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class="mw-list-item"><a href="/wiki/Forside" title="Gå til hovedsiden [z]" accesskey="z"><span>Forside</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Spesial:Tilfeldig" title="Vis en tilfeldig side [x]" accesskey="x"><span>Tilfeldig side</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Hjelp:Portal" title="Stedet for å få hjelp"><span>Hjelp</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Spesial:Siste_endringer" title="Liste over siste endringer på wikien. [r]" accesskey="r"><span>Siste endringer</span></a></li> </ul> </div> </div> <div id="p-prosjekt" class="vector-menu mw-portlet mw-portlet-prosjekt" > <div class="vector-menu-heading"> Prosjekt </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-Prosjektportal" class="mw-list-item"><a href="/wiki/Wikipedia:Portal"><span>Prosjektportal</span></a></li><li id="n-bidra" class="mw-list-item"><a href="/wiki/Wikipedia:Bidra_til_Wikipedia"><span>Hvordan bidra?</span></a></li><li id="n-tinget" class="mw-list-item"><a href="/wiki/Wikipedia:Tinget"><span>Tinget</span></a></li><li id="n-torget" class="mw-list-item"><a href="/wiki/Wikipedia:Torget"><span>Torget</span></a></li><li id="n-konkurranser" class="mw-list-item"><a href="/wiki/Wikipedia:Konkurranser"><span>Konkurranser</span></a></li> </ul> </div> </div> <div id="p-Wikipedia" class="vector-menu mw-portlet mw-portlet-Wikipedia" > <div class="vector-menu-heading"> Wikipedia </div> <div 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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="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_no.wikipedia.org&uselang=nb" class=""><span>Doner</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=Spesial:Opprett_konto&returnto=Bin%C3%A6rt+tallsystem" title="Du oppfordres til å opprette en konto og logge inn, men det er ikke obligatorisk" class=""><span>Opprett konto</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=Spesial:Logg_inn&returnto=Bin%C3%A6rt+tallsystem" title="Du oppfordres til å logge inn, men det er ikke obligatorisk [o]" accesskey="o" class=""><span>Logg inn</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 user-links-collapsible-item" title="Flere alternativer" > <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="Personlig" > <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">Personlig</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Brukermeny" > <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="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_no.wikipedia.org&uselang=nb"><span>Doner</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spesial:Opprett_konto&returnto=Bin%C3%A6rt+tallsystem" title="Du oppfordres til å opprette en konto og logge inn, men det er ikke obligatorisk"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Opprett konto</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spesial:Logg_inn&returnto=Bin%C3%A6rt+tallsystem" title="Du oppfordres til å logge inn, men det er ikke obligatorisk [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Logg inn</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="Nettsted"> <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="Innhold" 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">Innhold</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">flytt til sidefeltet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">skjul</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">(Til toppen)</div> </a> </li> <li id="toc-Historie" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Historie"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Historie</span> </div> </a> <ul id="toc-Historie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Fremstilling" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Fremstilling"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Fremstilling</span> </div> </a> <ul id="toc-Fremstilling-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Telling_binært" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Telling_binært"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Telling binært</span> </div> </a> <ul id="toc-Telling_binært-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Binær_aritmetikk" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Binær_aritmetikk"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Binær aritmetikk</span> </div> </a> <button aria-controls="toc-Binær_aritmetikk-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>Vis/skjul underseksjonen Binær aritmetikk</span> </button> <ul id="toc-Binær_aritmetikk-sublist" class="vector-toc-list"> <li id="toc-Addisjon" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Addisjon"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Addisjon</span> </div> </a> <ul id="toc-Addisjon-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Subtrahering" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Subtrahering"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Subtrahering</span> </div> </a> <ul id="toc-Subtrahering-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Multiplikasjon" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Multiplikasjon"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Multiplikasjon</span> </div> </a> <ul id="toc-Multiplikasjon-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dividering" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dividering"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Dividering</span> </div> </a> <ul id="toc-Dividering-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Bitvise_logiske_operasjoner" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bitvise_logiske_operasjoner"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Bitvise logiske operasjoner</span> </div> </a> <ul id="toc-Bitvise_logiske_operasjoner-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Konvertering_til_og_fra_andre_tallsystemer" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Konvertering_til_og_fra_andre_tallsystemer"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Konvertering til og fra andre tallsystemer</span> </div> </a> <button aria-controls="toc-Konvertering_til_og_fra_andre_tallsystemer-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>Vis/skjul underseksjonen Konvertering til og fra andre tallsystemer</span> </button> <ul id="toc-Konvertering_til_og_fra_andre_tallsystemer-sublist" class="vector-toc-list"> <li id="toc-Desimal" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Desimal"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>Desimal</span> </div> </a> <ul id="toc-Desimal-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Heksadesimalt" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Heksadesimalt"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>Heksadesimalt</span> </div> </a> <ul id="toc-Heksadesimalt-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Oktalt" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Oktalt"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>Oktalt</span> </div> </a> <ul id="toc-Oktalt-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Brøk" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Brøk"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Brøk</span> </div> </a> <ul id="toc-Brøk-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Se_også" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Se_også"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Se også</span> </div> </a> <ul id="toc-Se_også-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="Innhold" 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="Vis/skjul innholdsfortegnelsen" > <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">Vis/skjul innholdsfortegnelsen</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">Binært tallsystem</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="Gå til en artikkel på et annet språk. Tilgjengelig på 97 språk" > <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-97" 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">97 språk</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Totalssystemet" title="Totalssystemet – norsk nynorsk" lang="nn" hreflang="nn" data-title="Totalssystemet" data-language-autonym="Norsk nynorsk" data-language-local-name="norsk nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Bin%C3%A6re_talsystem" title="Binære talsystem – dansk" lang="da" hreflang="da" data-title="Binære talsystem" data-language-autonym="Dansk" data-language-local-name="dansk" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Bin%C3%A4ra_talsystemet" title="Binära talsystemet – svensk" lang="sv" hreflang="sv" data-title="Binära talsystemet" data-language-autonym="Svenska" data-language-local-name="svensk" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Tv%C3%ADundakerfi" title="Tvíundakerfi – islandsk" lang="is" hreflang="is" data-title="Tvíundakerfi" data-language-autonym="Íslenska" data-language-local-name="islandsk" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Bin%C3%AAre_getallestelsel" title="Binêre getallestelsel – afrikaans" lang="af" hreflang="af" data-title="Binêre getallestelsel" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><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%86%D8%A7%D8%A6%D9%8A" title="نظام عد ثنائي – arabisk" lang="ar" hreflang="ar" data-title="نظام عد ثنائي" data-language-autonym="العربية" data-language-local-name="arabisk" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Sistema_binariu" title="Sistema binariu – asturisk" lang="ast" hreflang="ast" data-title="Sistema binariu" data-language-autonym="Asturianu" data-language-local-name="asturisk" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/Ypykatu_ik%C3%B5irek%C3%B3va" title="Ypykatu ikõirekóva – guarani" lang="gn" hreflang="gn" data-title="Ypykatu ikõirekóva" data-language-autonym="Avañe'ẽ" data-language-local-name="guarani" class="interlanguage-link-target"><span>Avañe'ẽ</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/%C4%B0kili_say_sistemi" title="İkili say sistemi – aserbajdsjansk" lang="az" hreflang="az" data-title="İkili say sistemi" data-language-autonym="Azərbaycanca" data-language-local-name="aserbajdsjansk" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A7%DB%8C%DA%A9%DB%8C%E2%80%8C%D9%84%DB%8C_%D8%B3%D8%A7%DB%8C%DB%8C_%D8%B3%DB%8C%D8%B3%D8%AA%D9%85%DB%8C" title="ایکی‌لی سایی سیستمی – søraserbajdsjansk" lang="azb" hreflang="azb" data-title="ایکی‌لی سایی سیستمی" data-language-autonym="تۆرکجه" data-language-local-name="søraserbajdsjansk" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A6%E0%A7%8D%E0%A6%AC%E0%A6%BF%E0%A6%AE%E0%A6%BF%E0%A6%95_%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%AA%E0%A6%A6%E0%A7%8D%E0%A6%A7%E0%A6%A4%E0%A6%BF" title="দ্বিমিক সংখ্যাপদ্ধতি – bengali" lang="bn" hreflang="bn" data-title="দ্বিমিক সংখ্যাপদ্ধতি" data-language-autonym="বাংলা" data-language-local-name="bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/J%C4%AB-ch%C3%ACn-hoat" title="Jī-chìn-hoat – minnan" lang="nan" hreflang="nan" data-title="Jī-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-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%98%D0%BA%D0%B5%D0%BB%D0%B5_%D0%B8%D2%AB%D3%99%D0%BF%D0%BB%D3%99%D2%AF_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0%D2%BB%D1%8B" title="Икеле иҫәпләү системаһы – basjkirsk" lang="ba" hreflang="ba" data-title="Икеле иҫәпләү системаһы" data-language-autonym="Башҡортса" data-language-local-name="basjkirsk" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%94%D0%B2%D0%B0%D0%B9%D0%BA%D0%BE%D0%B2%D0%B0%D1%8F_%D1%81%D1%96%D1%81%D1%82%D1%8D%D0%BC%D0%B0_%D0%B7%D0%BB%D1%96%D1%87%D1%8D%D0%BD%D0%BD%D1%8F" title="Двайковая сістэма злічэння – belarusisk" lang="be" hreflang="be" data-title="Двайковая сістэма злічэння" data-language-autonym="Беларуская" data-language-local-name="belarusisk" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%94%D0%B2%D0%BE%D0%B8%D1%87%D0%BD%D0%B0_%D0%B1%D1%80%D0%BE%D0%B9%D0%BD%D0%B0_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0" title="Двоична бройна система – bulgarsk" lang="bg" hreflang="bg" data-title="Двоична бройна система" data-language-autonym="Български" data-language-local-name="bulgarsk" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Bin%C3%A4rzoihn" title="Binärzoihn – bairisk" lang="bar" hreflang="bar" data-title="Binärzoihn" data-language-autonym="Boarisch" data-language-local-name="bairisk" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Binarni_brojevni_sistem" title="Binarni brojevni sistem – bosnisk" lang="bs" hreflang="bs" data-title="Binarni brojevni sistem" data-language-autonym="Bosanski" data-language-local-name="bosnisk" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Enbonega%C3%B1_daouredel" title="Enbonegañ daouredel – bretonsk" lang="br" hreflang="br" data-title="Enbonegañ daouredel" data-language-autonym="Brezhoneg" data-language-local-name="bretonsk" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Sistema_binari" title="Sistema binari – katalansk" lang="ca" hreflang="ca" data-title="Sistema binari" data-language-autonym="Català" data-language-local-name="katalansk" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%98%D0%BA%D0%BA%C4%95%D0%BB%D0%BB%D0%B5_%D1%88%D1%83%D1%82_%D1%82%D1%8B%D1%82%C4%83%D0%BC%C4%95" title="Иккĕлле шут тытăмĕ – tsjuvasjisk" lang="cv" hreflang="cv" data-title="Иккĕлле шут тытăмĕ" data-language-autonym="Чӑвашла" data-language-local-name="tsjuvasjisk" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Dvojkov%C3%A1_soustava" title="Dvojková soustava – tsjekkisk" lang="cs" hreflang="cs" data-title="Dvojková soustava" data-language-autonym="Čeština" data-language-local-name="tsjekkisk" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Muravanembiri" title="Muravanembiri – shona" lang="sn" hreflang="sn" data-title="Muravanembiri" data-language-autonym="ChiShona" data-language-local-name="shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Rhif_deuaidd" title="Rhif deuaidd – walisisk" lang="cy" hreflang="cy" data-title="Rhif deuaidd" data-language-autonym="Cymraeg" data-language-local-name="walisisk" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Dualsystem" title="Dualsystem – tysk" lang="de" hreflang="de" data-title="Dualsystem" data-language-autonym="Deutsch" data-language-local-name="tysk" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Kahends%C3%BCsteem" title="Kahendsüsteem – estisk" lang="et" hreflang="et" data-title="Kahendsüsteem" data-language-autonym="Eesti" data-language-local-name="estisk" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%94%CF%85%CE%B1%CE%B4%CE%B9%CE%BA%CF%8C_%CF%83%CF%8D%CF%83%CF%84%CE%B7%CE%BC%CE%B1" title="Δυαδικό σύστημα – gresk" lang="el" hreflang="el" data-title="Δυαδικό σύστημα" data-language-autonym="Ελληνικά" data-language-local-name="gresk" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Binary_number" title="Binary number – engelsk" lang="en" hreflang="en" data-title="Binary number" data-language-autonym="English" data-language-local-name="engelsk" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Sistema_binario" title="Sistema binario – spansk" lang="es" hreflang="es" data-title="Sistema binario" data-language-autonym="Español" data-language-local-name="spansk" 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/Duuma_nombrosistemo" title="Duuma nombrosistemo – esperanto" lang="eo" hreflang="eo" data-title="Duuma nombrosistemo" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Zenbaki-sistema_bitar" title="Zenbaki-sistema bitar – baskisk" lang="eu" hreflang="eu" data-title="Zenbaki-sistema bitar" data-language-autonym="Euskara" data-language-local-name="baskisk" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%D9%82%D9%85_%D8%AF%D9%88%D8%AF%D9%88%DB%8C%DB%8C" title="رقم دودویی – persisk" lang="fa" hreflang="fa" data-title="رقم دودویی" data-language-autonym="فارسی" data-language-local-name="persisk" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Syst%C3%A8me_binaire" title="Système binaire – fransk" lang="fr" hreflang="fr" data-title="Système binaire" data-language-autonym="Français" data-language-local-name="fransk" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-fur mw-list-item"><a href="https://fur.wikipedia.org/wiki/Sisteme_binari" title="Sisteme binari – friuliansk" lang="fur" hreflang="fur" data-title="Sisteme binari" data-language-autonym="Furlan" data-language-local-name="friuliansk" class="interlanguage-link-target"><span>Furlan</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Uimhir_dh%C3%A9n%C3%A1rtha" title="Uimhir dhénártha – irsk" lang="ga" hreflang="ga" data-title="Uimhir dhénártha" data-language-autonym="Gaeilge" data-language-local-name="irsk" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/C%C3%B3digo_binario" title="Código binario – galisisk" lang="gl" hreflang="gl" data-title="Código binario" data-language-autonym="Galego" data-language-local-name="galisisk" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9D%B4%EC%A7%84%EB%B2%95" title="이진법 – koreansk" lang="ko" hreflang="ko" data-title="이진법" data-language-autonym="한국어" data-language-local-name="koreansk" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%A1%D5%B7%D5%BE%D5%A1%D6%80%D5%AF%D5%B4%D5%A1%D5%B6_%D5%A5%D6%80%D5%AF%D5%B8%D6%82%D5%A1%D5%AF%D5%A1%D5%B6_%D5%B0%D5%A1%D5%B4%D5%A1%D5%AF%D5%A1%D6%80%D5%A3" title="Հաշվարկման երկուական համակարգ – armensk" lang="hy" hreflang="hy" data-title="Հաշվարկման երկուական համակարգ" data-language-autonym="Հայերեն" data-language-local-name="armensk" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%A6%E0%A5%8D%E0%A4%B5%E0%A4%AF%E0%A4%BE%E0%A4%A7%E0%A4%BE%E0%A4%B0%E0%A5%80_%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE_%E0%A4%AA%E0%A4%A6%E0%A5%8D%E0%A4%A7%E0%A4%A4%E0%A4%BF" title="द्वयाधारी संख्या पद्धति – hindi" lang="hi" hreflang="hi" data-title="द्वयाधारी संख्या पद्धति" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Binarni_brojevni_sustav" title="Binarni brojevni sustav – kroatisk" lang="hr" hreflang="hr" data-title="Binarni brojevni sustav" data-language-autonym="Hrvatski" data-language-local-name="kroatisk" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Binara_nombrosistemo" title="Binara nombrosistemo – ido" lang="io" hreflang="io" data-title="Binara nombrosistemo" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Sistem_bilangan_biner" title="Sistem bilangan biner – indonesisk" lang="id" hreflang="id" data-title="Sistem bilangan biner" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesisk" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Systema_binari" title="Systema binari – interlingua" lang="ia" hreflang="ia" data-title="Systema binari" data-language-autonym="Interlingua" data-language-local-name="interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Sistema_numerico_binario" title="Sistema numerico binario – italiensk" lang="it" hreflang="it" data-title="Sistema numerico binario" data-language-autonym="Italiano" data-language-local-name="italiensk" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%91%D7%A1%D7%99%D7%A1_%D7%91%D7%99%D7%A0%D7%90%D7%A8%D7%99" title="בסיס בינארי – hebraisk" lang="he" hreflang="he" data-title="בסיס בינארי" data-language-autonym="עברית" data-language-local-name="hebraisk" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Sistem_wilangan_bin%C3%A8r" title="Sistem wilangan binèr – javanesisk" lang="jv" hreflang="jv" data-title="Sistem wilangan binèr" data-language-autonym="Jawa" data-language-local-name="javanesisk" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%A6%E0%B3%8D%E0%B2%B5%E0%B2%BF%E0%B2%AE%E0%B2%BE%E0%B2%A8_%E0%B2%B8%E0%B2%82%E0%B2%96%E0%B3%8D%E0%B2%AF%E0%B2%BE_%E0%B2%AA%E0%B2%A6%E0%B3%8D%E0%B2%A7%E0%B2%A4%E0%B2%BF" title="ದ್ವಿಮಾನ ಸಂಖ್ಯಾ ಪದ್ಧತಿ – kannada" lang="kn" hreflang="kn" data-title="ದ್ವಿಮಾನ ಸಂಖ್ಯಾ ಪದ್ಧತಿ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%97%E1%83%95%E1%83%9A%E1%83%98%E1%83%A1_%E1%83%9D%E1%83%A0%E1%83%9D%E1%83%91%E1%83%98%E1%83%97%E1%83%98_%E1%83%A1%E1%83%98%E1%83%A1%E1%83%A2%E1%83%94%E1%83%9B%E1%83%90" title="თვლის ორობითი სისტემა – georgisk" lang="ka" hreflang="ka" data-title="თვლის ორობითი სისტემა" data-language-autonym="ქართული" data-language-local-name="georgisk" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%95%D0%BA%D1%96%D0%BB%D1%96%D0%BA_%D1%81%D0%B0%D0%BD%D0%B0%D1%83_%D0%B6%D2%AF%D0%B9%D0%B5%D1%81%D1%96" title="Екілік санау жүйесі – kasakhisk" lang="kk" hreflang="kk" data-title="Екілік санау жүйесі" data-language-autonym="Қазақша" data-language-local-name="kasakhisk" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Sist%C3%A8m_bin%C3%A8" title="Sistèm binè – haitisk" lang="ht" hreflang="ht" data-title="Sistèm binè" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haitisk" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%AD%D0%BA%D0%B8%D0%BB%D0%B8%D0%BA_%D1%8D%D1%81%D0%B5%D0%BF%D1%82%D3%A9%D3%A9_%D1%82%D1%83%D1%82%D1%83%D0%BC%D1%83" title="Экилик эсептөө тутуму – kirgisisk" lang="ky" hreflang="ky" data-title="Экилик эсептөө тутуму" data-language-autonym="Кыргызча" data-language-local-name="kirgisisk" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Systema_numericum_binarium" title="Systema numericum binarium – latin" lang="la" hreflang="la" data-title="Systema numericum binarium" data-language-autonym="Latina" data-language-local-name="latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Bin%C4%81r%C4%81_skait%C4%AB%C5%A1anas_sist%C4%93ma" title="Binārā skaitīšanas sistēma – latvisk" lang="lv" hreflang="lv" data-title="Binārā skaitīšanas sistēma" data-language-autonym="Latviešu" data-language-local-name="latvisk" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Dvejetain%C4%97_skai%C4%8Diavimo_sistema" title="Dvejetainė skaičiavimo sistema – litauisk" lang="lt" hreflang="lt" data-title="Dvejetainė skaičiavimo sistema" data-language-autonym="Lietuvių" data-language-local-name="litauisk" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Sistema_binari" title="Sistema binari – lombardisk" lang="lmo" hreflang="lmo" data-title="Sistema binari" data-language-autonym="Lombard" data-language-local-name="lombardisk" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Kettes_sz%C3%A1mrendszer" title="Kettes számrendszer – ungarsk" lang="hu" hreflang="hu" data-title="Kettes számrendszer" data-language-autonym="Magyar" data-language-local-name="ungarsk" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk badge-Q17437796 badge-featuredarticle mw-list-item" title="utmerket artikkel-merke"><a href="https://mk.wikipedia.org/wiki/%D0%94%D0%B2%D0%BE%D0%B8%D1%87%D0%B5%D0%BD_%D0%B1%D1%80%D0%BE%D0%B5%D0%BD_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC" title="Двоичен броен систем – makedonsk" lang="mk" hreflang="mk" data-title="Двоичен броен систем" data-language-autonym="Македонски" data-language-local-name="makedonsk" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%A6%E0%B5%8D%E0%B4%B5%E0%B4%AF%E0%B4%BE%E0%B4%99%E0%B5%8D%E0%B4%95%E0%B4%B8%E0%B4%82%E0%B4%96%E0%B5%8D%E0%B4%AF%E0%B4%BE%E0%B4%B5%E0%B5%8D%E0%B4%AF%E0%B4%B5%E0%B4%B8%E0%B5%8D%E0%B4%A5" title="ദ്വയാങ്കസംഖ്യാവ്യവസ്ഥ – malayalam" lang="ml" hreflang="ml" data-title="ദ്വയാങ്കസംഖ്യാവ്യവസ്ഥ" data-language-autonym="മലയാളം" data-language-local-name="malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%A6%E0%A5%8D%E0%A4%B5%E0%A4%BF%E0%A4%AE%E0%A4%BE%E0%A4%A8_%E0%A4%AA%E0%A4%A6%E0%A5%8D%E0%A4%A7%E0%A4%A4" title="द्विमान पद्धत – marathi" lang="mr" hreflang="mr" data-title="द्विमान पद्धत" data-language-autonym="मराठी" data-language-local-name="marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Sistem_angka_perduaan" title="Sistem angka perduaan – malayisk" lang="ms" hreflang="ms" data-title="Sistem angka perduaan" data-language-autonym="Bahasa Melayu" data-language-local-name="malayisk" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/Sistema_binairo_(matem%C3%A1tica)" title="Sistema binairo (matemática) – mirandesisk" lang="mwl" hreflang="mwl" data-title="Sistema binairo (matemática)" data-language-autonym="Mirandés" data-language-local-name="mirandesisk" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A5%D0%BE%D1%91%D1%80%D1%82%D1%8B%D0%BD_%D1%82%D0%BE%D0%BE%D0%BB%D0%BB%D1%8B%D0%BD_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC" title="Хоёртын тооллын систем – mongolsk" lang="mn" hreflang="mn" data-title="Хоёртын тооллын систем" data-language-autonym="Монгол" data-language-local-name="mongolsk" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Binair_talstelsel" title="Binair talstelsel – nederlandsk" lang="nl" hreflang="nl" data-title="Binair talstelsel" data-language-autonym="Nederlands" data-language-local-name="nederlandsk" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%A6%E0%A5%8D%E0%A4%B5%E0%A4%AF%E0%A4%A7%E0%A4%BE%E0%A4%B0%E0%A5%80_%E0%A4%B8%E0%A4%99%E0%A5%8D%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="द्वयधारी सङ्ख्या – nepali" lang="ne" hreflang="ne" data-title="द्वयधारी सङ्ख्या" data-language-autonym="नेपाली" data-language-local-name="nepali" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E4%BA%8C%E9%80%B2%E6%B3%95" title="二進法 – japansk" lang="ja" hreflang="ja" data-title="二進法" data-language-autonym="日本語" data-language-local-name="japansk" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-mhr mw-list-item"><a href="https://mhr.wikipedia.org/wiki/%D0%9A%D0%BE%D0%BA%D1%8B%D1%82%D0%B0%D0%BD_%D1%87%D0%BE%D1%82%D1%80%D0%B0%D0%B4%D0%B0%D0%BC_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B5" title="Кокытан чотрадам системе – østmarisk" lang="mhr" hreflang="mhr" data-title="Кокытан чотрадам системе" data-language-autonym="Олык марий" data-language-local-name="østmarisk" class="interlanguage-link-target"><span>Олык марий</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Laklamee" title="Laklamee – oromo" lang="om" hreflang="om" data-title="Laklamee" data-language-autonym="Oromoo" data-language-local-name="oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Ikkilik_sanoq_sistemasi" title="Ikkilik sanoq sistemasi – usbekisk" lang="uz" hreflang="uz" data-title="Ikkilik sanoq sistemasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="usbekisk" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%AC%E0%A8%BE%E0%A8%87%E0%A8%A8%E0%A8%B0%E0%A9%80_%E0%A8%B8%E0%A9%B0%E0%A8%96%E0%A8%BF%E0%A8%86_%E0%A8%AA%E0%A9%8D%E0%A8%B0%E0%A8%A3%E0%A8%BE%E0%A8%B2%E0%A9%80" title="ਬਾਇਨਰੀ ਸੰਖਿਆ ਪ੍ਰਣਾਲੀ – panjabi" lang="pa" hreflang="pa" data-title="ਬਾਇਨਰੀ ਸੰਖਿਆ ਪ੍ਰਣਾਲੀ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="panjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Dw%C3%B3jkowy_system_liczbowy" title="Dwójkowy system liczbowy – polsk" lang="pl" hreflang="pl" data-title="Dwójkowy system liczbowy" data-language-autonym="Polski" data-language-local-name="polsk" 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_bin%C3%A1rio" title="Sistema de numeração binário – portugisisk" lang="pt" hreflang="pt" data-title="Sistema de numeração binário" data-language-autonym="Português" data-language-local-name="portugisisk" 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_binar" title="Sistem binar – rumensk" lang="ro" hreflang="ro" data-title="Sistem binar" data-language-autonym="Română" data-language-local-name="rumensk" 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%94%D0%B2%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="Двоичная система счисления – russisk" lang="ru" hreflang="ru" data-title="Двоичная система счисления" data-language-autonym="Русский" data-language-local-name="russisk" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-skr mw-list-item"><a href="https://skr.wikipedia.org/wiki/%D8%A8%D8%A7%D8%A6%D9%86%D8%B1%DB%8C_%D9%86%D9%85%D8%A8%D8%B1_%D8%B3%D8%B3%D9%B9%D9%85" title="بائنری نمبر سسٹم – saraiki" lang="skr" hreflang="skr" data-title="بائنری نمبر سسٹم" data-language-autonym="سرائیکی" data-language-local-name="saraiki" class="interlanguage-link-target"><span>سرائیکی</span></a></li><li class="interlanguage-link interwiki-nso mw-list-item"><a href="https://nso.wikipedia.org/wiki/Binary" title="Binary – nord-sotho" lang="nso" hreflang="nso" data-title="Binary" data-language-autonym="Sesotho sa Leboa" data-language-local-name="nord-sotho" class="interlanguage-link-target"><span>Sesotho sa Leboa</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Sistemi_binar" title="Sistemi binar – albansk" lang="sq" hreflang="sq" data-title="Sistemi binar" data-language-autonym="Shqip" data-language-local-name="albansk" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%AF%E0%B7%8A%E0%B7%80%E0%B7%92%E0%B6%B8%E0%B6%BA_%E0%B7%83%E0%B6%82%E0%B6%9B%E0%B7%8A%E2%80%8D%E0%B6%BA%E0%B7%8F_%E0%B6%B4%E0%B6%AF%E0%B7%8A%E0%B6%B0%E0%B6%AD%E0%B7%92%E0%B6%BA" title="ද්විමය සංඛ්‍යා පද්ධතිය – singalesisk" lang="si" hreflang="si" data-title="ද්විමය සංඛ්‍යා පද්ධතිය" data-language-autonym="සිංහල" data-language-local-name="singalesisk" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Binary_number" title="Binary number – enkel engelsk" lang="en-simple" hreflang="en-simple" data-title="Binary number" data-language-autonym="Simple English" data-language-local-name="enkel engelsk" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%A7%D9%86%DA%AF%D9%86_%D8%AC%D9%88_%DA%8F%D9%88%D9%86%D8%A7%D8%A6%D9%8A_%D8%B3%D8%B1%D8%B4%D8%AA%D9%88" title="انگن جو ڏونائي سرشتو – sindhi" lang="sd" hreflang="sd" data-title="انگن جو ڏونائي سرشتو" data-language-autonym="سنڌي" data-language-local-name="sindhi" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Dvojkov%C3%A1_%C4%8D%C3%ADseln%C3%A1_s%C3%BAstava" title="Dvojková číselná sústava – slovakisk" lang="sk" hreflang="sk" data-title="Dvojková číselná sústava" data-language-autonym="Slovenčina" data-language-local-name="slovakisk" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Dvoji%C5%A1ki_%C5%A1tevilski_sistem" title="Dvojiški številski sistem – slovensk" lang="sl" hreflang="sl" data-title="Dvojiški številski sistem" data-language-autonym="Slovenščina" data-language-local-name="slovensk" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Tiro_labaale" title="Tiro labaale – somali" lang="so" hreflang="so" data-title="Tiro labaale" 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%91%D0%B8%D0%BD%D0%B0%D1%80%D0%BD%D0%B8_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC" title="Бинарни систем – serbisk" lang="sr" hreflang="sr" data-title="Бинарни систем" data-language-autonym="Српски / srpski" data-language-local-name="serbisk" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Binarni_sistem" title="Binarni sistem – serbokroatisk" lang="sh" hreflang="sh" data-title="Binarni sistem" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroatisk" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Sistim_panomeran_bin%C3%A9r" title="Sistim panomeran binér – sundanesisk" lang="su" hreflang="su" data-title="Sistim panomeran binér" data-language-autonym="Sunda" data-language-local-name="sundanesisk" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Bin%C3%A4%C3%A4rij%C3%A4rjestelm%C3%A4" title="Binäärijärjestelmä – finsk" lang="fi" hreflang="fi" data-title="Binäärijärjestelmä" data-language-autonym="Suomi" data-language-local-name="finsk" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%98%D0%BA%D0%B5%D0%BB%D0%B5_%D0%B8%D1%81%D3%99%D0%BF%D0%BB%D3%99%D2%AF_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0%D1%81%D1%8B" title="Икеле исәпләү системасы – tatarisk" lang="tt" hreflang="tt" data-title="Икеле исәпләү системасы" data-language-autonym="Татарча / tatarça" data-language-local-name="tatarisk" class="interlanguage-link-target"><span>Татарча / tatarça</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%AD%E0%B8%87" title="เลขฐานสอง – thai" lang="th" hreflang="th" data-title="เลขฐานสอง" 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/%C4%B0kili_say%C4%B1_sistemi" title="İkili sayı sistemi – tyrkisk" lang="tr" hreflang="tr" data-title="İkili sayı sistemi" data-language-autonym="Türkçe" data-language-local-name="tyrkisk" 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%94%D0%B2%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="Двійкова система числення – ukrainsk" lang="uk" hreflang="uk" data-title="Двійкова система числення" data-language-autonym="Українська" data-language-local-name="ukrainsk" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AB%D9%86%D8%A7%D8%A6%DB%8C_%D8%B9%D8%AF%D8%AF%DB%8C_%D9%86%D8%B8%D8%A7%D9%85" title="ثنائی عددی نظام – urdu" lang="ur" hreflang="ur" data-title="ثنائی عددی نظام" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/H%E1%BB%87_nh%E1%BB%8B_ph%C3%A2n" title="Hệ nhị phân – vietnamesisk" lang="vi" hreflang="vi" data-title="Hệ nhị phân" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamesisk" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E4%BA%8C%E9%80%B2%E5%88%B6" title="二進制 – klassisk kinesisk" lang="lzh" hreflang="lzh" data-title="二進制" data-language-autonym="文言" data-language-local-name="klassisk kinesisk" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-vls mw-list-item"><a href="https://vls.wikipedia.org/wiki/Binair_reeknn" title="Binair reeknn – vestflamsk" lang="vls" hreflang="vls" data-title="Binair reeknn" data-language-autonym="West-Vlams" data-language-local-name="vestflamsk" class="interlanguage-link-target"><span>West-Vlams</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E4%BA%8C%E8%BF%9B%E5%88%B6" title="二进制 – wu" lang="wuu" hreflang="wuu" data-title="二进制" data-language-autonym="吴语" data-language-local-name="wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%91%D7%99%D7%A0%D7%90%D7%A8%D7%99%D7%A9%D7%A2_%D7%A1%D7%99%D7%A1%D7%98%D7%A2%D7%9D" title="בינארישע סיסטעם – jiddisk" lang="yi" hreflang="yi" data-title="בינארישע סיסטעם" data-language-autonym="ייִדיש" data-language-local-name="jiddisk" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E4%BA%8C%E9%80%B2%E5%88%B6" title="二進制 – kantonesisk" lang="yue" hreflang="yue" data-title="二進制" data-language-autonym="粵語" data-language-local-name="kantonesisk" 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%BA%8C%E8%BF%9B%E5%88%B6" title="二进制 – kinesisk" lang="zh" hreflang="zh" data-title="二进制" data-language-autonym="中文" data-language-local-name="kinesisk" 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/Q3913#sitelinks-wikipedia" title="Rediger lenker til artikkelen på andre språk" class="wbc-editpage">Rediger lenker</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="Navnerom"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet 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href="/w/index.php?title=Bin%C3%A6rt_tallsystem&action=edit" title="Rediger kildekoden for denne siden [e]" accesskey="e"><span>Rediger kilde</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&action=history" title="Tidligere sideversjoner av denne siden [h]" accesskey="h"><span>Vis historikk</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Sideverktøy"> <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="Verktøy" > <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" 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<div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Flere alternativer" > <div class="vector-menu-heading"> Handlinger </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/Bin%C3%A6rt_tallsystem"><span>Les</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&veaction=edit" title="Rediger siden [v]" accesskey="v"><span>Rediger</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&action=edit" title="Rediger kildekoden for denne siden [e]" accesskey="e"><span>Rediger kilde</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&action=history"><span>Vis historikk</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Generelt </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Spesial:Lenker_hit/Bin%C3%A6rt_tallsystem" title="Liste over alle wikisider som lenker hit [j]" accesskey="j"><span>Lenker hit</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Spesial:Relaterte_endringer/Bin%C3%A6rt_tallsystem" rel="nofollow" title="Siste endringer i sider som blir lenket fra denne siden [k]" accesskey="k"><span>Relaterte endringer</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=no" title="Last opp filer [u]" accesskey="u"><span>Last opp fil</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Spesial:Spesialsider" title="Liste over alle spesialsider [q]" accesskey="q"><span>Spesialsider</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&oldid=23244090" title="Permanent lenke til denne versjonen av siden"><span>Permanent lenke</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&action=info" title="Mer informasjon om denne siden"><span>Sideinformasjon</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Spesial:Siteringshjelp&page=Bin%C3%A6rt_tallsystem&id=23244090&wpFormIdentifier=titleform" title="Informasjon om hvordan denne siden kan siteres"><span>Siter denne siden</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Spesial:UrlShortener&url=https%3A%2F%2Fno.wikipedia.org%2Fwiki%2FBin%25C3%25A6rt_tallsystem"><span>Hent forkortet URL</span></a></li><li id="t-urlshortener-qrcode" 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ambox-Unsourced" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/Fil:Question_book-new.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span"><b>Kildeløs</b>: Denne artikkelen mangler <a href="/wiki/Wikipedia:Bruk_av_kilder" title="Wikipedia:Bruk av kilder">kildehenvisninger</a>, og opplysningene i den kan dermed være vanskelige å <a href="/wiki/Wikipedia:Verifiserbarhet" title="Wikipedia:Verifiserbarhet">verifisere</a>. Kildeløst materiale kan bli <a href="/wiki/Wikipedia:Verifiserbarhet#Bevisbyrden" title="Wikipedia:Verifiserbarhet">fjernet</a>. Helt uten kilder. <span class="date-container"><i>(<span class="date">10. okt. 2015</span>)</i></span></div></td></tr></tbody></table> <p>Det <b>binære <a href="/wiki/Tallsystem" title="Tallsystem">tallsystem</a></b> (også <i>totallsystemet</i>) representerer numeriske verdier ved å bruke to symboler, som oftest sifrene <a href="/wiki/0_(tall)" title="0 (tall)">0</a> og <a href="/wiki/1_(tall)" title="1 (tall)">1</a>. </p><p>Mer nøyaktig, er det binære tallsystem et <a href="/wiki/Posisjonssystem" title="Posisjonssystem">posisjonssystem</a> med <a href="/wiki/Grunntall" title="Grunntall">grunntall</a> <a href="/wiki/2_(tall)" title="2 (tall)">to</a>. På grunn av dens relative enkle implementasjon i <a href="/wiki/Elektronisk_krets" class="mw-redirect" title="Elektronisk krets">elektroniske kretser</a> blir totallsystemet brukt internt i så å si alle moderne <a href="/wiki/Datamaskin" title="Datamaskin">datamaskiner</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Historie">Historie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&veaction=edit&section=1" title="Rediger avsnitt: Historie" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&action=edit&section=1" title="Rediger kildekoden til seksjonen Historie"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Den første kjente beskrivelse av et totallsystem ble gjort av den <a href="/wiki/Indisk" class="mw-redirect" title="Indisk">indiske</a> <a href="/wiki/Matematiker" title="Matematiker">matematikeren</a> <a href="/wiki/Pingala" title="Pingala">Pingala</a> i sin <a href="/w/index.php?title=Chhandah-shastra&action=edit&redlink=1" class="new" title="Chhandah-shastra (ikke skrevet ennå)">Chhandah-shastra</a>, og er tidsfestet til det femte eller det andre århundret f.Kr. Pingala beskrev det binære tallsystem i sammenheng med en opplisting av <a href="/w/index.php?title=Vedisk_matematikk&action=edit&redlink=1" class="new" title="Vedisk matematikk (ikke skrevet ennå)">vediske</a> meter med korte eller lange vokaler. Ifølge den <a href="/wiki/India" title="India">indiske</a> tradisjon er Pingala den yngre broren til grammatikeren <a href="/wiki/Panini" class="mw-redirect" title="Panini">Panini</a>. </p><p>Selv om den britiske filosofoen <a href="/wiki/Francis_Bacon" title="Francis Bacon">Francis Bacon</a> tidligere hadde beskrevet et utviklet system for skjult binær enkoding til bruk i <a href="/wiki/Kryptering" title="Kryptering">kryptering</a>, ble det moderne binære totallsystem først fullt ut dokumentert av <a href="/wiki/Gottfried_Leibniz" title="Gottfried Leibniz">Gottfried Leibniz</a> i det <a href="/wiki/17._%C3%A5rhundre" title="17. århundre">17. århundre</a> i hans artikkel <i><a href="/w/index.php?title=Explication_de_l%27Arithm%C3%A9tique_Binaire&action=edit&redlink=1" class="new" title="Explication de l'Arithmétique Binaire (ikke skrevet ennå)">Explication de l'Arithmétique Binaire</a></i>. Mens Pingalas system bruker symbolene 1 og 2, bruker Leibniz 0 og 1 som det moderne totallsystemet. </p><p>Den <a href="/wiki/Storbritannia" title="Storbritannia">britiske</a> matematikeren <a href="/wiki/George_Boole" title="George Boole">George Boole</a> publiserte i <a href="/wiki/1854" title="1854">1854</a> en forskningsartikkel som beskrev et <a href="/wiki/Logikk" title="Logikk">logisk</a> system som senere skulle bli kjent som <a href="/wiki/Boolsk_algebra" title="Boolsk algebra">boolsk algebra</a>. Det viste seg at hans logiske system var nyttig i utviklingen av det binære system, særlig i implementeringen av den i elektroniske kretser. </p><p><a href="/wiki/Claude_Shannon" class="mw-redirect" title="Claude Shannon">Claude Shannon</a> skrev sin masteravhandling <i>A Symbolic Analysis of Relay and Switching Circuits</i> i <a href="/wiki/1937" title="1937">1937</a>. Denne beskrev for første gang i historien boolsk algebra og binær <a href="/wiki/Aritmetikk" title="Aritmetikk">aritmetikk</a> implementert med elektroniske reléer og brytere. Avhandlingen grunnla praktisk talt teorien bak design av <a href="/w/index.php?title=Digitale_kretser&action=edit&redlink=1" class="new" title="Digitale kretser (ikke skrevet ennå)">digitale kretser</a>. </p><p><a href="/w/index.php?title=George_Stibitz&action=edit&redlink=1" class="new" title="George Stibitz (ikke skrevet ennå)">George Stibitz</a>, som da jobbet ved <a href="/wiki/Bell_Labs" class="mw-redirect" title="Bell Labs">Bell Labs</a>, ferdigstilte i <a href="/wiki/November" title="November">november</a> <a href="/wiki/1937" title="1937">1937</a> en relebasert datamaskin som han kalte for «Modell K» (etter «<b>k</b>jøkken», hvor han hadde satt den sammen), som kunne regne ved å bruke binær addisjon. Bell Labs godkjente derfor et forskningsprogram i slutten av <a href="/wiki/1938" title="1938">1938</a> med Stibitz ved roret. Deres <a href="/w/index.php?title=Complex_Number_Computer&action=edit&redlink=1" class="new" title="Complex Number Computer (ikke skrevet ennå)">Complex Number Computer</a>, som ble ferdig den <a href="/wiki/8._januar" title="8. januar">8. januar</a> <a href="/wiki/1940" title="1940">1940</a> kunne regne med <a href="/wiki/Komplekse_tall" class="mw-redirect" title="Komplekse tall">komplekse tall</a>. </p><p>I en demonstrasjon ved <a href="/w/index.php?title=American_Mathematical_Society&action=edit&redlink=1" class="new" title="American Mathematical Society (ikke skrevet ennå)">American Mathematical Society</a>-konferansen ved <a href="/w/index.php?title=Darthmouth_College&action=edit&redlink=1" class="new" title="Darthmouth College (ikke skrevet ennå)">Darthmouth College</a> den <a href="/wiki/11._september" title="11. september">11. september</a> <a href="/wiki/1940" title="1940">1940</a> kunne Stibbitz sende kommandoer over telefonlinjen til maskinen med en <a href="/wiki/Fjernskriver" title="Fjernskriver">fjernskriver</a>. Det var den første beregningsbaserte maskinen som noengang hadde blitt kontrollert over en telefonlinje. Noen av deltagerne på konferansen som overvar demonstrasjonen var <a href="/wiki/John_von_Neumann" title="John von Neumann">John von Neumann</a>, <a href="/wiki/John_Mauchly" title="John Mauchly">John Mauchly</a> og <a href="/wiki/Norbert_Wiener" title="Norbert Wiener">Norbert Wiener</a> som skrev om dette i sine memoarer. </p> <div class="mw-heading mw-heading2"><h2 id="Fremstilling">Fremstilling</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&veaction=edit&section=2" title="Rediger avsnitt: Fremstilling" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&action=edit&section=2" title="Rediger kildekoden til seksjonen Fremstilling"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Et binært tall kan bli representert ved enhver sekvens av <a href="/wiki/Bit" title="Bit">biter</a> (binary digits, <i>binære siffer</i>), som i sin tur kan bli representert ved hjelp av enhver mekanisme som er i stand til å være i to gjensidige utelukkende tilstander. De følgende sekvenser av symboler kunne alle bli tolket som forskjellige binære numeriske verdier: </p> <pre>1 1 0 1 0 0 1 1 | | - | − - | | x x o x o o x x J J N J N N J J på på av på av av på på sann sann usann sann usann usann sann sann </pre> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fil:Binary_clock.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/27/Binary_clock.svg/300px-Binary_clock.svg.png" decoding="async" width="300" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/27/Binary_clock.svg/450px-Binary_clock.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/27/Binary_clock.svg/600px-Binary_clock.svg.png 2x" data-file-width="539" data-file-height="395" /></a><figcaption>En <a href="/w/index.php?title=Bin%C3%A6r_klokke&action=edit&redlink=1" class="new" title="Binær klokke (ikke skrevet ennå)">binær klokke</a> kan bruke <a href="/wiki/LED" class="mw-redirect" title="LED">LED</a> for å uttrykke binære verdier. I denne klokken viser hver kolonne av LED-lys et binært tall.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fil:Binary_clock_samui_moon.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Binary_clock_samui_moon.jpg/250px-Binary_clock_samui_moon.jpg" decoding="async" width="250" height="188" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Binary_clock_samui_moon.jpg/375px-Binary_clock_samui_moon.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Binary_clock_samui_moon.jpg/500px-Binary_clock_samui_moon.jpg 2x" data-file-width="2272" data-file-height="1704" /></a><figcaption>Binært armbåndsur som viser tiden 3:25. De fire øverste diodene er for timer, de seks nederste er for minutter. Man summerer de diodene som lyser. 1 + 2 = 3 og 1 + 8 + 16 = 25 (3:25)</figcaption></figure> <p>Den binære verdien som blir representert i hvert tilfelle er avhengig av verdien som man gir hvert symbol. I en datamaskin kan de numeriske verdiene bli representert av to forskjellige <a href="/wiki/Elektrisk_spenning" title="Elektrisk spenning">spenninger</a>; på en <a href="/wiki/Magnetisk" class="mw-redirect" title="Magnetisk">magnetisk</a> <a href="/wiki/Disk" class="mw-disambig" title="Disk">disk</a> kan magnetiske <a href="/wiki/Polaritet" class="mw-disambig" title="Polaritet">polariteter</a> bli bruk. En «positiv», «ja» eller «på» -tilstand er ikke nødvendigvis lik den numeriske verdien av én; det avhenger av hvilken arkitektur som er i bruk. </p><p>På samme måte som man som oftest skriver tall ved å bruke <a href="/wiki/Arabiske_tall" title="Arabiske tall">arabiske tall</a> blir binære tall som oftest skrevet ved å bruke symbolene <b>0</b> og <b>1</b>. Binære tall blir ofte markert med senket skrift eller med en endelse) for å indikere grunntallet. De følgende skrivemåtene er ekvivalente: </p> <dl><dd>100101 binary (eksplisitt markering av format)</dd> <dd>100101b (en ending som indikerer binært format)</dd> <dd>bin 100101 (en prefiks som indikerer binært format)</dd> <dd>100101<sub>2</sub> (senket skrift som indikerer grunntall-2 notasjon)</dd></dl> <p>Binære tallverdier blir som oftest uttalt ved å uttale hvert enkelt siffer for å kunne skille dem fra desimale tall. For eksempel blir det binære tallet «100» uttalt «en null null» i stedet for «hundre» for å markere eksplisitt at det er et binært tall, og siden det er mer korrekt. Siden det binære tallet «100» er likt fire desimalt ville det vært forvirrende og numerisk ukorrekt å kalle tallet for «hundre». Er man vant med å jobbe med binære tallverdier er det både nærliggende og korrekt å kalle tallet for «fire». </p> <div class="mw-heading mw-heading2"><h2 id="Telling_binært"><span id="Telling_bin.C3.A6rt"></span>Telling binært</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&veaction=edit&section=3" title="Rediger avsnitt: Telling binært" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&action=edit&section=3" title="Rediger kildekoden til seksjonen Telling binært"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Å telle i det binære tallsystem er likt som å telle i hvilket som helst annet tallsystem. Man starter med et enkelt siffer, og tellingen fortsetter gjennom hvert symbol i økende rekkefølge. Det desimale tallsystemet bruker symbolene <b>0</b> til <b>9</b>, mens det binære bruker bare symbolene <b>0</b> og <b>1</b>. </p><p>Når man ikke har flere symbol for det første sifferet, øker man det neste høyere sifferet, og tellingen starter på nytt igjen på 0. I det desimale tallsystemet går tellingen slik: </p> <dl><dd>00, 01, 02, ... 07, 08, 09 (man begynner på nytt igjen på sifferet helt til høyre, og 0 blir økt)</dd> <dd><b>1</b>0, 11, 12, ... 17, 18, 19 (man begynner på nytt igjen på sifferet helt til høyre, og 1 blir økt)</dd> <dd><b>2</b>0, 21, 22, ...</dd></dl> <p>Når sifferet helt til høyre når 9, starter tellingen igjen på 0, og det andre sifferet blir økt. </p><p>Tellingen er lik i totallsystemet, men siden man bare har to symboler er det slik at når 1 blir nådd, starter tellingen på 0 igjen, og siffert til venstre øker: </p> <dl><dd>000, 001 (sifferet til høyre starter på nytt, og den andre 0 øker)</dd> <dd>0<b>1</b>0, 011 (sifrene i midten og helt til høyre starter på nytt, og 0-tallet helt til venstre øker)</dd> <dd><b>1</b>00, 101 (sifferet helt til høyre begynner på nytt, 0-tallet i midten øker)</dd> <dd>1<b>1</b>0, 111...</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Binær_aritmetikk"><span id="Bin.C3.A6r_aritmetikk"></span>Binær aritmetikk</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&veaction=edit&section=4" title="Rediger avsnitt: Binær aritmetikk" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&action=edit&section=4" title="Rediger kildekoden til seksjonen Binær aritmetikk"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Aritmetikk i totallsystemet er veldig likt aritmetikk i andre tallsystemer. Addisjon, subtrahering, multiplikasjon og divisjon kan gjøres på binære tall. </p> <div class="mw-heading mw-heading3"><h3 id="Addisjon">Addisjon</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&veaction=edit&section=5" title="Rediger avsnitt: Addisjon" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&action=edit&section=5" title="Rediger kildekoden til seksjonen Addisjon"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Den enkleste aritmetiske operasjon binært er addisjon. Å legge til to ensiffrede binære tall er relativt enkelt: </p> <dl><dd>0 + 0 = 0</dd> <dd>0 + 1 = 1</dd> <dd>1 + 0 = 1</dd> <dd>1 + 1 = 10 (1 i mente)</dd> <dd>1 + 1 + 1 = 11 (1 i mente)</dd></dl> <p>Å addere to «1»-verdier gir verdien «10» som er ekvivalent med den desimale verdien 2. Dette er likt det som skjer i det desimale tallsystemet når enkelt ensiffrede tall er lagt sammen; hvis resultatet overstiger verdien av grunntallet (10), blir sifferet til venstre økt: </p> <dl><dd>5 + 5 = 10</dd> <dd>7 + 9 = 16</dd></dl> <p>Dette er kjent som <i>mente</i> i de fleste tallsystemer. </p> <pre> 1 1 1 1 1 (mente) 0 1 1 0 1 + 1 0 1 1 1 ------------- = 1 0 0 1 0 0 </pre> <p>I dette eksempelet blir to tall lagt sammen: 01101 (13 desimalt) og 10111 (23 desimalt). Den øverste raden viser mentesifrene som blir brukt. Hvis man starter i kolonnen ytterst til høyre ser vi at 1 + 1 = 10. 1-tallet blir satt opp i mente, og 0-sifferet er skrevet nederst i kolonnen til høyre. Den andre kolonnen fra høyre er lagt sammen: 1 + 0 + 1 = 10 igjen; 1-tallet blir overført i mente og 0 er skrevet på bunnen. Den tredje kolonnen: 1 + 1 + 1 = 11. Denne gangen blir 1-tallet overført og et 1-tall er skrevet nederst. Hvis man fortsetter på denne måten får man sluttsvaret 100100. </p> <div class="mw-heading mw-heading3"><h3 id="Subtrahering">Subtrahering</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&veaction=edit&section=6" title="Rediger avsnitt: Subtrahering" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&action=edit&section=6" title="Rediger kildekoden til seksjonen Subtrahering"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Subtrahering virker på stort sett samme måte: </p> <dl><dd>0 - 0 = 0</dd> <dd>0 - 1 = 1 (med låning)</dd> <dd>1 - 0 = 1</dd> <dd>1 - 1 = 0</dd></dl> <p>Et binært tall kan bli subtrahert fra et annet på følgende måte: </p> <pre> * * * * (kolonner med stjerne har blitt lånt fra) 1 1 0 1 1 1 0 – 1 0 1 1 1 ---------------- = 1 0 1 0 1 1 1 </pre> <p>Å subtrahere et positivt tall er ekvivalent til å <i>addere</i> et negativt tall med lik <a href="/wiki/Absoluttverdi" title="Absoluttverdi">absoluttverdi</a>; datamaskiner bruker vanligvis <a href="/wiki/Toerkomplement" title="Toerkomplement">toerkomplement</a> notasjonen for å representere negative verdier. Denne notasjonen eliminerer behovet for en eget "trekke-fra"-operasjon. For flere detaljer, se <a href="/wiki/Toerkomplement" title="Toerkomplement">toerkomplement</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Multiplikasjon">Multiplikasjon</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&veaction=edit&section=7" title="Rediger avsnitt: Multiplikasjon" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&action=edit&section=7" title="Rediger kildekoden til seksjonen Multiplikasjon"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Multiplisering i det binære tallsystemet er tilsvarende metoden i det desimale tallsystemet. To tall <i>A</i> og <i>B</i> kan bli mulitplisert ved delvise produkter: for hvert siffer i <i>B</i> blir produktet av det sifferet i <i>A</i> utregnet og skrevet på en ny linje, et hakk til venstre for hver gang. Summen av alle disse delvise produktene gir sluttresultatet. </p><p>Siden det bare finnes to siffer i det binære tallsystemet, finnes det bare to mulige resultat av hver delvise multiplisering: </p> <ul><li>Hvis sifferet i <i>B</i> er 0, blir det delvise produktet også 0</li> <li>Hvis sifferet i <i>B</i> er 1, blir det delvise produktet likt <i>A</i></li></ul> <p>For eksempel blir de binære tallene 1011 og 1010 multiplisert som følger: </p> <pre> 1 0 1 1 (A) × 1 0 1 0 (B) --------- 0 0 0 0 ← Tilsvarer til null i B 1 0 1 1 ← Tilsvarer til en i B 0 0 0 0 + 1 0 1 1 --------------- = 1 1 0 1 1 1 0 </pre> <div class="mw-heading mw-heading3"><h3 id="Dividering">Dividering</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&veaction=edit&section=8" title="Rediger avsnitt: Dividering" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&action=edit&section=8" title="Rediger kildekoden til seksjonen Dividering"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Dividering i det binære tallsystemet er likt metoden brukt i det desimale tallsystem: </p><p><br /> </p> <div class="mw-heading mw-heading2"><h2 id="Bitvise_logiske_operasjoner">Bitvise logiske operasjoner</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&veaction=edit&section=9" title="Rediger avsnitt: Bitvise logiske operasjoner" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&action=edit&section=9" title="Rediger kildekoden til seksjonen Bitvise logiske operasjoner"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Selv om det ikke er direkte relatert til den numeriske tolkningen av binære symboler, kan sekvenser av bits bli manipulert ved å bruke <a href="/wiki/Boolsk_algebra" title="Boolsk algebra">Boolske</a> <a href="/w/index.php?title=Logiske_operatorer&action=edit&redlink=1" class="new" title="Logiske operatorer (ikke skrevet ennå)">logisk operator</a>. Når en streng med binære symboler blir manipulert på denne måten kalles det en <a href="/w/index.php?title=Bitvis_operasjon&action=edit&redlink=1" class="new" title="Bitvis operasjon (ikke skrevet ennå)">bitvis operasjon</a>. </p><p>De logiske operandene <a href="/w/index.php?title=Logisk_konjuksjon&action=edit&redlink=1" class="new" title="Logisk konjuksjon (ikke skrevet ennå)">AND</a>, <a href="/w/index.php?title=Logisk_disjunksjon&action=edit&redlink=1" class="new" title="Logisk disjunksjon (ikke skrevet ennå)">OR</a> og <a href="/wiki/Eksklusiv_disjunksjon" title="Eksklusiv disjunksjon">Eksklusiv disjunksjon</a> kan bli utført på samsvarende bits på to binære tall. Den logiske <a href="/wiki/Negasjon" title="Negasjon">NOT</a> operasjonen kan bli utført på individuelle bits i et enkelt binærtall. </p><p>Slike operasjoner kan enkelte ganger bli brukt som aritmetiske snarveier, og kan også ha andre fordeler ved utregning. For eksempel kan man kutte av den siste biten av et binært tall (også kjent som binærskifting), tilsvarer å dele på to desimalt. </p><p>Se <a href="/w/index.php?title=Bitvis_operasjon&action=edit&redlink=1" class="new" title="Bitvis operasjon (ikke skrevet ennå)">bitvis operasjon</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Konvertering_til_og_fra_andre_tallsystemer">Konvertering til og fra andre tallsystemer</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&veaction=edit&section=10" title="Rediger avsnitt: Konvertering til og fra andre tallsystemer" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&action=edit&section=10" title="Rediger kildekoden til seksjonen Konvertering til og fra andre tallsystemer"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Desimal">Desimal</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&veaction=edit&section=11" title="Rediger avsnitt: Desimal" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&action=edit&section=11" title="Rediger kildekoden til seksjonen Desimal"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Denne metoden fungerer for konvertering fra alle grunntall, men det finnes bedre metoder for grunntall som er kvadrater av to, som for de oktale og heksadesimale tallsystemene beskrevet under. </p><p>Siffre i posisjoneringstallsystemer på lavere eller mindre signifikante posisjoner representerer stadig lavere potenser av grunntallet. Starteksponenten er en mindre enn antall siffre i tallet. Et femsifret tall starter med en eksponent på fire. I det desimale systemet er grunntallet ti, så sifferet helt til venstre i et femsiffret tall representerer 10<sup>4</sup> (titusen) posisjonen. F.eks.: </p> <dl><dd><b>97352<sub>10</sub></b> er lik: <dl><dd><b>9</b> ganger 10<sup>4</sup> (9 × 10000 = <b>90000</b>) pluss</dd> <dd><b>7</b> ganger 10<sup>3</sup> (7 × 1000 = <b>7000</b>) pluss</dd> <dd><b>3</b> ganger 10<sup>2</sup> (3 × 100 = <b>300</b>) pluss</dd> <dd><b>5</b> ganger 10<sup>1</sup> (5 × 10 = <b>50</b>) pluss</dd> <dd><b>2</b> ganger 10<sup>0</sup> (2 × 1 = <b>2</b>)</dd></dl></dd></dl> <p>Å multiplisere med grunntallet er enkelt. Man flytter siffrene et hakk til venstre, og 0 er lagt til høyresiden av tallet. For eksempel, <b>9735</b> ganger 10 er lik <b>97350</b>. Derfor er en måte å tolke en streng med siffer er at det siste sifferet [?]. <b>97352</b> er lik <b>9735</b> ganger 10 pluss <b>2</b>. Et eksempel på binær form er <b>1101100111<sub>2</sub></b> er lik <b>110110011<sub>2</sub></b> ganger 2 pluss <b>1</b>. Dette er essensen i konverteringsmetoden. I hvert steg skriver en nummeret som skal konverteres som 2*k + 0 eller 2*k + 1 for et heltall k som </p><p>blir det nye tallet som skal konverteres. </p> <dl><dd><b>118<sub>10</sub></b> er lik <dl><dd><b>59</b> x 2 + <b>0</b></dd> <dd>(<b>29</b> x 2 + <b>1</b>) x 2 + <b>0</b></dd> <dd>((<b>14</b> x 2 + <b>1</b>) x 2 + <b>1</b>) x 2 + <b>0</b></dd> <dd>(((<b>7</b> x 2 + <b>0</b>) x 2 + <b>1</b>) x 2 + <b>1</b>) x 2 + <b>0</b></dd> <dd>((((<b>3</b> x 2 + <b>1</b>) x 2 + <b>0</b>) x 2 + <b>1</b>) x 2 + <b>1</b>) x 2 + <b>0</b></dd> <dd>(((((<b>1</b> x 2 + <b>1</b>) x 2 + <b>1</b>) x 2 + <b>0</b>) x 2 + <b>1</b>) x 2 + <b>1</b>) x 2 + <b>0</b></dd> <dd><b>1</b> x 2<sup>6</sup> + <b>1</b> x 2<sup>5</sup> + <b>1</b> x 2<sup>4</sup> + <b>0</b> x 2<sup>3</sup> + <b>1</b> x</dd></dl></dd></dl> <p>2<sup>2</sup> + <b>1</b> x 2<sup>1</sup> + <b>0</b> x 2<sup>0</sup> </p> <dl><dd><dl><dd>'<i>1110110<sub>2</sub></i></dd></dl></dd></dl> <p>Så <a href="/wiki/Algoritme" title="Algoritme">algoritmen</a> for å konvertere en heltallsdesimaltall til sin binære form er å dele tallet på to, og skrive resten på ett-posisjonen. Resultatet er igjen dividert på to, og resten skrevet på den neste posisjonen til venstre. Denne prosessen gjentar man til nummeret når null. </p><p>For eksempel er 118<sub>10</sub> binært: </p> <table class="wikitable"> <tbody><tr> <th>Operasjon</th> <th>Rest </th></tr> <tr> <td>118/2 = 59</td> <td align="center">0 </td></tr> <tr> <td>59/2 = 29</td> <td align="center">1 </td></tr> <tr> <td>29/2 = 14</td> <td align="center">1 </td></tr> <tr> <td>14/2 = 7</td> <td align="center">0 </td></tr> <tr> <td>7/2 = 3</td> <td align="center">1 </td></tr> <tr> <td>3/2 = 1</td> <td align="center">1 </td></tr> <tr> <td>1/2 = 0</td> <td align="center">1 </td></tr></tbody></table> <p>Hvis man leser sekvensen av rester fra bunnen og oppover får man det binære tallet 1110110<sub>2</sub>. </p><p>For å konvertere fra binært til desimalt gjør man det hele omvendt. Man starter fra venstre, og dobler resultatet og legger til neste siffer til det ikke finnes flere. I eksempelet konverteres 110010101101<sub>2</sub> til desimalform: </p> <table class="wikitable"> <tbody><tr> <th>Resultat</th> <th>Gjenværende siffer </th></tr> <tr> <td><b>0</b></td> <td align="center">110010101101 </td></tr> <tr> <td>0*2 + 1 = <b>1</b></td> <td align="center">10010101101 </td></tr> <tr> <td>1*2 + 1 = <b>3</b></td> <td align="center">0010101101 </td></tr> <tr> <td>3*2 + 0 = <b>6</b></td> <td align="center">010101101 </td></tr> <tr> <td>6*2 + 0 = <b>12</b></td> <td align="center">10101101 </td></tr> <tr> <td>12*2 + 1 = <b>25</b></td> <td align="center">0101101 </td></tr> <tr> <td>25*2 + 0 = <b>50</b></td> <td align="center">101101 </td></tr> <tr> <td>50*2 + 1 = <b>101</b></td> <td align="center">01101 </td></tr> <tr> <td>101*2 + 0 = <b>202</b></td> <td align="center">1101 </td></tr> <tr> <td>202*2 + 1 = <b>405</b></td> <td align="center">101 </td></tr> <tr> <td>405*2 + 1 = <b>811</b></td> <td align="center">01 </td></tr> <tr> <td>811*2 + 0 = <b>1622</b></td> <td align="center">1 </td></tr> <tr> <td>1622*2 + 1 = <b>3245</b></td> <td align="center"> </td></tr></tbody></table> <p>og resultatet er 3245<sub>10</sub>. </p> <div class="mw-heading mw-heading3"><h3 id="Heksadesimalt">Heksadesimalt</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&veaction=edit&section=12" title="Rediger avsnitt: Heksadesimalt" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&action=edit&section=12" title="Rediger kildekoden til seksjonen Heksadesimalt"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Da heksadesimaltallenes basis 16 = 2<sup>4</sup>, vil en konvertering være særlig enkel - et heksadesimalt siffer representerer en gruppe av fire binære sifre. </p> <table class="wikitable"> <tbody><tr> <th>Heksadesimalt</th> <th>Binært </th></tr> <tr> <td>0</td> <td align="center">0000 </td></tr> <tr> <td>1</td> <td align="center">0001 </td></tr> <tr> <td>2</td> <td align="center">0010 </td></tr> <tr> <td>3</td> <td align="center">0011 </td></tr> <tr> <td>4</td> <td align="center">0100 </td></tr> <tr> <td>5</td> <td align="center">0101 </td></tr> <tr> <td>6</td> <td align="center">0110 </td></tr> <tr> <td>7</td> <td align="center">0111 </td></tr> <tr> <td>8</td> <td align="center">1000 </td></tr> <tr> <td>9</td> <td align="center">1001 </td></tr> <tr> <td>A</td> <td align="center">1010 </td></tr> <tr> <td>B</td> <td align="center">1011 </td></tr> <tr> <td>C</td> <td align="center">1100 </td></tr> <tr> <td>D</td> <td align="center">1101 </td></tr> <tr> <td>E</td> <td align="center">1110 </td></tr> <tr> <td>F</td> <td align="center">1111 </td></tr></tbody></table> <p>Eksempel: 3F8<sub>16</sub> = 001111111000<sub>2</sub> </p><p>Også desimale tall kan legges til i tabellen. Da vil ikke tabellen vise bokstaver etter 1001 (9) i binære tallsystemet, men resten av tallene som 10, 11 og 12 og videre feks: </p><p>Desimale tall til venstre nedenfor . binære tall til høyre nedenfor. </p> <pre> 0 0000 1 0001 2 0010 3 0011 4 0100 5 0101 6 0110 7 0111 8 1000 9 1001 10 1010 11 1011 12 1100 13 1101 14 1110 15 1111 </pre> <div class="mw-heading mw-heading3"><h3 id="Oktalt">Oktalt</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&veaction=edit&section=13" title="Rediger avsnitt: Oktalt" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&action=edit&section=13" title="Rediger kildekoden til seksjonen Oktalt"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Oktaltallenes basis er 2<sup>3</sup> – et oktalt siffer representerer en gruppe av tre binære siffre. </p> <table class="wikitable"> <tbody><tr> <th>Oktalt</th> <th>Binært </th></tr> <tr> <td>0</td> <td align="center">000 </td></tr> <tr> <td>1</td> <td align="center">001 </td></tr> <tr> <td>2</td> <td align="center">010 </td></tr> <tr> <td>3</td> <td align="center">011 </td></tr> <tr> <td>4</td> <td align="center">100 </td></tr> <tr> <td>5</td> <td align="center">101 </td></tr> <tr> <td>6</td> <td align="center">110 </td></tr> <tr> <td>7</td> <td align="center">111 </td></tr></tbody></table> <p>Eksempel: 173<sub>8</sub> = 001111011<sub>2</sub> </p> <div class="mw-heading mw-heading2"><h2 id="Brøk"><span id="Br.C3.B8k"></span>Brøk</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&veaction=edit&section=14" title="Rediger avsnitt: Brøk" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&action=edit&section=14" title="Rediger kildekoden til seksjonen Brøk"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>I <a href="/wiki/Titallsystemet" title="Titallsystemet">titallsystemet</a> heter desimalene tideler, hundredeler, tusendeler, titusendeler, hundretusendeler osv. Disse tallene er henholdsvis 10<sup>−1</sup>, 10<sup>−2</sup>, 10<sup>−3</sup>, 10<sup>−4</sup>, 10<sup>−5</sup>. </p><p>Sifrene til høyre for kommaet i totallsystemet representerer (i rekkefølge fra venstre mot høyre) 2<sup>−1</sup>, 2<sup>−2</sup>, 2<sup>−3</sup>, 2<sup>−4</sup>, 2<sup>−5</sup> osv. Disse tallene er med andre ord 1/2, 1/4, 1/8, 1/16 og 1/32. </p><p>Tallet 0,01 i totallsystemet er en firedel. Ved å summere 0,1 og 0,001 får man at tallet 0,101 i totallsystemet er en halv pluss en åttedel, det vil si fem åttedeler. </p> <div class="mw-heading mw-heading2"><h2 id="Se_også"><span id="Se_ogs.C3.A5"></span>Se også</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&veaction=edit&section=15" title="Rediger avsnitt: Se også" class="mw-editsection-visualeditor"><span>rediger</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Bin%C3%A6rt_tallsystem&action=edit&section=15" title="Rediger kildekoden til seksjonen Se også"><span>rediger kilde</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Bin%C3%A6r_logikk" class="mw-redirect" title="Binær logikk">Binær logikk</a></li> <li><a href="/wiki/Toerpotens" title="Toerpotens">Toerpotens</a></li></ul> <div class="navbox-styles"><style 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