en-fonipa"><a href="/wiki/Help:IPA/English" title="Help:IPA/English">/<span style="border-bottom:1px dotted"><span title="/ˈ/: primary stress follows">ˈ</span><span title="'t' in 'tie'">t</span><span title="/ɜːr/: 'ur' in 'fur'">ɜːr</span><span title="'n' in 'nigh'">n</span><span title="/ər/: 'er' in 'letter'">ər</span><span title="/i/: 'y' in 'happy'">i</span></span>/</a></span></span> <a href="/wiki/Numeral_system" title="Numeral system">numeral system</a> (also called <b>base 3</b> or <b>trinary</b><sup id="cite_ref-Kindra2022_1-0" class="reference"><a href="#cite_note-Kindra2022-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>) has <a href="/wiki/3_(number)" class="mw-redirect" title="3 (number)">three</a> as its <a href="/wiki/Radix" title="Radix">base</a>. Analogous to a <a href="/wiki/Bit" title="Bit">bit</a>, a ternary <a href="/wiki/Numerical_digit" title="Numerical digit">digit</a> is a <b>trit</b> (<b>tri</b>nary dig<b>it</b>). One trit is equivalent to <a href="/wiki/Binary_logarithm" title="Binary logarithm">log<sub>2</sub></a> 3 (about 1.58496) bits of <a href="/wiki/Units_of_information" title="Units of information">information</a>. </p><p>Although <i>ternary</i> most often refers to a system in which the three digits are all non–negative numbers; specifically <a href="/wiki/0_(number)" class="mw-redirect" title="0 (number)">0</a>, <a href="/wiki/1_(number)" class="mw-redirect" title="1 (number)">1</a>, and <a href="/wiki/2_(number)" class="mw-redirect" title="2 (number)">2</a>, the adjective also lends its name to the <a href="/wiki/Balanced_ternary" title="Balanced ternary">balanced ternary</a> system; comprising the digits <a href="/wiki/%E2%88%921" title="−1">−1</a>, 0 and +1, used in comparison logic and <a href="/wiki/Ternary_computer" title="Ternary computer">ternary computers</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Comparison_to_other_bases">Comparison to other bases</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ternary_numeral_system&action=edit&section=1" title="Edit section: Comparison to other bases"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Representations of <a href="/wiki/Integer_number" class="mw-redirect" title="Integer number">integer numbers</a> in ternary do not get uncomfortably lengthy as quickly as in <a href="/wiki/Binary_numeral_system" class="mw-redirect" title="Binary numeral system">binary</a>. For example, <a href="/wiki/Decimal" title="Decimal">decimal</a> <a href="/wiki/365_(number)" title="365 (number)">365</a><sub>(10)</sub> or <a href="/wiki/Senary" title="Senary">senary</a> <span style="white-space:nowrap">1<span style="margin-left:0.25em">405</span></span><sub>(6)</sub> corresponds to binary <span style="white-space:nowrap">1<span style="margin-left:0.25em">0110</span><span style="margin-left:0.25em">1101</span></span><sub>(2)</sub> (nine <a href="/wiki/Bit" title="Bit">bits</a>) and to ternary <span style="white-space:nowrap">111<span style="margin-left:0.25em">112</span></span><sub>(3)</sub> (six digits). However, they are still far less compact than the corresponding representations in bases such as <a href="/wiki/Decimal" title="Decimal">decimal</a> – see below for a compact way to codify ternary using nonary (base 9) and <a href="/wiki/Septemvigesimal" class="mw-redirect" title="Septemvigesimal">septemvigesimal</a> (base 27). </p> <table class="wikitable" style="float:right; text-align:center"> <caption>A ternary <a href="/wiki/Multiplication_table" title="Multiplication table">multiplication table</a> </caption> <tbody><tr> <th>×</th> <th><b>1</b></th> <th><b>2</b></th> <th><b>10</b></th> <th><b>11</b></th> <th><b>12</b></th> <th><b>20</b></th> <th><b>21</b></th> <th><b>22</b></th> <th><b>100</b> </th></tr> <tr> <th><b>1</b> </th> <td>1</td> <td>2</td> <td>10</td> <td>11</td> <td>12</td> <td>20</td> <td>21</td> <td>22</td> <td>100 </td></tr> <tr> <th><b>2</b> </th> <td>2</td> <td>11</td> <td>20</td> <td>22</td> <td>101</td> <td>110</td> <td>112</td> <td>121</td> <td>200 </td></tr> <tr> <th><b>10</b> </th> <td>10</td> <td>20</td> <td>100</td> <td>110</td> <td>120</td> <td>200</td> <td>210</td> <td>220</td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">000</span></span> </td></tr> <tr> <th><b>11</b> </th> <td>11</td> <td>22</td> <td>110</td> <td>121</td> <td>202</td> <td>220</td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">001</span></span></td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">012</span></span></td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">100</span></span> </td></tr> <tr> <th><b>12</b> </th> <td>12</td> <td>101</td> <td>120</td> <td>202</td> <td>221</td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">010</span></span> </td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">022</span></span></td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">111</span></span></td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">200</span></span> </td></tr> <tr> <th><b>20</b> </th> <td>20</td> <td>110</td> <td>200</td> <td>220</td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">010</span></span></td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">100</span></span> </td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">120</span></span></td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">210</span></span></td> <td><span style="white-space:nowrap">2<span style="margin-left:0.25em">000</span></span> </td></tr> <tr> <th><b>21</b> </th> <td>21</td> <td>112</td> <td>210</td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">001</span></span></td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">022</span></span></td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">120</span></span> </td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">211</span></span></td> <td><span style="white-space:nowrap">2<span style="margin-left:0.25em">002</span></span></td> <td><span style="white-space:nowrap">2<span style="margin-left:0.25em">100</span></span> </td></tr> <tr> <th><b>22</b> </th> <td>22</td> <td>121</td> <td>220</td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">012</span></span></td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">111</span></span></td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">210</span></span> </td> <td><span style="white-space:nowrap">2<span style="margin-left:0.25em">002</span></span></td> <td><span style="white-space:nowrap">2<span style="margin-left:0.25em">101</span></span></td> <td><span style="white-space:nowrap">2<span style="margin-left:0.25em">200</span></span> </td></tr> <tr> <th><b>100</b> </th> <td>100</td> <td>200</td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">000</span></span></td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">100</span></span></td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">200</span></span></td> <td><span style="white-space:nowrap">2<span style="margin-left:0.25em">000</span></span> </td> <td><span style="white-space:nowrap">2<span style="margin-left:0.25em">100</span></span></td> <td><span style="white-space:nowrap">2<span style="margin-left:0.25em">200</span></span></td> <td><span style="white-space:nowrap">10<span style="margin-left:0.25em">000</span></span> </td></tr></tbody></table> <dl><dd><table class="wikitable"> <caption><b>Numbers from 0 to 3<sup>3</sup> − 1 in standard ternary</b> </caption> <tbody><tr align="center"> <th>Ternary </th> <td>0</td> <td>1</td> <td>2</td> <td>10</td> <td>11</td> <td>12</td> <td>20</td> <td>21</td> <td>22 </td></tr> <tr align="center"> <th>Binary </th> <td>0</td> <td>1</td> <td>10</td> <td>11</td> <td>100</td> <td>101</td> <td>110</td> <td>111</td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">000</span></span> </td></tr> <tr align="center"> <th>Senary </th> <td>0</td> <td>1</td> <td>2</td> <td>3</td> <td>4</td> <td>5</td> <td>10</td> <td>11</td> <td>12 </td></tr> <tr align="center"> <th>Decimal </th> <th>0</th> <th>1</th> <th>2</th> <th>3</th> <th>4</th> <th>5</th> <th>6</th> <th>7</th> <th>8 </th></tr> <tr> <td colspan="10" style="background-color:white;"> </td></tr> <tr align="center"> <th>Ternary </th> <td>100</td> <td>101</td> <td>102</td> <td>110</td> <td>111</td> <td>112</td> <td>120</td> <td>121</td> <td>122 </td></tr> <tr align="center"> <th>Binary </th> <td>1001</td> <td>1010</td> <td>1011</td> <td>1100</td> <td>1101</td> <td>1110</td> <td>1111 </td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">0000</span></span></td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">0001</span></span> </td></tr> <tr align="center"> <th>Senary </th> <td>13</td> <td>14</td> <td>15</td> <td>20</td> <td>21</td> <td>22</td> <td>23</td> <td>24</td> <td>25 </td></tr> <tr align="center"> <th>Decimal </th> <th>9</th> <th>10</th> <th>11</th> <th>12</th> <th>13</th> <th>14</th> <th>15</th> <th>16</th> <th>17 </th></tr> <tr> <td colspan="10" style="background-color:white;"> </td></tr> <tr align="center"> <th>Ternary </th> <td>200</td> <td>201</td> <td>202</td> <td>210</td> <td>211</td> <td>212</td> <td>220</td> <td>221</td> <td>222 </td></tr> <tr align="center"> <th>Binary </th> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">0010</span></span></td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">0011</span></span></td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">0100</span></span></td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">0101</span></span></td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">0110</span></span> </td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">0111</span></span></td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">1000</span></span></td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">1001</span></span></td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">1010</span></span> </td></tr> <tr align="center"> <th>Senary </th> <td>30</td> <td>31</td> <td>32</td> <td>33</td> <td>34</td> <td>35</td> <td>40</td> <td>41</td> <td>42 </td></tr> <tr align="center"> <th>Decimal </th> <th>18</th> <th>19</th> <th>20</th> <th>21</th> <th>22</th> <th>23</th> <th>24</th> <th>25</th> <th>26 </th></tr></tbody></table></dd></dl> <dl><dd></dd></dl> <dl><dd><table class="wikitable"> <caption><b>Powers of 3 in ternary</b> </caption> <tbody><tr align="center"> <th>Ternary </th> <td>1</td> <td>10</td> <td>100</td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">000</span></span></td> <td><span style="white-space:nowrap">10<span style="margin-left:0.25em">000</span></span> </td></tr> <tr align="center"> <th>Binary </th> <td>1</td> <td>11</td> <td>1001</td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">1011</span></span></td> <td><span style="white-space:nowrap">101<span style="margin-left:0.25em">0001</span></span> </td></tr> <tr align="center"> <th>Senary </th> <td>1</td> <td>3</td> <td>13</td> <td>43</td> <td>213 </td></tr> <tr align="center"> <th>Decimal </th> <td>1</td> <td>3</td> <td>9</td> <td>27</td> <td>81 </td></tr> <tr align="center"> <th>Power </th> <th><span style="font-size:120%">3</span><sup>0</sup></th> <th><span style="font-size:120%">3</span><sup>1</sup></th> <th><span style="font-size:120%">3</span><sup>2</sup> </th> <th><span style="font-size:120%">3</span><sup>3</sup></th> <th><span style="font-size:120%">3</span><sup>4</sup> </th></tr> <tr> <td colspan="10" style="background-color:white;"> </td></tr> <tr align="center"> <th>Ternary </th> <td><span style="white-space:nowrap">100<span style="margin-left:0.25em">000</span></span></td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">000</span><span style="margin-left:0.25em">000</span></span></td> <td><span style="white-space:nowrap">10<span style="margin-left:0.25em">000</span><span style="margin-left:0.25em">000</span></span> </td> <td><span style="white-space:nowrap">100<span style="margin-left:0.25em">000</span><span style="margin-left:0.25em">000</span></span></td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">000</span><span style="margin-left:0.25em">000</span><span style="margin-left:0.25em">000</span></span> </td></tr> <tr align="center"> <th>Binary </th> <td><span style="white-space:nowrap">1111<span style="margin-left:0.25em">0011</span></span></td> <td><span style="white-space:nowrap">10<span style="margin-left:0.25em">1101</span><span style="margin-left:0.25em">1001</span></span></td> <td><span style="white-space:nowrap">1000<span style="margin-left:0.25em">1000</span><span style="margin-left:0.25em">1011</span></span> </td> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">1001</span><span style="margin-left:0.25em">1010</span><span style="margin-left:0.25em">0001</span></span></td> <td><span style="white-space:nowrap">100<span style="margin-left:0.25em">1100</span><span style="margin-left:0.25em">1110</span><span style="margin-left:0.25em">0011</span></span> </td></tr> <tr align="center"> <th>Senary </th> <td><span style="white-space:nowrap">1<span style="margin-left:0.25em">043</span></span></td> <td><span style="white-space:nowrap">3<span style="margin-left:0.25em">213</span></span></td> <td><span style="white-space:nowrap">14<span style="margin-left:0.25em">043</span></span></td> <td><span style="white-space:nowrap">50<span style="margin-left:0.25em">213</span></span></td> <td><span style="white-space:nowrap">231<span style="margin-left:0.25em">043</span></span> </td></tr> <tr align="center"> <th>Decimal </th> <td>243</td> <td>729</td> <td><span style="white-space:nowrap">2<span style="margin-left:0.25em">187</span></span></td> <td><span style="white-space:nowrap">6<span style="margin-left:0.25em">561</span></span></td> <td><span style="white-space:nowrap">19<span style="margin-left:0.25em">683</span></span> </td></tr> <tr align="center"> <th>Power </th> <th><span style="font-size:120%">3</span><sup>5</sup></th> <th><span style="font-size:120%">3</span><sup>6</sup></th> <th><span style="font-size:120%">3</span><sup>7</sup> </th> <th><span style="font-size:120%">3</span><sup>8</sup></th> <th><span style="font-size:120%">3</span><sup>9</sup> </th></tr></tbody></table></dd></dl> <p>As for <a href="/wiki/Rational_number" title="Rational number">rational numbers</a>, ternary offers a convenient way to represent <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">3</span></span>⁠</span> as same as senary (as opposed to its cumbersome representation as an infinite string of <a href="/wiki/Recurring_decimal" class="mw-redirect" title="Recurring decimal">recurring digits</a> in decimal); but a major drawback is that, in turn, ternary does not offer a finite representation for <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span> (nor for <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">4</span></span>⁠</span>, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">8</span></span>⁠</span>, etc.), because <a href="/wiki/2_(number)" class="mw-redirect" title="2 (number)">2</a> is not a <a href="/wiki/Prime_number" title="Prime number">prime</a> <a href="/wiki/Factorization" title="Factorization">factor</a> of the base; as with base two, one-tenth (decimal<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">10</span></span>⁠</span>, senary <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">14</span></span>⁠</span>) is not representable exactly (that would need e.g. decimal); nor is one-sixth (senary <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">10</span></span>⁠</span>, decimal <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">6</span></span>⁠</span>). </p> <dl><dd><table class="wikitable"> <caption><b>Fractions in ternary</b> </caption> <tbody><tr align="center"> <th>Fraction </th> <td><b><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span></b></td> <td><b><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">3</span></span>⁠</span></b></td> <td><b><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">4</span></span>⁠</span></b></td> <td><b><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">5</span></span>⁠</span></b></td> <td><b><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">6</span></span>⁠</span></b></td> <td><b><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">7</span></span>⁠</span></b></td> <td><b><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">8</span></span>⁠</span></b></td> <td><b><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">9</span></span>⁠</span></b></td> <td><b><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">10</span></span>⁠</span></b></td> <td><b><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">11</span></span>⁠</span></b></td> <td><b><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">12</span></span>⁠</span></b></td> <td><b><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">13</span></span>⁠</span></b> </td></tr> <tr align="center"> <th>Ternary </th> <td>0.<span style="text-decoration:overline;">1</span></td> <td>0.1</td> <td>0.<span style="text-decoration:overline;">02</span></td> <td>0.<span style="text-decoration:overline;">0121</span></td> <td>0.0<span style="text-decoration:overline;">1</span></td> <td>0.<span style="text-decoration:overline;">010212</span></td> <td>0.<span style="text-decoration:overline;">01</span></td> <td>0.01</td> <td>0.<span style="text-decoration:overline;">0022</span></td> <td>0.<span style="text-decoration:overline;">00211</span></td> <td>0.0<span style="text-decoration:overline;">02</span></td> <td>0.<span style="text-decoration:overline;">002</span> </td></tr> <tr align="center"> <th>Binary </th> <td>0.1</td> <td>0.<span style="text-decoration:overline;">01</span></td> <td>0.01</td> <td>0.<span style="text-decoration:overline;">0011</span></td> <td>0.0<span style="text-decoration:overline;">01</span></td> <td>0.<span style="text-decoration:overline;">001</span></td> <td>0.001</td> <td>0.<span style="text-decoration:overline;">000111</span></td> <td>0.0<span style="text-decoration:overline;">0011</span></td> <td>0.<span style="text-decoration:overline;">0001011101</span></td> <td>0.00<span style="text-decoration:overline;">01</span></td> <td>0.<span style="text-decoration:overline;">000100111011</span> </td></tr> <tr align="center"> <th>Senary </th> <td>0.3</td> <td>0.2</td> <td>0.13</td> <td>0.<span style="text-decoration:overline;">1</span></td> <td>0.1</td> <td>0.<span style="text-decoration:overline;">05</span></td> <td>0.043</td> <td>0.04</td> <td>0.0<span style="text-decoration:overline;">3</span></td> <td>0.<span style="text-decoration:overline;">0313452421</span></td> <td>0.03</td> <td>0.<span style="text-decoration:overline;">024340531215</span> </td></tr> <tr align="center"> <th>Decimal </th> <th>0.5</th> <th>0.<span style="text-decoration:overline;">3</span></th> <th>0.25</th> <th>0.2</th> <th>0.1<span style="text-decoration:overline;">6</span></th> <th>0.<span style="text-decoration:overline;">142857</span></th> <th>0.125 </th> <th>0.<span style="text-decoration:overline;">1</span></th> <th>0.1</th> <th>0.<span style="text-decoration:overline;">09</span></th> <th>0.08<span style="text-decoration:overline;">3</span></th> <th>0.<span style="text-decoration:overline;">076923</span> </th></tr></tbody></table></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Sum_of_the_digits_in_ternary_as_opposed_to_binary">Sum of the digits in ternary as opposed to binary</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ternary_numeral_system&action=edit&section=2" title="Edit section: Sum of the digits in ternary as opposed to binary"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The value of a binary number with <i>n</i> bits that are all 1 is <span class="texhtml">2<sup><i>n</i></sup> − 1</span>. </p><p>Similarly, for a number <i>N</i>(<i>b</i>, <i>d</i>) with base <i>b</i> and <i>d</i> digits, all of which are the maximal digit value <span class="texhtml"><i>b</i> − 1</span>, we can write: </p> <dl><dd><span class="texhtml"><i>N</i>(<i>b</i>, <i>d</i>) = (<i>b</i> − 1)<i>b</i><sup><i>d</i>−1</sup> + (<i>b</i> − 1)<i>b</i><sup><i>d</i>−2</sup> + … + (<i>b</i> − 1)<i>b</i><sup>1</sup> + (<i>b</i> − 1)<i>b</i><sup>0</sup>,</span></dd> <dd><span class="texhtml"><span style="color:white"><i>N</i>(<i>b</i>, <i>d</i>)</span> = (<i>b</i> − 1)(<i>b</i><sup><i>d</i>−1</sup> + <i>b</i><sup><i>d</i>−2</sup> + … + <i>b</i><sup>1</sup> + 1),</span></dd> <dd><span class="texhtml"><span style="color:white"><i>N</i>(<i>b</i>, <i>d</i>)</span> = (<i>b</i> − 1)<i>M</i></span>.</dd> <dd><span class="texhtml"><i>bM</i> = <i>b</i><sup><i>d</i></sup> + <i>b</i><sup><i>d</i>−1</sup> + … + <i>b</i><sup>2</sup> + <i>b</i><sup>1</sup></span> and</dd> <dd><span class="texhtml">−<i>M</i> = −<i>b</i><sup><i>d</i>−1</sup> − <i>b</i><sup><i>d</i>−2</sup> − ... − b<sup>1</sup> − 1</span>, so</dd> <dd><span class="texhtml"><i>bM</i> − <i>M</i> = <i>b</i><sup><i>d</i></sup> − 1</span>, or</dd> <dd><span class="texhtml"><i>M</i> = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><i>b</i><sup><i>d</i></sup> − 1</span><span class="sr-only">/</span><span class="den"><i>b</i> − 1</span></span>⁠</span>.</span></dd></dl> <p>Then </p> <dl><dd><span class="texhtml"><i>N</i>(<i>b</i>, <i>d</i>) = (<i>b</i> − 1)<i>M</i>,</span></dd> <dd><span class="texhtml"><span style="color:white"><i>N</i>(<i>b</i>, <i>d</i>)</span> = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">(<i>b</i> − 1)(<i>b</i><sup><i>d</i></sup> − 1)</span><span class="sr-only">/</span><span class="den"><i>b</i> − 1</span></span>⁠</span>,</span></dd> <dd><span class="texhtml"><span style="color:white"><i>N</i>(<i>b</i>, <i>d</i>)</span> = <i>b</i><sup><i>d</i></sup> − 1.</span></dd></dl> <p>For a three-digit ternary number, <span class="texhtml"><i>N</i>(3, 3) = 3<sup>3</sup> − 1 = 26 = 2 × 3<sup>2</sup> + 2 × 3<sup>1</sup> + 2 × 3<sup>0</sup> = 18 + 6 + 2</span>. </p> <div class="mw-heading mw-heading3"><h3 id="Compact_ternary_representation:_base_9_and_27">Compact ternary representation: base 9 and 27</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ternary_numeral_system&action=edit&section=3" title="Edit section: Compact ternary representation: base 9 and 27"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Nonary (base 9, each digit is two ternary digits) or <a href="/wiki/Septemvigesimal" class="mw-redirect" title="Septemvigesimal">septemvigesimal</a> (base 27, each digit is three ternary digits) can be used for compact representation of ternary, similar to how <a href="/wiki/Octal" title="Octal">octal</a> and <a href="/wiki/Hexadecimal" title="Hexadecimal">hexadecimal</a> systems are used in place of <a href="/wiki/Binary_numeral_system" class="mw-redirect" title="Binary numeral system">binary</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Practical_usage">Practical usage</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ternary_numeral_system&action=edit&section=4" title="Edit section: Practical usage"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Fewest_weights_balance_puzzle.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/Fewest_weights_balance_puzzle.svg/220px-Fewest_weights_balance_puzzle.svg.png" decoding="async" width="220" height="330" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/78/Fewest_weights_balance_puzzle.svg/330px-Fewest_weights_balance_puzzle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/78/Fewest_weights_balance_puzzle.svg/440px-Fewest_weights_balance_puzzle.svg.png 2x" data-file-width="512" data-file-height="768" /></a><figcaption>Use of ternary numbers to balance an unknown integer weight from 1 to 40 kg with weights of 1, 3, 9 and 27 kg (4 ternary digits actually gives 3<sup>4</sup> = 81 possible combinations: −40 to +40, but only the positive values are useful)</figcaption></figure> <p>In certain analog logic, the state of the circuit is often expressed ternary. This is most commonly seen in <a href="/wiki/CMOS" title="CMOS">CMOS</a> circuits, and also in <a href="/wiki/Transistor%E2%80%93transistor_logic" title="Transistor–transistor logic">transistor–transistor logic</a> with <a href="/wiki/Push%E2%80%93pull_output" title="Push–pull output">totem-pole output</a>. The output is said to either be low (<a href="/wiki/Ground_(electricity)" title="Ground (electricity)">grounded</a>), high, or open (<a href="/wiki/High_impedance" title="High impedance">high-<i>Z</i></a>). In this configuration the output of the circuit is actually not connected to any <a href="/wiki/Voltage" title="Voltage">voltage</a> reference at all. Where the signal is usually grounded to a certain reference, or at a certain voltage level, the state is said to be high <a href="/wiki/Electrical_impedance" title="Electrical impedance">impedance</a> because it is open and serves its own reference. Thus, the actual voltage level is sometimes unpredictable. </p><p>A rare "ternary point" in common use is for defensive statistics in American <a href="/wiki/Baseball" title="Baseball">baseball</a> (usually just for <a href="/wiki/Pitcher" title="Pitcher">pitchers</a>), to denote fractional parts of an inning. Since the team on offense is allowed three <a href="/wiki/Out_(baseball)" title="Out (baseball)">outs</a>, each out is considered one third of a defensive inning and is denoted as <b>.1</b>. For example, if a player pitched all of the 4th, 5th and 6th innings, plus achieving 2 outs in the 7th inning, his <a href="/wiki/Innings_pitched" title="Innings pitched">innings pitched</a> column for that game would be listed as <b>3.2</b>, the equivalent of <style data-mw-deduplicate="TemplateStyles:r1154941027">.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="frac">3<span class="sr-only">+</span><span class="num">2</span>⁄<span class="den">3</span></span> (which is sometimes used as an alternative by some record keepers). In this usage, only the fractional part of the number is written in ternary form.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>Ternary numbers can be used to convey self-similar structures like the <a href="/wiki/Sierpi%C5%84ski_triangle" title="Sierpiński triangle">Sierpinski triangle</a> or the <a href="/wiki/Cantor_set" title="Cantor set">Cantor set</a> conveniently. Additionally, it turns out that the ternary representation is useful for defining the Cantor set and related point sets, because of the way the Cantor set is constructed. The Cantor set consists of the points from 0 to 1 that have a ternary expression that does not contain any instance of the digit 1.<sup id="cite_ref-Soltanifar_2006_1_4-0" class="reference"><a href="#cite_note-Soltanifar_2006_1-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Soltanifar_2006_2_5-0" class="reference"><a href="#cite_note-Soltanifar_2006_2-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Any terminating expansion in the ternary system is equivalent to the expression that is identical up to the term preceding the last non-zero term followed by the term one less than the last non-zero term of the first expression, followed by an infinite tail of twos. For example: 0.1020 is equivalent to 0.1012222... because the expansions are the same until the "two" of the first expression, the two was decremented in the second expansion, and trailing zeros were replaced with trailing twos in the second expression. </p><p>Ternary is the integer base with the lowest <a href="/wiki/Radix_economy" class="mw-redirect" title="Radix economy">radix economy</a>, followed closely by <a href="/wiki/Binary_numeral_system" class="mw-redirect" title="Binary numeral system">binary</a> and <a href="/wiki/Quaternary_numeral_system" title="Quaternary numeral system">quaternary</a>. This is due to its proximity to the <a href="/wiki/Mathematical_constant" title="Mathematical constant">mathematical constant</a> <a href="/wiki/E_(mathematical_constant)" title="E (mathematical constant)"><i>e</i></a>. It has been used for some computing systems because of this efficiency. It is also used to represent three-option <i>trees</i>, such as phone menu systems, which allow a simple path to any branch. </p><p>A form of <a href="/wiki/Redundant_binary_representation" title="Redundant binary representation">redundant binary representation</a> called a binary signed-digit number system, a form of <a href="/wiki/Signed-digit_representation" title="Signed-digit representation">signed-digit representation</a>, is sometimes used in low-level software and hardware to accomplish fast addition of integers because it can eliminate <a href="/wiki/Carry_(arithmetic)" title="Carry (arithmetic)">carries</a>.<sup id="cite_ref-Phatak_1994_6-0" class="reference"><a href="#cite_note-Phatak_1994-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Binary-coded_ternary">Binary-coded ternary</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ternary_numeral_system&action=edit&section=5" title="Edit section: Binary-coded ternary"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Simulation of ternary computers using binary computers, or interfacing between ternary and binary computers, can involve use of binary-coded ternary (BCT) numbers, with two or three bits used to encode each trit.<sup id="cite_ref-Frieder_1975_7-0" class="reference"><a href="#cite_note-Frieder_1975-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Parhami_2013_8-0" class="reference"><a href="#cite_note-Parhami_2013-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> BCT encoding is analogous to <a href="/wiki/Binary-coded_decimal" title="Binary-coded decimal">binary-coded decimal</a> (BCD) encoding. If the trit values 0, 1 and 2 are encoded 00, 01 and 10, conversion in either direction between binary-coded ternary and binary can be done in <a href="/wiki/Time_complexity#Logarithmic_time" title="Time complexity">logarithmic time</a>.<sup id="cite_ref-Jones_2016_1_9-0" class="reference"><a href="#cite_note-Jones_2016_1-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> A library of <a href="/wiki/C_(programming_language)" title="C (programming language)">C code</a> supporting BCT arithmetic is available.<sup id="cite_ref-Jones_2016_2_10-0" class="reference"><a href="#cite_note-Jones_2016_2-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Tryte">Tryte</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ternary_numeral_system&action=edit&section=6" title="Edit section: Tryte"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Some <a href="/wiki/Ternary_computer" title="Ternary computer">ternary computers</a> such as the <a href="/wiki/Setun" title="Setun">Setun</a> defined a <b>tryte</b> to be six trits<sup id="cite_ref-Impagliazzo_2006_11-0" class="reference"><a href="#cite_note-Impagliazzo_2006-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> or approximately 9.5 <a href="/wiki/Bit" title="Bit">bits</a> (holding more information than the <i>de facto</i> <a href="/wiki/Binary_number" title="Binary number">binary</a> <a href="/wiki/Byte" title="Byte">byte</a>).<sup id="cite_ref-Brousentsov_2010_12-0" class="reference"><a href="#cite_note-Brousentsov_2010-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ternary_numeral_system&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Qutrit" title="Qutrit">Qutrit</a></li> <li><a href="/wiki/Setun" title="Setun">Setun</a>, a <a href="/wiki/Ternary_computer" title="Ternary computer">ternary computer</a></li> <li><a href="/wiki/Ternary_logic" class="mw-redirect" title="Ternary logic">Ternary logic</a></li> <li><i><a href="/wiki/Taixuanjing" title="Taixuanjing">Taixuanjing</a></i></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ternary_numeral_system&action=edit&section=8" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-Kindra2022-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kindra2022_1-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFKindraRogalevOsipovZlyvko2022" class="citation journal cs1">Kindra, Vladimir; Rogalev, Nikolay; Osipov, Sergey; Zlyvko, Olga; Naumov, Vladimir (2022). <a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Finventions7030056">"Research and Development of Trinary Power Cycles"</a>. <i>Inventions</i>. <b>7</b> (3): 56. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Finventions7030056">10.3390/inventions7030056</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2411-5134">2411-5134</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Inventions&rft.atitle=Research+and+Development+of+Trinary+Power+Cycles&rft.volume=7&rft.issue=3&rft.pages=56&rft.date=2022&rft_id=info%3Adoi%2F10.3390%2Finventions7030056&rft.issn=2411-5134&rft.aulast=Kindra&rft.aufirst=Vladimir&rft.au=Rogalev%2C+Nikolay&rft.au=Osipov%2C+Sergey&rft.au=Zlyvko%2C+Olga&rft.au=Naumov%2C+Vladimir&rft_id=https%3A%2F%2Fdoi.org%2F10.3390%252Finventions7030056&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATernary+numeral+system" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAshley_MacLennan2019" class="citation web cs1">Ashley MacLennan (2019-01-09). <a rel="nofollow" class="external text" href="https://www.blessyouboys.com/2019/1/9/18172095/baseball-stats-for-beginners-earned-run-average-field-independent-pitching-explained">"A complete beginner's guide to baseball stats: Pitching statistics, and what they mean"</a>. <i>Bless You Boys</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2020-07-30</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Bless+You+Boys&rft.atitle=A+complete+beginner%27s+guide+to+baseball+stats%3A+Pitching+statistics%2C+and+what+they+mean&rft.date=2019-01-09&rft.au=Ashley+MacLennan&rft_id=https%3A%2F%2Fwww.blessyouboys.com%2F2019%2F1%2F9%2F18172095%2Fbaseball-stats-for-beginners-earned-run-average-field-independent-pitching-explained&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATernary+numeral+system" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.mlb.com/stats/team/pitching/innings-pitched?split=rp">"Stats - Team - Pitching"</a>. MLB (Major League Baseball)<span class="reference-accessdate">. Retrieved <span class="nowrap">2020-07-30</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Stats+-+Team+-+Pitching&rft.pub=MLB+%28Major+League+Baseball%29&rft_id=https%3A%2F%2Fwww.mlb.com%2Fstats%2Fteam%2Fpitching%2Finnings-pitched%3Fsplit%3Drp&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATernary+numeral+system" class="Z3988"></span></span> </li> <li id="cite_note-Soltanifar_2006_1-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-Soltanifar_2006_1_4-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSoltanifar2006" class="citation journal cs1">Soltanifar, Mohsen (2006). "On A sequence of cantor Fractals". <i>Rose Hulman Undergraduate Mathematics Journal</i>. <b>7</b> (1). Paper 9.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Rose+Hulman+Undergraduate+Mathematics+Journal&rft.atitle=On+A+sequence+of+cantor+Fractals&rft.volume=7&rft.issue=1&rft.date=2006&rft.aulast=Soltanifar&rft.aufirst=Mohsen&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATernary+numeral+system" class="Z3988"></span></span> </li> <li id="cite_note-Soltanifar_2006_2-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-Soltanifar_2006_2_5-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSoltanifar2006" class="citation journal cs1">Soltanifar, Mohsen (2006). "A Different Description of A Family of Middle–α Cantor Sets". <i>American Journal of Undergraduate Research</i>. <b>5</b> (2): 9–12.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Undergraduate+Research&rft.atitle=A+Different+Description+of+A+Family+of+Middle%E2%80%93%CE%B1+Cantor+Sets&rft.volume=5&rft.issue=2&rft.pages=9-12&rft.date=2006&rft.aulast=Soltanifar&rft.aufirst=Mohsen&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATernary+numeral+system" class="Z3988"></span></span> </li> <li id="cite_note-Phatak_1994-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-Phatak_1994_6-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPhatakKoren1994" class="citation journal cs1">Phatak, D. S.; Koren, I. (1994). <a rel="nofollow" class="external text" href="http://www.cs.umbc.edu/~phatak/publications/hsdtrc.pdf">"Hybrid signed–digit number systems: a unified framework for redundant number representations with bounded carry propagation chains"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/IEEE_Transactions_on_Computers" title="IEEE Transactions on Computers">IEEE Transactions on Computers</a></i>. <b>43</b> (8): 880–891. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.352.6407">10.1.1.352.6407</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F12.295850">10.1109/12.295850</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Computers&rft.atitle=Hybrid+signed%E2%80%93digit+number+systems%3A+a+unified+framework+for+redundant+number+representations+with+bounded+carry+propagation+chains&rft.volume=43&rft.issue=8&rft.pages=880-891&rft.date=1994&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.352.6407%23id-name%3DCiteSeerX&rft_id=info%3Adoi%2F10.1109%2F12.295850&rft.aulast=Phatak&rft.aufirst=D.+S.&rft.au=Koren%2C+I.&rft_id=http%3A%2F%2Fwww.cs.umbc.edu%2F~phatak%2Fpublications%2Fhsdtrc.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATernary+numeral+system" class="Z3988"></span></span> </li> <li id="cite_note-Frieder_1975-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-Frieder_1975_7-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFriederLuk1975" class="citation journal cs1">Frieder, Gideon; Luk, Clement (February 1975). "Algorithms for Binary Coded Balanced and Ordinary Ternary Operations". <i><a href="/wiki/IEEE_Transactions_on_Computers" title="IEEE Transactions on Computers">IEEE Transactions on Computers</a></i>. <b>C-24</b> (2): 212–215. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FT-C.1975.224188">10.1109/T-C.1975.224188</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:38704739">38704739</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Transactions+on+Computers&rft.atitle=Algorithms+for+Binary+Coded+Balanced+and+Ordinary+Ternary+Operations&rft.volume=C-24&rft.issue=2&rft.pages=212-215&rft.date=1975-02&rft_id=info%3Adoi%2F10.1109%2FT-C.1975.224188&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A38704739%23id-name%3DS2CID&rft.aulast=Frieder&rft.aufirst=Gideon&rft.au=Luk%2C+Clement&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATernary+numeral+system" class="Z3988"></span></span> </li> <li id="cite_note-Parhami_2013-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-Parhami_2013_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFParhamiMcKeown2013" class="citation book cs1">Parhami, Behrooz; McKeown, Michael (2013-11-03). "Arithmetic with binary-encoded balanced ternary numbers". <i>2013 Asilomar Conference on Signals, Systems and Computers</i>. Pacific Grove, California, US. pp. 1130–1133. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FACSSC.2013.6810470">10.1109/ACSSC.2013.6810470</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4799-2390-8" title="Special:BookSources/978-1-4799-2390-8"><bdi>978-1-4799-2390-8</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:9603084">9603084</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Arithmetic+with+binary-encoded+balanced+ternary+numbers&rft.btitle=2013+Asilomar+Conference+on+Signals%2C+Systems+and+Computers&rft.place=Pacific+Grove%2C+California%2C+US&rft.pages=1130-1133&rft.date=2013-11-03&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A9603084%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1109%2FACSSC.2013.6810470&rft.isbn=978-1-4799-2390-8&rft.aulast=Parhami&rft.aufirst=Behrooz&rft.au=McKeown%2C+Michael&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATernary+numeral+system" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: location missing publisher (<a href="/wiki/Category:CS1_maint:_location_missing_publisher" title="Category:CS1 maint: location missing publisher">link</a>)</span></span> </li> <li id="cite_note-Jones_2016_1-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-Jones_2016_1_9-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJones2016" class="citation web cs1">Jones, Douglas W. (June 2016). <a rel="nofollow" class="external text" href="http://www.cs.uiowa.edu/~jones/ternary/bct.shtml">"Binary Coded Ternary and its Inverse"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Binary+Coded+Ternary+and+its+Inverse&rft.date=2016-06&rft.aulast=Jones&rft.aufirst=Douglas+W.&rft_id=http%3A%2F%2Fwww.cs.uiowa.edu%2F~jones%2Fternary%2Fbct.shtml&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATernary+numeral+system" class="Z3988"></span></span> </li> <li id="cite_note-Jones_2016_2-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-Jones_2016_2_10-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJones2015" class="citation web cs1">Jones, Douglas W. (2015-12-29). <a rel="nofollow" class="external text" href="http://www.cs.uiowa.edu/~jones/ternary/libtern.shtml">"Ternary Data Types for C Programmers"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Ternary+Data+Types+for+C+Programmers&rft.date=2015-12-29&rft.aulast=Jones&rft.aufirst=Douglas+W.&rft_id=http%3A%2F%2Fwww.cs.uiowa.edu%2F~jones%2Fternary%2Flibtern.shtml&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATernary+numeral+system" class="Z3988"></span></span> </li> <li id="cite_note-Impagliazzo_2006-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-Impagliazzo_2006_11-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFImpagliazzoProydakov2006" class="citation conference cs1">Impagliazzo, John; Proydakov, Eduard (2006). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=-jSqCAAAQBAJ"><i>Perspectives on Soviet and Russian Computing</i></a>. First IFIP WG 9.7 Conference, SoRuCom 2006. Petrozavodsk, Russia: <a href="/wiki/Springer_(publisher)" class="mw-redirect" title="Springer (publisher)">Springer</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-64222816-2" title="Special:BookSources/978-3-64222816-2"><bdi>978-3-64222816-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.btitle=Perspectives+on+Soviet+and+Russian+Computing&rft.place=Petrozavodsk%2C+Russia&rft.pub=Springer&rft.date=2006&rft.isbn=978-3-64222816-2&rft.aulast=Impagliazzo&rft.aufirst=John&rft.au=Proydakov%2C+Eduard&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D-jSqCAAAQBAJ&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATernary+numeral+system" class="Z3988"></span></span> </li> <li id="cite_note-Brousentsov_2010-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-Brousentsov_2010_12-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBrousentsovMaslovRamil_AlvarezZhogolev" class="citation web cs1">Brousentsov, N. P.; Maslov, S. P.; Ramil Alvarez, J.; Zhogolev, E. A. <a rel="nofollow" class="external text" href="http://www.computer-museum.ru/english/setun.htm">"Development of ternary computers at Moscow State University"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2010-01-20</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Development+of+ternary+computers+at+Moscow+State+University&rft.aulast=Brousentsov&rft.aufirst=N.+P.&rft.au=Maslov%2C+S.+P.&rft.au=Ramil+Alvarez%2C+J.&rft.au=Zhogolev%2C+E.+A.&rft_id=http%3A%2F%2Fwww.computer-museum.ru%2Fenglish%2Fsetun.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATernary+numeral+system" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ternary_numeral_system&action=edit&section=9" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHayes2001" class="citation journal cs1"><a href="/wiki/Brian_Hayes_(scientist)" title="Brian Hayes (scientist)">Hayes, Brian</a> (November–December 2001). <a rel="nofollow" class="external text" href="http://bit-player.org/wp-content/extras/bph-publications/AmSci-2001-11-Hayes-ternary.pdf">"Third base"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/American_Scientist" title="American Scientist">American Scientist</a></i>. <b>89</b> (6). <a href="/wiki/Sigma_Xi" title="Sigma Xi">Sigma Xi</a>, the Scientific Research Society: 490–494. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1511%2F2001.40.3268">10.1511/2001.40.3268</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20191030114823/http://bit-player.org/wp-content/extras/bph-publications/AmSci-2001-11-Hayes-ternary.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 2019-10-30<span class="reference-accessdate">. Retrieved <span class="nowrap">2020-04-12</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Scientist&rft.atitle=Third+base&rft.volume=89&rft.issue=6&rft.pages=490-494&rft.date=2001-11%2F2001-12&rft_id=info%3Adoi%2F10.1511%2F2001.40.3268&rft.aulast=Hayes&rft.aufirst=Brian&rft_id=http%3A%2F%2Fbit-player.org%2Fwp-content%2Fextras%2Fbph-publications%2FAmSci-2001-11-Hayes-ternary.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ATernary+numeral+system" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Ternary_numeral_system&action=edit&section=10" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.washingtonart.net/whealton/ternary.html">Ternary Arithmetic</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110514130533/http://www.washingtonart.net/whealton/ternary.html">Archived</a> 2011-05-14 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="http://www.mortati.com/glusker/fowler/index.htm">The ternary calculating machine of Thomas Fowler</a></li> <li><a rel="nofollow" class="external text" href="http://www.mathsisfun.com/numbers/convert-base.php?to=ternary">Ternary Base Conversion</a> – includes fractional part, from Maths Is Fun</li> <li><a rel="nofollow" class="external text" href="http://www.americanscientist.org/issues/pub/third-base/3">Gideon Frieder's replacement ternary numeral system</a></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Data_types" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Data_types" title="Template:Data types"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Data_types" title="Template talk:Data types"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Data_types" title="Special:EditPage/Template:Data types"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Data_types" style="font-size:114%;margin:0 4em"><a href="/wiki/Data_type" title="Data type">Data types</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Units_of_information" title="Units of information">Uninterpreted</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bit" title="Bit">Bit</a></li> <li><a href="/wiki/Byte" title="Byte">Byte</a></li> <li><a class="mw-selflink selflink">Trit</a></li> <li><a class="mw-selflink-fragment" href="#Tryte">Tryte</a></li> <li><a href="/wiki/Word_(computer_architecture)" title="Word (computer architecture)">Word</a></li> <li><a href="/wiki/Bit_array" title="Bit array">Bit array</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Numeric</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Arbitrary-precision_arithmetic" title="Arbitrary-precision arithmetic">Arbitrary-precision or bignum</a></li> <li><a href="/wiki/Complex_data_type" title="Complex data type">Complex</a></li> <li><a href="/wiki/Decimal_data_type" title="Decimal data type">Decimal</a></li> <li><a href="/wiki/Fixed-point_arithmetic" title="Fixed-point arithmetic">Fixed point</a></li> <li><a href="/wiki/Floating-point_arithmetic" title="Floating-point arithmetic">Floating point</a> <ul><li>Reduced precision <ul><li><a href="/wiki/Minifloat" title="Minifloat">Minifloat</a></li> <li><a href="/wiki/Half-precision_floating-point_format" title="Half-precision floating-point format">Half precision</a></li> <li><a href="/wiki/Bfloat16_floating-point_format" title="Bfloat16 floating-point format">bfloat16</a></li></ul></li> <li><a href="/wiki/Single-precision_floating-point_format" title="Single-precision floating-point format">Single precision</a></li> <li><a href="/wiki/Double-precision_floating-point_format" title="Double-precision floating-point format">Double precision</a></li> <li><a href="/wiki/Quadruple-precision_floating-point_format" title="Quadruple-precision floating-point format">Quadruple precision</a></li> <li><a href="/wiki/Octuple-precision_floating-point_format" title="Octuple-precision floating-point format">Octuple precision</a></li> <li><a href="/wiki/Extended_precision" title="Extended precision">Extended precision</a> <ul><li><a href="/wiki/Long_double" title="Long double">Long double</a></li></ul></li></ul></li> <li><a href="/wiki/Integer_(computer_science)" title="Integer (computer science)">Integer</a> <ul><li><a href="/wiki/Signedness" title="Signedness">signedness</a></li></ul></li> <li><a href="/wiki/Interval_arithmetic#Implementations" title="Interval arithmetic">Interval</a></li> <li><a href="/wiki/Rational_data_type" title="Rational data type">Rational</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Pointer_(computer_programming)" title="Pointer (computer programming)">Pointer</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Memory_address" title="Memory address">Address</a> <ul><li><a href="/wiki/Physical_address" title="Physical address">physical</a></li> <li><a href="/wiki/Virtual_address_space" title="Virtual address space">virtual</a></li></ul></li> <li><a href="/wiki/Reference_(computer_science)" title="Reference (computer science)">Reference</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Plain_text" title="Plain text">Text</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Character_(computing)" title="Character (computing)">Character</a></li> <li><a href="/wiki/String_(computer_science)" title="String (computer science)">String</a> <ul><li><a href="/wiki/Null-terminated_string" title="Null-terminated string">null-terminated</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Composite_data_type" title="Composite data type">Composite</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Algebraic_data_type" title="Algebraic data type">Algebraic data type</a> <ul><li><a href="/wiki/Generalized_algebraic_data_type" title="Generalized algebraic data type">generalized</a></li></ul></li> <li><a href="/wiki/Array_data_type" class="mw-redirect" title="Array data type">Array</a></li> <li><a href="/wiki/Associative_array" title="Associative array">Associative array</a></li> <li><a href="/wiki/Class_(computer_programming)" title="Class (computer programming)">Class</a></li> <li><a href="/wiki/Dependent_type" title="Dependent type">Dependent</a></li> <li><a href="/wiki/Intuitionistic_type_theory#Equality_type" title="Intuitionistic type theory">Equality</a></li> <li><a href="/wiki/Inductive_type" title="Inductive type">Inductive</a></li> <li><a href="/wiki/Intersection_type" title="Intersection type">Intersection</a></li> <li><a href="/wiki/List_(abstract_data_type)" title="List (abstract data type)">List</a></li> <li><a href="/wiki/Object_(computer_science)" title="Object (computer science)">Object</a> <ul><li><a href="/wiki/Metaobject" title="Metaobject">metaobject</a></li></ul></li> <li><a href="/wiki/Option_type" title="Option type">Option type</a></li> <li><a href="/wiki/Product_type" title="Product type">Product</a></li> <li><a href="/wiki/Record_(computer_science)" title="Record (computer science)">Record or Struct</a></li> <li><a href="/wiki/Refinement_type" title="Refinement type">Refinement</a></li> <li><a href="/wiki/Set_(abstract_data_type)" title="Set (abstract data type)">Set</a></li> <li><a href="/wiki/Union_type" title="Union type">Union</a> <ul><li><a href="/wiki/Tagged_union" title="Tagged union">tagged</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Boolean_data_type" title="Boolean data type">Boolean</a></li> <li><a href="/wiki/Bottom_type" title="Bottom type">Bottom type</a></li> <li><a href="/wiki/Container_(abstract_data_type)" title="Container (abstract data type)">Collection</a></li> <li><a href="/wiki/Enumerated_type" title="Enumerated type">Enumerated type</a></li> <li><a href="/wiki/Exception_handling" title="Exception handling">Exception</a></li> <li><a href="/wiki/Function_type" title="Function type">Function type</a></li> <li><a href="/wiki/Opaque_data_type" title="Opaque data type">Opaque data type</a></li> <li><a href="/wiki/Recursive_data_type" title="Recursive data type">Recursive data type</a></li> <li><a href="/wiki/Semaphore_(programming)" title="Semaphore (programming)">Semaphore</a></li> <li><a href="/wiki/Stream_(computing)" title="Stream (computing)">Stream</a></li> <li><a href="/wiki/Strongly_typed_identifier" title="Strongly typed identifier">Strongly typed identifier</a></li> <li><a href="/wiki/Top_type" title="Top type">Top type</a></li> <li><a href="/wiki/Type_class" title="Type class">Type class</a></li> <li><a href="/wiki/Empty_type" title="Empty type">Empty type</a></li> <li><a href="/wiki/Unit_type" title="Unit type">Unit type</a></li> <li><a href="/wiki/Void_type" title="Void type">Void</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related<br />topics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Abstract_data_type" title="Abstract data type">Abstract data type</a></li> <li><a href="/wiki/Boxing_(computer_science)" class="mw-redirect" title="Boxing (computer science)">Boxing</a></li> <li><a href="/wiki/Data_structure" title="Data structure">Data structure</a></li> <li><a href="/wiki/Generic_programming" title="Generic programming">Generic</a></li> <li><a href="/wiki/Kind_(type_theory)" title="Kind (type theory)">Kind</a> <ul><li><a href="/wiki/Metaclass" title="Metaclass">metaclass</a></li></ul></li> <li><a href="/wiki/Parametric_polymorphism" title="Parametric polymorphism">Parametric polymorphism</a></li> <li><a href="/wiki/Primitive_data_type" title="Primitive data type">Primitive data type</a></li> <li><a href="/wiki/Interface_(object-oriented_programming)" title="Interface (object-oriented programming)">Interface</a></li> <li><a href="/wiki/Subtyping" title="Subtyping">Subtyping</a></li> <li><a href="/wiki/Type_constructor" title="Type constructor">Type constructor</a></li> <li><a href="/wiki/Type_conversion" title="Type conversion">Type conversion</a></li> <li><a href="/wiki/Type_system" title="Type system">Type system</a></li> <li><a href="/wiki/Type_theory" title="Type theory">Type theory</a></li> <li><a href="/wiki/Variable_(computer_science)" title="Variable (computer science)">Variable</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Ternary_numeral_system&oldid=1253065951">https://en.wikipedia.org/w/index.php?title=Ternary_numeral_system&oldid=1253065951</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Computer_arithmetic" title="Category:Computer arithmetic">Computer arithmetic</a></li><li><a href="/wiki/Category:Positional_numeral_systems" title="Category:Positional numeral systems">Positional numeral systems</a></li><li><a href="/wiki/Category:Ternary_computers" title="Category:Ternary computers">Ternary computers</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:CS1_maint:_location_missing_publisher" title="Category:CS1 maint: location missing publisher">CS1 maint: location missing publisher</a></li><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:Use_dmy_dates_from_May_2019" title="Category:Use dmy dates from May 2019">Use dmy dates from May 2019</a></li><li><a href="/wiki/Category:Pages_using_sidebar_with_the_child_parameter" title="Category:Pages using sidebar with the child parameter">Pages using sidebar with the child parameter</a></li><li><a href="/wiki/Category:Webarchive_template_wayback_links" title="Category:Webarchive template wayback links">Webarchive template wayback links</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 24 October 2024, at 05:35<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. By using this site, you agree to the <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use" class="extiw" title="foundation:Special:MyLanguage/Policy:Terms of Use">Terms of Use</a> and <a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy" class="extiw" title="foundation:Special:MyLanguage/Policy:Privacy policy">Privacy Policy</a>. Wikipedia® is a registered trademark of the <a rel="nofollow" class="external text" href="https://wikimediafoundation.org/">Wikimedia Foundation, Inc.</a>, a non-profit organization.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Privacy policy</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:About">About Wikipedia</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:General_disclaimer">Disclaimers</a></li> <li id="footer-places-contact"><a href="//en.wikipedia.org/wiki/Wikipedia:Contact_us">Contact Wikipedia</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Developers</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/en.wikipedia.org">Statistics</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie statement</a></li> <li id="footer-places-mobileview"><a href="//en.m.wikipedia.org/w/index.php?title=Ternary_numeral_system&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Mobile view</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-7c4dcdbb87-r9h8k","wgBackendResponseTime":222,"wgPageParseReport":{"limitreport":{"cputime":"0.612","walltime":"0.791","ppvisitednodes":{"value":3875,"limit":1000000},"postexpandincludesize":{"value":98722,"limit":2097152},"templateargumentsize":{"value":3864,"limit":2097152},"expansiondepth":{"value":12,"limit":100},"expensivefunctioncount":{"value":2,"limit":500},"unstrip-depth":{"value":1,"limit":20},"unstrip-size":{"value":89764,"limit":5000000},"entityaccesscount":{"value":0,"limit":400},"timingprofile":["100.00% 661.252 1 -total"," 28.27% 186.940 1 Template:Reflist"," 19.65% 129.953 6 Template:Cite_journal"," 18.99% 125.552 1 Template:Table_Numeral_Systems"," 18.38% 121.569 1 Template:Sidebar_with_collapsible_groups"," 12.59% 83.284 1 Template:Sidebar_with_collapsible_lists"," 12.20% 80.661 1 Template:Short_description"," 10.77% 71.202 1 Template:Data_types"," 10.49% 69.367 1 Template:Navbox"," 8.43% 55.722 2 Template:Pagetype"]},"scribunto":{"limitreport-timeusage":{"value":"0.350","limit":"10.000"},"limitreport-memusage":{"value":6440921,"limit":52428800}},"cachereport":{"origin":"mw-web.codfw.main-5857dfdcd6-9lbh6","timestamp":"20241203065451","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Ternary numeral system","url":"https:\/\/en.wikipedia.org\/wiki\/Ternary_numeral_system","sameAs":"http:\/\/www.wikidata.org\/entity\/Q1056486","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q1056486","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2002-07-20T19:16:25Z","dateModified":"2024-10-24T05:35:27Z","headline":"numeral system with three as its base"}</script> </body> </html>