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subsection</span> </button> <ul id="toc-History_of_binary_codes-sublist" class="vector-toc-list"> <li id="toc-Invention" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Invention"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Invention</span> </div> </a> <ul id="toc-Invention-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Previous_Ideas" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Previous_Ideas"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Previous Ideas</span> </div> </a> <ul id="toc-Previous_Ideas-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Boolean_Logical_System" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Boolean_Logical_System"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Boolean Logical System</span> </div> </a> <ul id="toc-Boolean_Logical_System-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Other_forms_of_binary_code" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Other_forms_of_binary_code"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Other forms of binary code</span> </div> </a> <button aria-controls="toc-Other_forms_of_binary_code-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 Other forms of binary code subsection</span> </button> <ul id="toc-Other_forms_of_binary_code-sublist" class="vector-toc-list"> <li id="toc-Braille" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Braille"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Braille</span> </div> </a> <ul id="toc-Braille-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bagua" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bagua"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Bagua</span> </div> </a> <ul id="toc-Bagua-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ifá,_Ilm_Al-Raml_and_Geomancy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ifá,_Ilm_Al-Raml_and_Geomancy"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Ifá, Ilm Al-Raml and Geomancy</span> </div> </a> <ul id="toc-Ifá,_Ilm_Al-Raml_and_Geomancy-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Coding_systems" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Coding_systems"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Coding systems</span> </div> </a> <button aria-controls="toc-Coding_systems-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 Coding systems subsection</span> </button> <ul id="toc-Coding_systems-sublist" class="vector-toc-list"> <li id="toc-ASCII_code" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#ASCII_code"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>ASCII code</span> </div> </a> <ul id="toc-ASCII_code-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Binary-coded_decimal" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Binary-coded_decimal"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Binary-coded decimal</span> </div> </a> <ul id="toc-Binary-coded_decimal-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Early_uses_of_binary_codes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Early_uses_of_binary_codes"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Early uses of binary codes</span> </div> </a> <ul id="toc-Early_uses_of_binary_codes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Current_uses_of_binary" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Current_uses_of_binary"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Current uses of binary</span> </div> </a> <ul id="toc-Current_uses_of_binary-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Weight_of_binary_codes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Weight_of_binary_codes"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Weight of binary codes</span> </div> </a> <ul id="toc-Weight_of_binary_codes-sublist" class="vector-toc-list"> </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">7</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">8</span> <span>References</span> </div> </a> <ul id="toc-References-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">9</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" title="Table of Contents" > <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> 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Available in 31 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-31" 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">31 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/%D8%B1%D9%85%D8%B2_%D8%AB%D9%86%D8%A7%D8%A6%D9%8A" title="رمز ثنائي – Arabic" lang="ar" hreflang="ar" data-title="رمز ثنائي" data-language-autonym="العربية" data-language-local-name="Arabic" 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/C%C3%B3digu_binariu" title="Códigu binariu – Asturian" lang="ast" hreflang="ast" data-title="Códigu binariu" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%91%D1%96%D0%BD%D0%B0%D1%80%D0%BD%D1%8B_%D0%BA%D0%BE%D0%B4" title="Бінарны код – Belarusian" lang="be" hreflang="be" data-title="Бінарны код" data-language-autonym="Беларуская" data-language-local-name="Belarusian" 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%B5%D0%BD_%D0%BA%D0%BE%D0%B4" title="Двоичен код – Bulgarian" lang="bg" hreflang="bg" data-title="Двоичен код" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Codi_binari" title="Codi binari – Catalan" lang="ca" hreflang="ca" data-title="Codi binari" 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/Bin%C3%A1rn%C3%AD_k%C3%B3d" title="Binární kód – Czech" lang="cs" hreflang="cs" data-title="Binární kód" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Bin%C3%A4rcode" title="Binärcode – German" lang="de" hreflang="de" data-title="Binärcode" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/C%C3%B3digo_binario" title="Código binario – Spanish" lang="es" hreflang="es" data-title="Código binario" 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/Duuma_kodo" title="Duuma kodo – Esperanto" lang="eo" hreflang="eo" data-title="Duuma kodo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%DA%A9%D8%AF%D9%87%D8%A7%DB%8C_%D8%AF%D9%88%D8%AF%D9%88%DB%8C%DB%8C" title="کدهای دودویی – Persian" lang="fa" hreflang="fa" data-title="کدهای دودویی" data-language-autonym="فارسی" data-language-local-name="Persian" 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/Code_binaire" title="Code binaire – French" lang="fr" hreflang="fr" data-title="Code binaire" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/C%C3%B3d_d%C3%A9n%C3%A1rtha" title="Cód dénártha – Irish" lang="ga" hreflang="ga" data-title="Cód dénártha" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</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_%EC%BD%94%EB%93%9C" title="이진 코드 – Korean" lang="ko" hreflang="ko" data-title="이진 코드" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</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%95%E0%A5%82%E0%A4%9F" title="द्वयाधारी कूट – Hindi" lang="hi" hreflang="hi" data-title="द्वयाधारी कूट" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9C%D3%99%D0%BB%D1%96%D0%BC%D0%B5%D1%82%D1%82%D0%B5%D1%80_%D0%B0%D0%BB%D0%BC%D0%B0%D1%81%D1%82%D1%8B%D1%80%D1%83%D2%93%D0%B0_%D0%B0%D1%80%D0%BD%D0%B0%D0%BB%D2%93%D0%B0%D0%BD_%D0%B5%D0%BA%D1%96%D0%BB%D1%96%D0%BA_%D0%BA%D0%BE%D0%B4" title="Мәліметтер алмастыруға арналған екілік код – Kazakh" lang="kk" hreflang="kk" data-title="Мәліметтер алмастыруға арналған екілік код" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Bin%C4%81rais_kods" title="Binārais kods – Latvian" lang="lv" hreflang="lv" data-title="Binārais kods" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Bin%C3%A4rcode" title="Binärcode – Luxembourgish" lang="lb" hreflang="lb" data-title="Binärcode" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%91%D0%B8%D0%BD%D0%B0%D1%80%D0%B5%D0%BD_%D0%BA%D0%BE%D0%B4" title="Бинарен код – Macedonian" lang="mk" hreflang="mk" data-title="Бинарен код" data-language-autonym="Македонски" data-language-local-name="Macedonian" 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%AC%E0%B5%88%E0%B4%A8%E0%B4%B1%E0%B4%BF_%E0%B4%95%E0%B5%8B%E0%B4%A1%E0%B5%8D" title="ബൈനറി കോഡ് – Malayalam" lang="ml" hreflang="ml" data-title="ബൈനറി കോഡ്" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Kod_perduaan" title="Kod perduaan – Malay" lang="ms" hreflang="ms" data-title="Kod perduaan" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Binaire_code" title="Binaire code – Dutch" lang="nl" hreflang="nl" data-title="Binaire code" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Bin%C3%A6r_kode" title="Binær kode – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Binær kode" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Bin%C3%A6rkode" title="Binærkode – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Binærkode" 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-mhr mw-list-item"><a href="https://mhr.wikipedia.org/wiki/%D0%A6%D0%B8%D1%84%D1%80_%D0%BA%D0%BE%D0%B4%D0%BB%D1%8B%D0%BC%D0%B0%D1%88" title="Цифр кодлымаш – Eastern Mari" lang="mhr" hreflang="mhr" data-title="Цифр кодлымаш" data-language-autonym="Олык марий" data-language-local-name="Eastern Mari" class="interlanguage-link-target"><span>Олык марий</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Ikkilik_kod" title="Ikkilik kod – Uzbek" lang="uz" hreflang="uz" data-title="Ikkilik kod" 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-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%94%D0%B2%D0%BE%D0%B8%D1%87%D0%BD%D1%8B%D0%B9_%D0%BA%D0%BE%D0%B4" title="Двоичный код – Russian" lang="ru" hreflang="ru" data-title="Двоичный код" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-nso mw-list-item"><a href="https://nso.wikipedia.org/wiki/Letlase_la_pedi" title="Letlase la pedi – Northern Sotho" lang="nso" hreflang="nso" data-title="Letlase la pedi" data-language-autonym="Sesotho sa Leboa" data-language-local-name="Northern Sotho" class="interlanguage-link-target"><span>Sesotho sa Leboa</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Bin%C3%A1rny_k%C3%B3d" title="Binárny kód – Slovak" lang="sk" hreflang="sk" data-title="Binárny kód" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%AC%E0%B1%88%E0%B0%A8%E0%B0%B0%E0%B1%80_%E0%B0%95%E0%B1%8B%E0%B0%A1%E0%B1%8D" title="బైనరీ కోడ్ – Telugu" lang="te" hreflang="te" data-title="బైనరీ కోడ్" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C4%B0kili_kod" title="İkili kod – Turkish" lang="tr" hreflang="tr" data-title="İkili kod" 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%94%D0%B2%D1%96%D0%B9%D0%BA%D0%BE%D0%B2%D0%B8%D0%B9_%D0%BA%D0%BE%D0%B4" title="Двійковий код – Ukrainian" lang="uk" hreflang="uk" data-title="Двійковий код" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a 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bits).</figcaption></figure> <p>A <b>binary code</b> represents <a href="/wiki/Plain_text" title="Plain text">text</a>, <a href="/wiki/Instruction_set" class="mw-redirect" title="Instruction set">computer processor instructions</a>, or any other <a href="/wiki/Data" title="Data">data</a> using a two-symbol system. The two-symbol system used is often "0" and "1" from the <a href="/wiki/Binary_number" title="Binary number">binary number system</a>. The binary code assigns a pattern of binary digits, also known as <a href="/wiki/Bit" title="Bit">bits</a>, to each character, instruction, etc. For example, a binary <a href="/wiki/String_(computer_science)" title="String (computer science)">string</a> of eight bits (which is also called a byte) can represent any of 256 possible values and can, therefore, represent a wide variety of different items. </p><p>In computing and telecommunications, binary codes are used for various methods of <a href="/wiki/Encoding" class="mw-redirect" title="Encoding">encoding</a> data, such as <a href="/wiki/Character_string" class="mw-redirect" title="Character string">character strings</a>, into bit strings. Those methods may use fixed-width or <a href="/wiki/Variable-length_code" title="Variable-length code">variable-width</a> strings. In a fixed-width binary code, each letter, digit, or other character is represented by a bit string of the same length; that bit string, interpreted as a <a href="/wiki/Binary_number" title="Binary number">binary number</a>, is usually displayed in code tables in <a href="/wiki/Octal" title="Octal">octal</a>, <a href="/wiki/Decimal" title="Decimal">decimal</a> or <a href="/wiki/Hexadecimal" title="Hexadecimal">hexadecimal</a> notation. There are many <a href="/wiki/Character_sets" class="mw-redirect" title="Character sets">character sets</a> and many <a href="/wiki/Character_encoding" title="Character encoding">character encodings</a> for them. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Binary_to_Hexadecimal_or_Decimal.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/af/Binary_to_Hexadecimal_or_Decimal.jpg/220px-Binary_to_Hexadecimal_or_Decimal.jpg" decoding="async" width="220" height="407" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/a/af/Binary_to_Hexadecimal_or_Decimal.jpg 1.5x" data-file-width="238" data-file-height="440" /></a><figcaption>Binary to Hexadecimal or Decimal</figcaption></figure> <p>A <a href="/wiki/Bit_string" class="mw-redirect" title="Bit string">bit string</a>, interpreted as a binary number, can be <a href="/wiki/Binary_number#Decimal" title="Binary number">translated into a decimal number</a>. For example, the <a href="/wiki/Letter_case" title="Letter case">lower case</a> <i>a</i>, if represented by the bit string <code>01100001</code> (as it is in the standard <a href="/wiki/ASCII" title="ASCII">ASCII</a> code), can also be represented as the decimal number 97. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History_of_binary_codes">History of binary codes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binary_code&action=edit&section=1" title="Edit section: History of binary codes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Binary_number#History" title="Binary number">Binary number § History</a></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Disputed plainlinks metadata ambox ambox-content ambox-disputed" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/System-search.svg/45px-System-search.svg.png" decoding="async" width="45" height="45" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/System-search.svg/68px-System-search.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/17/System-search.svg/90px-System-search.svg.png 2x" data-file-width="48" data-file-height="48" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section's <b>factual accuracy is <a href="/wiki/Wikipedia:Accuracy_dispute" title="Wikipedia:Accuracy dispute">disputed</a></b>.<span class="hide-when-compact"> Relevant discussion may be found on the <a href="/wiki/Talk:Binary_code#Disputed" title="Talk:Binary code">talk page</a>. Please help to ensure that disputed statements are <a href="/wiki/Wikipedia:Reliable_sources" title="Wikipedia:Reliable sources">reliably sourced</a>.</span> <span class="date-container"><i>(<span class="date">April 2015</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Gottfried_Wilhelm_Leibniz,_Bernhard_Christoph_Francke.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Gottfried_Wilhelm_Leibniz%2C_Bernhard_Christoph_Francke.jpg/170px-Gottfried_Wilhelm_Leibniz%2C_Bernhard_Christoph_Francke.jpg" decoding="async" width="170" height="210" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Gottfried_Wilhelm_Leibniz%2C_Bernhard_Christoph_Francke.jpg/255px-Gottfried_Wilhelm_Leibniz%2C_Bernhard_Christoph_Francke.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Gottfried_Wilhelm_Leibniz%2C_Bernhard_Christoph_Francke.jpg/340px-Gottfried_Wilhelm_Leibniz%2C_Bernhard_Christoph_Francke.jpg 2x" data-file-width="4486" data-file-height="5538" /></a><figcaption><a href="/wiki/Gottfried_Leibniz" class="mw-redirect" title="Gottfried Leibniz">Gottfried Leibniz</a></figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Invention">Invention</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binary_code&action=edit&section=2" title="Edit section: Invention"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The modern binary number system, the basis for binary code, is an invention by <a href="/wiki/Gottfried_Leibniz" class="mw-redirect" title="Gottfried Leibniz">Gottfried Leibniz</a> in 1689 and appears in his article <i>Explication de l'Arithmétique Binaire (</i>English: <i>Explanation of the Binary Arithmetic</i>) which uses only the characters 1 and 0, and some remarks on its usefulness. Leibniz's system uses 0 and 1, like the modern binary numeral system. Binary numerals were central to Leibniz's intellectual and theological ideas. He believed that binary numbers were symbolic of the Christian idea of <i><a href="/wiki/Creatio_ex_nihilo" title="Creatio ex nihilo">creatio ex nihilo</a></i> or creation out of nothing.<sup id="cite_ref-on_1-0" class="reference"><a href="#cite_note-on-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-lnz_2-0" class="reference"><a href="#cite_note-lnz-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>In Leibniz's view, binary numbers represented a fundamental form of creation, reflecting the simplicity and unity of the divine.<sup id="cite_ref-lnz_2-1" class="reference"><a href="#cite_note-lnz-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Leibniz was also attempting to find a way to translate logical reasoning into pure mathematics. He viewed the binary system as a means of simplifying complex logical and mathematical processes, believing that it could be used to express all concepts of arithmetic and logic.<sup id="cite_ref-lnz_2-2" class="reference"><a href="#cite_note-lnz-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Previous_Ideas">Previous Ideas</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binary_code&action=edit&section=3" title="Edit section: Previous Ideas"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Leibniz explained in his work that he encountered the <i><a href="/wiki/I_Ching" title="I Ching">I Ching</a></i> by <a href="/wiki/Fu_Xi" class="mw-redirect" title="Fu Xi">Fu Xi</a><sup id="cite_ref-lnz_2-3" class="reference"><a href="#cite_note-lnz-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> that dates from the 9th century BC in China,<sup id="cite_ref-HackerMoore2002_3-0" class="reference"><a href="#cite_note-HackerMoore2002-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> through French Jesuit <a href="/wiki/Joachim_Bouvet" title="Joachim Bouvet">Joachim Bouvet</a> and noted with fascination how its <a href="/wiki/Hexagram_(I_Ching)" title="Hexagram (I Ching)">hexagrams</a> correspond to the binary numbers from 0 to 111111, and concluded that this mapping was evidence of major Chinese accomplishments in the sort of philosophical visual binary <a href="/wiki/Mathematics" title="Mathematics">mathematics</a> he admired.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-smith_5-0" class="reference"><a href="#cite_note-smith-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Leibniz saw the hexagrams as an affirmation of the universality of his own religious belief.<sup id="cite_ref-smith_5-1" class="reference"><a href="#cite_note-smith-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> After Leibniz ideas were ignored, the book had confirmed his theory that life could be simplified or reduced down to a series of straightforward propositions. He created a system consisting of rows of zeros and ones. During this time period, Leibniz had not yet found a use for this system.<sup id="cite_ref-Gottfried_Leibniz_6-0" class="reference"><a href="#cite_note-Gottfried_Leibniz-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> The binary system of the <i>I Ching</i> is based on the duality of <a href="/wiki/Yin_and_yang" title="Yin and yang">yin and yang</a>.<sup id="cite_ref-scientific_7-0" class="reference"><a href="#cite_note-scientific-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Slit_drum" title="Slit drum">Slit drums</a> with binary tones are used to encode messages across Africa and Asia.<sup id="cite_ref-scientific_7-1" class="reference"><a href="#cite_note-scientific-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> The Indian scholar <a href="/wiki/Pingala" title="Pingala">Pingala</a> (around 5th–2nd centuries BC) developed a binary system for describing <a href="/wiki/Prosody_(poetry)" class="mw-redirect" title="Prosody (poetry)">prosody</a> in his <i>Chandashutram</i>.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Mangareva" title="Mangareva">Mangareva</a> people in <a href="/wiki/French_Polynesia" title="French Polynesia">French Polynesia</a> were using a hybrid binary-<a href="/wiki/Decimal" title="Decimal">decimal</a> system before 1450.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> In the 11th century, scholar and philosopher <a href="/wiki/Shao_Yong" title="Shao Yong">Shao Yong</a> developed a method for arranging the hexagrams which corresponds, albeit unintentionally, to the sequence 0 to 63, as represented in binary, with yin as 0, yang as 1 and the <a href="/wiki/Least_significant_bit" class="mw-redirect" title="Least significant bit">least significant bit</a> on top. The ordering is also the <a href="/wiki/Lexicographical_order" class="mw-redirect" title="Lexicographical order">lexicographical order</a> on <a href="/wiki/Sextuple" class="mw-redirect" title="Sextuple">sextuples</a> of elements chosen from a two-element set.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:George_Boole_color.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/George_Boole_color.jpg/170px-George_Boole_color.jpg" decoding="async" width="170" height="227" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/George_Boole_color.jpg/255px-George_Boole_color.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ce/George_Boole_color.jpg/340px-George_Boole_color.jpg 2x" data-file-width="600" data-file-height="800" /></a><figcaption><a href="/wiki/George_Boole" title="George Boole">George Boole</a></figcaption></figure><p>In 1605 <a href="/wiki/Francis_Bacon" title="Francis Bacon">Francis Bacon</a> discussed a system whereby letters of the alphabet could be reduced to sequences of binary digits, which could then be encoded as scarcely visible variations in the font in any random text.<sup id="cite_ref-Bacon1605_12-0" class="reference"><a href="#cite_note-Bacon1605-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> Importantly for the general theory of binary encoding, he added that this method could be used with any objects at all: "provided those objects be capable of a twofold difference only; as by Bells, by Trumpets, by Lights and Torches, by the report of Muskets, and any instruments of like nature".<sup id="cite_ref-Bacon1605_12-1" class="reference"><a href="#cite_note-Bacon1605-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><div class="mw-heading mw-heading3"><h3 id="Boolean_Logical_System">Boolean Logical System</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binary_code&action=edit&section=4" title="Edit section: Boolean Logical System"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/George_Boole" title="George Boole">George Boole</a> published a paper in 1847 called 'The Mathematical Analysis of Logic' that describes an algebraic system of logic, now known as <a href="/wiki/Boolean_algebra_(logic)" class="mw-redirect" title="Boolean algebra (logic)">Boolean algebra</a>. Boole's system was based on binary, a yes-no, on-off approach that consisted of the three most basic operations: AND, OR, and NOT.<sup id="cite_ref-Boolean_operations_13-0" class="reference"><a href="#cite_note-Boolean_operations-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> This system was not put into use until a graduate student from <a href="/wiki/Massachusetts_Institute_of_Technology" title="Massachusetts Institute of Technology">Massachusetts Institute of Technology</a>, <a href="/wiki/Claude_Shannon" title="Claude Shannon">Claude Shannon</a>, noticed that the Boolean algebra he learned was similar to an electric circuit. In 1937, Shannon wrote his master's thesis, <i><a href="/wiki/A_Symbolic_Analysis_of_Relay_and_Switching_Circuits" title="A Symbolic Analysis of Relay and Switching Circuits">A Symbolic Analysis of Relay and Switching Circuits</a></i>, which implemented his findings. Shannon's thesis became a starting point for the use of the binary code in practical applications such as computers, electric circuits, and more.<sup id="cite_ref-Claude_Shannon_14-0" class="reference"><a href="#cite_note-Claude_Shannon-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Other_forms_of_binary_code">Other forms of binary code</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binary_code&action=edit&section=5" title="Edit section: Other forms of binary code"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/List_of_binary_codes" title="List of binary codes">List of binary codes</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Original_research plainlinks metadata ambox ambox-content ambox-Original_research" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/40px-Ambox_important.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/60px-Ambox_important.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/b/b4/Ambox_important.svg/80px-Ambox_important.svg.png 2x" data-file-width="40" data-file-height="40" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>possibly contains <a href="/wiki/Wikipedia:No_original_research" title="Wikipedia:No original research">original research</a></b>.<span class="hide-when-compact"> Please <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Binary_code&action=edit">improve it</a> by <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verifying</a> the claims made and adding <a href="/wiki/Wikipedia:Citing_sources#Inline_citations" title="Wikipedia:Citing sources">inline citations</a>. Statements consisting only of original research should be removed.</span> <span class="date-container"><i>(<span class="date">March 2015</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Bagua-name-earlier.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Bagua-name-earlier.svg/220px-Bagua-name-earlier.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Bagua-name-earlier.svg/330px-Bagua-name-earlier.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Bagua-name-earlier.svg/440px-Bagua-name-earlier.svg.png 2x" data-file-width="547" data-file-height="547" /></a><figcaption>Daoist Bagua</figcaption></figure> <p>The bit string is not the only type of binary code: in fact, a binary system in general, is any system that allows only two choices such as a switch in an electronic system or a simple true or false test. </p> <div class="mw-heading mw-heading3"><h3 id="Braille">Braille</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binary_code&action=edit&section=6" title="Edit section: Braille"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Braille" title="Braille">Braille</a> is a type of binary code that is widely used by the blind to read and write by touch, named for its creator, Louis Braille. This system consists of grids of six dots each, three per column, in which each dot has two states: raised or not raised. The different combinations of raised and flattened dots are capable of representing all letters, numbers, and punctuation signs. </p> <div class="mw-heading mw-heading3"><h3 id="Bagua">Bagua <span class="anchor" id="BaGua"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binary_code&action=edit&section=7" title="Edit section: Bagua"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <i><a href="/wiki/Bagua" title="Bagua">bagua</a></i> are diagrams used in <i><a href="/wiki/Feng_shui" title="Feng shui">feng shui</a>,</i> <a href="/wiki/Taoist" class="mw-redirect" title="Taoist">Taoist</a> <a href="/wiki/Cosmology" title="Cosmology">cosmology</a> and <i><a href="/wiki/I_Ching" title="I Ching">I Ching</a></i> studies. The <i>ba gua</i> consists of 8 trigrams; <i>bā</i> meaning 8 and <i>guà</i> meaning divination figure. The same word is used for the 64 guà (hexagrams). Each figure combines three lines (<i>yáo</i>) that are either broken (<a href="/wiki/Yin_and_yang" title="Yin and yang"><i>yin</i></a>) or unbroken (<i>yang</i>). The relationships between the trigrams are represented in two arrangements, the primordial, "Earlier Heaven" or "Fuxi" <i>bagua</i>, and the manifested, "Later Heaven", or "King Wen" <i>bagua</i>.<sup id="cite_ref-wilhelm_15-0" class="reference"><a href="#cite_note-wilhelm-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> (See also, the <a href="/wiki/King_Wen_sequence" title="King Wen sequence">King Wen sequence</a> of the 64 hexagrams). </p> <div class="mw-heading mw-heading3"><h3 id="Ifá,_Ilm_Al-Raml_and_Geomancy"><span id="If.C3.A1.2C_Ilm_Al-Raml_and_Geomancy"></span>Ifá, Ilm Al-Raml and Geomancy<span class="anchor" id="Ifá"></span></h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binary_code&action=edit&section=8" title="Edit section: Ifá, Ilm Al-Raml and Geomancy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/If%C3%A1" title="Ifá">Ifá</a>/Ifé system of divination in African religions, such as of <a href="/wiki/Yoruba_people" title="Yoruba people">Yoruba</a>, <a href="/wiki/Igbo_people" title="Igbo people">Igbo</a>, and <a href="/wiki/Ewe_people" title="Ewe people">Ewe</a>, consists of an elaborate traditional ceremony producing 256 oracles made up by 16 symbols with 256 = 16 x 16. An initiated priest, or <a href="/wiki/Babalawo" title="Babalawo">Babalawo</a>, who had memorized oracles, would request sacrifice from consulting clients and make prayers. Then, divination nuts or a pair of chains are used to produce random binary numbers,<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> which are drawn with sandy material on an "Opun" figured wooden tray representing the totality of fate. </p><p>Through the spread of <a href="/wiki/Islamic" class="mw-redirect" title="Islamic">Islamic</a> culture, Ifé/Ifá was assimilated as the "Science of Sand" (ilm al-raml), which then spread further and became "Science of Reading the Signs on the Ground" (<a href="/wiki/Geomancy" title="Geomancy">Geomancy</a>) in Europe. </p><p>This was thought to be another possible route from which computer science was inspired,<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> as Geomancy arrived at Europe at an earlier stage (about 12th Century, described by <a href="/wiki/Hugo_of_Santalla" title="Hugo of Santalla">Hugh of Santalla</a>) than <a href="/wiki/I_Ching" title="I Ching">I Ching</a> (17th Century, described by <a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Gottfried Wilhelm Leibniz</a>). </p> <div class="mw-heading mw-heading2"><h2 id="Coding_systems">Coding systems</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binary_code&action=edit&section=9" title="Edit section: Coding systems"><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:2D_Binary_Index.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/2D_Binary_Index.svg/220px-2D_Binary_Index.svg.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/2D_Binary_Index.svg/330px-2D_Binary_Index.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/2D_Binary_Index.svg/440px-2D_Binary_Index.svg.png 2x" data-file-width="512" data-file-height="512" /></a><figcaption>An example of a recursive <a href="/wiki/Binary_space_partitioning" title="Binary space partitioning">binary space partitioning</a> <a href="/wiki/Quadtree" title="Quadtree">quadtree</a> for a 2D index.</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="ASCII_code">ASCII code</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binary_code&action=edit&section=10" title="Edit section: ASCII code"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/American_Standard_Code_for_Information_Interchange" class="mw-redirect" title="American Standard Code for Information Interchange">American Standard Code for Information Interchange</a> (ASCII), uses a 7-bit binary code to represent text and other characters within computers, communications equipment, and other devices. Each letter or symbol is assigned a number from 0 to 127. For example, lowercase "a" is represented by <code>1100001</code> as a bit string (which is decimal 97). </p> <div class="mw-heading mw-heading3"><h3 id="Binary-coded_decimal">Binary-coded decimal</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binary_code&action=edit&section=11" title="Edit section: Binary-coded decimal"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Binary-coded_decimal" title="Binary-coded decimal">Binary-coded decimal</a> (BCD) is a binary encoded representation of integer values that uses a 4-bit <a href="/wiki/Nibble" title="Nibble">nibble</a> to encode decimal digits. Four binary bits can encode up to 16 distinct values; but, in BCD-encoded numbers, only ten values in each nibble are legal, and encode the decimal digits zero, through nine. The remaining six values are illegal and may cause either a machine exception or unspecified behavior, depending on the computer implementation of BCD arithmetic. </p><p>BCD arithmetic is sometimes preferred to floating-point numeric formats in commercial and financial applications where the complex rounding behaviors of floating-point numbers is inappropriate.<sup id="cite_ref-Cowlishaw_GDA_18-0" class="reference"><a href="#cite_note-Cowlishaw_GDA-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Early_uses_of_binary_codes">Early uses of binary codes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binary_code&action=edit&section=12" title="Edit section: Early uses of binary codes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>1875: <a href="/wiki/%C3%89mile_Baudot" title="Émile Baudot">Émile Baudot</a> "Addition of binary strings in his ciphering system," which, eventually, led to the ASCII of today.</li> <li>1884: The <a href="/wiki/Linotype_machine" title="Linotype machine">Linotype machine</a> where the matrices are sorted to their corresponding channels after use by a binary-coded slide rail.</li> <li>1932: <a href="/wiki/C._E._Wynn-Williams" title="C. E. Wynn-Williams">C. E. Wynn-Williams</a> "Scale of Two" counter<sup id="cite_ref-Glaser_19-0" class="reference"><a href="#cite_note-Glaser-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup></li> <li>1937: <a href="/wiki/Alan_Turing" title="Alan Turing">Alan Turing</a> electro-mechanical binary multiplier</li> <li>1937: <a href="/wiki/George_Stibitz" title="George Stibitz">George Stibitz</a> <a href="/wiki/Excess_three_code" class="mw-redirect" title="Excess three code">"excess three" code</a> in the <a href="/wiki/George_Stibitz#Computer" title="George Stibitz">Complex Computer</a><sup id="cite_ref-Glaser_19-1" class="reference"><a href="#cite_note-Glaser-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup></li> <li>1937: <a href="/wiki/Atanasoff%E2%80%93Berry_Computer" class="mw-redirect" title="Atanasoff–Berry Computer">Atanasoff–Berry Computer</a><sup id="cite_ref-Glaser_19-2" class="reference"><a href="#cite_note-Glaser-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup></li> <li>1938: <a href="/wiki/Konrad_Zuse" title="Konrad Zuse">Konrad Zuse</a> <a href="/wiki/Z1_(computer)" title="Z1 (computer)">Z1</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Current_uses_of_binary">Current uses of binary</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binary_code&action=edit&section=13" title="Edit section: Current uses of binary"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Most modern computers use binary encoding for instructions and data. <a href="/wiki/CD" class="mw-redirect" title="CD">CDs</a>, <a href="/wiki/DVD" title="DVD">DVDs</a>, and <a href="/wiki/Blu-ray_Disc" class="mw-redirect" title="Blu-ray Disc">Blu-ray Discs</a> represent sound and video digitally in binary form. Telephone calls are carried digitally on long-distance and mobile phone networks using <a href="/wiki/Pulse-code_modulation" title="Pulse-code modulation">pulse-code modulation</a>, and on <a href="/wiki/Voice_over_IP" title="Voice over IP">voice over IP</a> networks. </p> <div class="mw-heading mw-heading2"><h2 id="Weight_of_binary_codes">Weight of binary codes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binary_code&action=edit&section=14" title="Edit section: Weight of binary codes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The weight of a binary code, as defined in the table of <a href="/wiki/Constant-weight_code" title="Constant-weight code">constant-weight codes</a>,<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> is the <a href="/wiki/Hamming_weight" title="Hamming weight">Hamming weight</a> of the binary words coding for the represented words or sequences. </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=Binary_code&action=edit&section=15" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Binary_number" title="Binary number">Binary number</a></li> <li><a href="/wiki/List_of_binary_codes" title="List of binary codes">List of binary codes</a></li> <li><a href="/wiki/Binary_file" title="Binary file">Binary file</a></li> <li><a href="/wiki/Unicode" title="Unicode">Unicode</a></li> <li><a href="/wiki/Gray_code" title="Gray code">Gray code</a></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=Binary_code&action=edit&section=16" 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-on-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-on_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="CITEREFYuen-Ting_Lai1998" class="citation book cs1">Yuen-Ting Lai (1998). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=U9dOmVt81UAC&pg=PA149"><i>Leibniz, Mysticism and Religion</i></a>. Springer. pp. <span class="nowrap">149–</span>150. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7923-5223-5" title="Special:BookSources/978-0-7923-5223-5"><bdi>978-0-7923-5223-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Leibniz%2C+Mysticism+and+Religion&rft.pages=%3Cspan+class%3D%22nowrap%22%3E149-%3C%2Fspan%3E150&rft.pub=Springer&rft.date=1998&rft.isbn=978-0-7923-5223-5&rft.au=Yuen-Ting+Lai&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DU9dOmVt81UAC%26pg%3DPA149&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABinary+code" class="Z3988"></span></span> </li> <li id="cite_note-lnz-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-lnz_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-lnz_2-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-lnz_2-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-lnz_2-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text">Leibniz G., Explication de l'Arithmétique Binaire, Die Mathematische Schriften, ed. C. Gerhardt, Berlin 1879, vol.7, p.223; Engl. transl.<a rel="nofollow" class="external autonumber" href="http://www.leibniz-translations.com/binary.htm">[1]</a></span> </li> <li id="cite_note-HackerMoore2002-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-HackerMoore2002_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEdward_HackerSteve_MooreLorraine_Patsco2002" class="citation book cs1">Edward Hacker; Steve Moore; Lorraine Patsco (2002). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=S5hLpfFiMCQC&pg=PR13"><i>I Ching: An Annotated Bibliography</i></a>. Routledge. p. 13. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-415-93969-0" title="Special:BookSources/978-0-415-93969-0"><bdi>978-0-415-93969-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=I+Ching%3A+An+Annotated+Bibliography&rft.pages=13&rft.pub=Routledge&rft.date=2002&rft.isbn=978-0-415-93969-0&rft.au=Edward+Hacker&rft.au=Steve+Moore&rft.au=Lorraine+Patsco&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DS5hLpfFiMCQC%26pg%3DPR13&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABinary+code" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAiton1985" class="citation book cs1">Aiton, Eric J. 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Smith (2008). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Da_oP3sJs1oC&pg=PA4153"><i>Leibniz: What Kind of Rationalist?: What Kind of Rationalist?</i></a>. Springer. p. 415. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4020-8668-7" title="Special:BookSources/978-1-4020-8668-7"><bdi>978-1-4020-8668-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Leibniz%3A+What+Kind+of+Rationalist%3F%3A+What+Kind+of+Rationalist%3F&rft.pages=415&rft.pub=Springer&rft.date=2008&rft.isbn=978-1-4020-8668-7&rft.au=J.E.H.+Smith&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DDa_oP3sJs1oC%26pg%3DPA4153&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABinary+code" class="Z3988"></span></span> </li> <li id="cite_note-Gottfried_Leibniz-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-Gottfried_Leibniz_6-0">^</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="http://www.kerryr.net/pioneers/leibniz.htm">"Gottfried Wilhelm Leibniz (1646 - 1716)"</a>. <i>www.kerryr.net</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.kerryr.net&rft.atitle=Gottfried+Wilhelm+Leibniz+%281646+-+1716%29&rft_id=http%3A%2F%2Fwww.kerryr.net%2Fpioneers%2Fleibniz.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABinary+code" class="Z3988"></span></span> </li> <li id="cite_note-scientific-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-scientific_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-scientific_7-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJonathan_Shectman2003" class="citation book cs1">Jonathan Shectman (2003). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=SsbChdIiflsC&pg=PA29"><i>Groundbreaking Scientific Experiments, Inventions, and Discoveries of the 18th Century</i></a>. 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Princeton, NJ: Princeton University Press. pp. 266, 269. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-09750-3" title="Special:BookSources/978-0-691-09750-3"><bdi>978-0-691-09750-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+I+Ching+or+Book+of+Changes&rft.place=Princeton%2C+NJ&rft.pages=266%2C+269&rft.pub=Princeton+University+Press&rft.date=1950&rft.isbn=978-0-691-09750-3&rft.aulast=Wilhelm&rft.aufirst=Richard&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DbbU9AAAAIAAJ%26pg%3DPA266&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABinary+code" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOlupona2014" class="citation book cs1">Olupona, Jacob K. (2014). <a rel="nofollow" class="external text" href="https://www.worldcat.org/oclc/839396781"><i>African Religions: A Very Short Introduction</i></a>. Oxford: <a href="/wiki/Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>. p. 45. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-979058-6" title="Special:BookSources/978-0-19-979058-6"><bdi>978-0-19-979058-6</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/839396781">839396781</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=African+Religions%3A+A+Very+Short+Introduction&rft.place=Oxford&rft.pages=45&rft.pub=Oxford+University+Press&rft.date=2014&rft_id=info%3Aoclcnum%2F839396781&rft.isbn=978-0-19-979058-6&rft.aulast=Olupona&rft.aufirst=Jacob+K.&rft_id=https%3A%2F%2Fwww.worldcat.org%2Foclc%2F839396781&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABinary+code" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEglash2007" class="citation web cs1">Eglash, Ron (June 2007). <a rel="nofollow" class="external text" href="https://www.ted.com/talks/ron_eglash_the_fractals_at_the_heart_of_african_designs/up-next#t-13472">"The fractals at the heart of African designs"</a>. <i>www.ted.com</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210727161435/https://www.ted.com/talks/ron_eglash_the_fractals_at_the_heart_of_african_designs/up-next">Archived</a> from the original on 2021-07-27<span class="reference-accessdate">. Retrieved <span class="nowrap">2021-04-15</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.ted.com&rft.atitle=The+fractals+at+the+heart+of+African+designs&rft.date=2007-06&rft.aulast=Eglash&rft.aufirst=Ron&rft_id=https%3A%2F%2Fwww.ted.com%2Ftalks%2Fron_eglash_the_fractals_at_the_heart_of_african_designs%2Fup-next%23t-13472&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABinary+code" class="Z3988"></span></span> </li> <li id="cite_note-Cowlishaw_GDA-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-Cowlishaw_GDA_18-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCowlishaw2015" class="citation web cs1"><a href="/wiki/Mike_F._Cowlishaw" class="mw-redirect" title="Mike F. Cowlishaw">Cowlishaw, Mike F.</a> (2015) [1981, 2008]. <a rel="nofollow" class="external text" href="http://speleotrove.com/decimal/">"General Decimal Arithmetic"</a>. IBM<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-01-02</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=General+Decimal+Arithmetic&rft.pub=IBM&rft.date=2015&rft.aulast=Cowlishaw&rft.aufirst=Mike+F.&rft_id=http%3A%2F%2Fspeleotrove.com%2Fdecimal%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABinary+code" class="Z3988"></span></span> </li> <li id="cite_note-Glaser-19"><span class="mw-cite-backlink">^ <a href="#cite_ref-Glaser_19-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Glaser_19-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Glaser_19-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFGlaser1971">Glaser 1971</a></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.research.att.com/~njas/codes/Andw/">Table of Constant Weight Binary Codes</a></span> </li> </ol></div></div> <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=Binary_code&action=edit&section=17" 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="https://web.archive.org/web/20160923014940/http://www.baconlinks.com/docs/BILITERAL.doc">Sir Francis Bacon's BiLiteral Cypher system</a><sup><a href="/wiki/Template:Usurped/doc" title="Template:Usurped/doc">[usurped]</a></sup>, predates binary number system.</li> <li><span class="citation mathworld" id="Reference-Mathworld-Error-Correcting_Code"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeisstein" class="citation web cs1"><a href="/wiki/Eric_W._Weisstein" title="Eric W. Weisstein">Weisstein, Eric W.</a> <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/Error-CorrectingCode.html">"Error-Correcting Code"</a>. <i><a href="/wiki/MathWorld" title="MathWorld">MathWorld</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MathWorld&rft.atitle=Error-Correcting+Code&rft.au=Weisstein%2C+Eric+W.&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FError-CorrectingCode.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABinary+code" class="Z3988"></span></span></li> <li><a rel="nofollow" class="external text" href="http://www.win.tue.nl/~aeb/codes/binary.html">Table of general binary codes</a>. An updated version of the tables of bounds for small general binary codes given in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFM.R._BestA.E._BrouwerF.J._MacWilliamsA.M._Odlyzko1978" class="citation cs2">M.R. Best; A.E. Brouwer; F.J. MacWilliams; A.M. Odlyzko; N.J.A. Sloane (1978), "Bounds for Binary Codes of Length Less than 25", <i>IEEE Trans. Inf. Theory</i>, <b>24</b>: <span class="nowrap">81–</span>93, <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=10.1.1.391.9930">10.1.1.391.9930</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%2Ftit.1978.1055827">10.1109/tit.1978.1055827</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=IEEE+Trans.+Inf.+Theory&rft.atitle=Bounds+for+Binary+Codes+of+Length+Less+than+25&rft.volume=24&rft.pages=%3Cspan+class%3D%22nowrap%22%3E81-%3C%2Fspan%3E93&rft.date=1978&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.391.9930%23id-name%3DCiteSeerX&rft_id=info%3Adoi%2F10.1109%2Ftit.1978.1055827&rft.au=M.R.+Best&rft.au=A.E.+Brouwer&rft.au=F.J.+MacWilliams&rft.au=A.M.+Odlyzko&rft.au=N.J.A.+Sloane&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABinary+code" class="Z3988"></span>.</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20170423014446/http://www.eng.tau.ac.il/~litsyn/tableand/">Table of Nonlinear Binary Codes</a>. Maintained by Simon Litsyn, E. M. Rains, and N. J. A. Sloane. Updated until 1999.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGlaser1971" class="citation book cs1">Glaser, Anton (1971). "Chapter VII Applications to Computers". <i>History of Binary and other Nondecimal Numeration</i>. Tomash. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-938228-00-4" title="Special:BookSources/978-0-938228-00-4"><bdi>978-0-938228-00-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Chapter+VII+Applications+to+Computers&rft.btitle=History+of+Binary+and+other+Nondecimal+Numeration&rft.pub=Tomash&rft.date=1971&rft.isbn=978-0-938228-00-4&rft.aulast=Glaser&rft.aufirst=Anton&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABinary+code" class="Z3988"></span> cites some pre-ENIAC milestones.</li> <li><a rel="nofollow" class="external text" href="https://www.amazon.it/01010011-01100101-01100111-01110010-01110100/dp/B0CHD5Q8W1/ref=sr_1_1?qid=1694173977&refinements=p_27:%22Luigi+Usai%22&s=books&sr=1-1&ufe=app_do:amzn1.fos.9d4f9b77-768c-4a4e-94ad-33674c20ab35">First book in the world fully written in binary code</a>: (<abbr>IT</abbr>) Luigi Usai, <i>01010011 01100101 01100111 01110010 01100101 01110100 01101001</i>, Independently published, 2023, ISBN 979-8-8604-3980-1. <small>URL consulted September 8, 2023</small>.</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" 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=Binary_code&oldid=1275721453">https://en.wikipedia.org/w/index.php?title=Binary_code&oldid=1275721453</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_data" title="Category:Computer data">Computer data</a></li><li><a href="/wiki/Category:English_inventions" title="Category:English inventions">English inventions</a></li><li><a href="/wiki/Category:Encodings" title="Category:Encodings">Encodings</a></li><li><a href="/wiki/Category:Gottfried_Wilhelm_Leibniz" title="Category:Gottfried Wilhelm Leibniz">Gottfried Wilhelm Leibniz</a></li><li><a href="/wiki/Category:2_(number)" title="Category:2 (number)">2 (number)</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: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:Accuracy_disputes_from_April_2015" title="Category:Accuracy disputes from April 2015">Accuracy disputes from April 2015</a></li><li><a href="/wiki/Category:All_accuracy_disputes" title="Category:All accuracy disputes">All accuracy disputes</a></li><li><a href="/wiki/Category:Articles_that_may_contain_original_research_from_March_2015" title="Category:Articles that may contain original research from March 2015">Articles that may contain original research from March 2015</a></li><li><a href="/wiki/Category:All_articles_that_may_contain_original_research" title="Category:All articles that may contain original research">All articles that may contain original research</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 14 February 2025, at 17:55<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. 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