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</ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Binary number</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 97 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-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 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <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 – Arabic" lang="ar" hreflang="ar" data-title="نظام عد 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/Sistema_binariu" title="Sistema binariu – Asturian" lang="ast" hreflang="ast" data-title="Sistema binariu" data-language-autonym="Asturianu" data-language-local-name="Asturian" 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 – Azerbaijani" lang="az" hreflang="az" data-title="İkili say sistemi" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" 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 – South Azerbaijani" lang="azb" hreflang="azb" data-title="ایکی‌لی سایی سیستمی" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" 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 – Bangla" lang="bn" hreflang="bn" data-title="দ্বিমিক সংখ্যাপদ্ধতি" data-language-autonym="বাংলা" data-language-local-name="Bangla" 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 – Bashkir" lang="ba" hreflang="ba" data-title="Икеле иҫәпләү системаһы" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" 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 – Belarusian" lang="be" hreflang="be" data-title="Двайковая сістэма злічэння" 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%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 – Bulgarian" lang="bg" hreflang="bg" data-title="Двоична бройна система" data-language-autonym="Български" data-language-local-name="Bulgarian" 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 – Bavarian" lang="bar" hreflang="bar" data-title="Binärzoihn" data-language-autonym="Boarisch" data-language-local-name="Bavarian" 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 – Bosnian" lang="bs" hreflang="bs" data-title="Binarni brojevni sistem" data-language-autonym="Bosanski" data-language-local-name="Bosnian" 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 – Breton" lang="br" hreflang="br" data-title="Enbonegañ daouredel" data-language-autonym="Brezhoneg" data-language-local-name="Breton" 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 – Catalan" lang="ca" hreflang="ca" data-title="Sistema binari" data-language-autonym="Català" data-language-local-name="Catalan" 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 – Chuvash" lang="cv" hreflang="cv" data-title="Иккĕлле шут тытăмĕ" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" 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 – Czech" lang="cs" hreflang="cs" data-title="Dvojková soustava" data-language-autonym="Čeština" data-language-local-name="Czech" 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 – Welsh" lang="cy" hreflang="cy" data-title="Rhif deuaidd" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</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 – Danish" lang="da" hreflang="da" data-title="Binære talsystem" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Dualsystem" title="Dualsystem – German" lang="de" hreflang="de" data-title="Dualsystem" data-language-autonym="Deutsch" data-language-local-name="German" 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 – Estonian" lang="et" hreflang="et" data-title="Kahendsüsteem" data-language-autonym="Eesti" data-language-local-name="Estonian" 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 – Greek" lang="el" hreflang="el" data-title="Δυαδικό σύστημα" data-language-autonym="Ελληνικά" data-language-local-name="Greek" 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 – English" lang="en" hreflang="en" data-title="Binary number" data-language-autonym="English" data-language-local-name="English" 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 – Spanish" lang="es" hreflang="es" data-title="Sistema 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_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 – Basque" lang="eu" hreflang="eu" data-title="Zenbaki-sistema bitar" data-language-autonym="Euskara" data-language-local-name="Basque" 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 – Persian" lang="fa" hreflang="fa" data-title="رقم 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/Syst%C3%A8me_binaire" title="Système binaire – French" lang="fr" hreflang="fr" data-title="Système binaire" data-language-autonym="Français" data-language-local-name="French" 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 – Friulian" lang="fur" hreflang="fur" data-title="Sisteme binari" data-language-autonym="Furlan" data-language-local-name="Friulian" 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 – Irish" lang="ga" hreflang="ga" data-title="Uimhir dhénártha" data-language-autonym="Gaeilge" data-language-local-name="Irish" 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 – Galician" lang="gl" hreflang="gl" data-title="Código binario" data-language-autonym="Galego" data-language-local-name="Galician" 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 – Korean" lang="ko" hreflang="ko" data-title="이진법" data-language-autonym="한국어" data-language-local-name="Korean" 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 – Armenian" lang="hy" hreflang="hy" data-title="Հաշվարկման երկուական համակարգ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" 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 – Croatian" lang="hr" hreflang="hr" data-title="Binarni brojevni sustav" data-language-autonym="Hrvatski" data-language-local-name="Croatian" 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 – Indonesian" lang="id" hreflang="id" data-title="Sistem bilangan biner" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" 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-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Tv%C3%ADundakerfi" title="Tvíundakerfi – Icelandic" lang="is" hreflang="is" data-title="Tvíundakerfi" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</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 – Italian" lang="it" hreflang="it" data-title="Sistema numerico binario" data-language-autonym="Italiano" data-language-local-name="Italian" 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 – Hebrew" lang="he" hreflang="he" data-title="בסיס בינארי" data-language-autonym="עברית" data-language-local-name="Hebrew" 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 – Javanese" lang="jv" hreflang="jv" data-title="Sistem wilangan binèr" data-language-autonym="Jawa" data-language-local-name="Javanese" 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 – Georgian" lang="ka" hreflang="ka" data-title="თვლის ორობითი სისტემა" data-language-autonym="ქართული" data-language-local-name="Georgian" 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 – Kazakh" lang="kk" hreflang="kk" data-title="Екілік санау жүйесі" data-language-autonym="Қазақша" data-language-local-name="Kazakh" 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 – Haitian Creole" lang="ht" hreflang="ht" data-title="Sistèm binè" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-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 – Kyrgyz" lang="ky" hreflang="ky" data-title="Экилик эсептөө тутуму" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" 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 – Latvian" lang="lv" hreflang="lv" data-title="Binārā skaitīšanas sistēma" data-language-autonym="Latviešu" data-language-local-name="Latvian" 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 – Lithuanian" lang="lt" hreflang="lt" data-title="Dvejetainė skaičiavimo sistema" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" 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 – Lombard" lang="lmo" hreflang="lmo" data-title="Sistema binari" data-language-autonym="Lombard" data-language-local-name="Lombard" 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 – Hungarian" lang="hu" hreflang="hu" data-title="Kettes számrendszer" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><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 – Macedonian" lang="mk" hreflang="mk" data-title="Двоичен броен систем" 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%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 – Malay" lang="ms" hreflang="ms" data-title="Sistem angka 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-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/Sistema_binairo_(matem%C3%A1tica)" title="Sistema binairo (matemática) – Mirandese" lang="mwl" hreflang="mwl" data-title="Sistema binairo (matemática)" data-language-autonym="Mirandés" data-language-local-name="Mirandese" 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 – Mongolian" lang="mn" hreflang="mn" data-title="Хоёртын тооллын систем" data-language-autonym="Монгол" data-language-local-name="Mongolian" 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 – Dutch" lang="nl" hreflang="nl" data-title="Binair talstelsel" data-language-autonym="Nederlands" data-language-local-name="Dutch" 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 – Japanese" lang="ja" hreflang="ja" data-title="二進法" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Bin%C3%A6rt_tallsystem" title="Binært tallsystem – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Binært tallsystem" 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/Totalssystemet" title="Totalssystemet – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Totalssystemet" 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%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 – Eastern Mari" lang="mhr" hreflang="mhr" data-title="Кокытан чотрадам системе" 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-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 – Uzbek" lang="uz" hreflang="uz" data-title="Ikkilik sanoq sistemasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-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 – Punjabi" lang="pa" hreflang="pa" data-title="ਬਾਇਨਰੀ ਸੰਖਿਆ ਪ੍ਰਣਾਲੀ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" 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 – Polish" lang="pl" hreflang="pl" data-title="Dwójkowy system liczbowy" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Sistema_de_numera%C3%A7%C3%A3o_bin%C3%A1rio" title="Sistema de numeração binário – Portuguese" lang="pt" hreflang="pt" data-title="Sistema de numeração binário" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Sistem_binar" title="Sistem binar – Romanian" lang="ro" hreflang="ro" data-title="Sistem binar" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%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 – Russian" lang="ru" hreflang="ru" data-title="Двоичная система счисления" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-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 – Northern Sotho" lang="nso" hreflang="nso" data-title="Binary" 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-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Sistemi_binar" title="Sistemi binar – Albanian" lang="sq" hreflang="sq" data-title="Sistemi binar" data-language-autonym="Shqip" data-language-local-name="Albanian" 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 – Sinhala" lang="si" hreflang="si" data-title="ද්විමය සංඛ්‍යා පද්ධතිය" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</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 – Slovak" lang="sk" hreflang="sk" data-title="Dvojková číselná sústava" data-language-autonym="Slovenčina" data-language-local-name="Slovak" 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 – Slovenian" lang="sl" hreflang="sl" data-title="Dvojiški številski sistem" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" 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 – Serbian" lang="sr" hreflang="sr" data-title="Бинарни систем" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Binarni_sistem" title="Binarni sistem – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Binarni sistem" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" 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 – Sundanese" lang="su" hreflang="su" data-title="Sistim panomeran binér" data-language-autonym="Sunda" data-language-local-name="Sundanese" 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 – Finnish" lang="fi" hreflang="fi" data-title="Binäärijärjestelmä" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</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 – Swedish" lang="sv" hreflang="sv" data-title="Binära talsystemet" data-language-autonym="Svenska" data-language-local-name="Swedish" 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data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Simple English Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p>The <b>binary numeral system</b> is a way to <a href="/wiki/Write" class="mw-redirect" title="Write">write</a> <a href="/wiki/Number" title="Number">numbers</a> using only two <a href="/wiki/Digit" class="mw-redirect" title="Digit">digits</a>: 0 and 1. These are used in <a href="/wiki/Computer" title="Computer">computers</a> as a series of "off" and "on" switches. In binary, each digit's <a href="/wiki/Place_value" title="Place value">place value</a> is twice as much as that of the next digit to the right (since each digit holds two values). In <a href="/wiki/Decimal_numeral_system" class="mw-redirect" title="Decimal numeral system">decimal</a> - the system that humans normally use - each digit holds ten values, and the place value increases by a power of ten (ones, tens, hundreds, etc.). The place value of the rightmost digit, in either case, is 1. </p> <table border="1" style="float:right; margin-left:10px"> <tbody><tr> <td>0</td> <td><b>0000</b></td> <td>0+0+0+0 </td></tr> <tr> <td>1</td> <td><b>0001</b></td> <td>0+0+0+1 </td></tr> <tr> <td>2</td> <td><b>0010</b></td> <td>0+0+2+0 </td></tr> <tr> <td>3</td> <td><b>0011</b></td> <td>0+0+2+1 </td></tr> <tr> <td>4</td> <td><b>00100</b></td> <td>0+0+4+0+0 </td></tr> <tr> <td>5</td> <td><b>00101</b></td> <td>0+0+4+0+1 </td></tr> <tr> <td>6</td> <td><b>00110</b></td> <td>0+0+4+2+0 </td></tr> <tr> <td>7</td> <td><b>00111</b></td> <td>0+0+4+2+1 </td></tr> <tr> <td>8</td> <td><b>01000</b></td> <td>0+8+0+0+0 </td></tr> <tr> <td>9</td> <td><b>01001</b></td> <td>0+8+0+0+1 </td></tr> <tr> <td>10</td> <td><b>01010</b></td> <td>0+8+0+2+0 </td></tr> <tr> <td>11</td> <td><b>01011</b></td> <td>0+8+0+2+1 </td></tr> <tr> <td>12</td> <td><b>01100</b></td> <td>0+8+4+0+0 </td></tr> <tr> <td>13</td> <td><b>01101</b></td> <td>0+8+4+0+1 </td></tr> <tr> <td>14</td> <td><b>01110</b></td> <td>0+8+4+2+0 </td></tr> <tr> <td>15</td> <td><b>01111</b></td> <td>0+8+4+2+1 </td></tr> <tr> <td>16</td> <td><b>10000</b></td> <td>16+0+0+0+0 </td></tr> <tr> <td>17</td> <td><b>10001</b></td> <td>16+0+0+0+1 </td></tr> <tr> <td>18</td> <td><b>10010</b></td> <td>16+0+0+2+0 </td></tr> <tr> <td>19</td> <td><b>10011</b></td> <td>16+0+0+2+1 </td></tr> <tr> <td>20</td> <td><b>10100</b></td> <td>16+0+4+0+0 </td></tr> <tr> <td>21</td> <td><b>10101</b></td> <td>16+0+4+0+1 </td></tr> <tr> <td>22</td> <td><b>10110</b></td> <td>16+0+4+2+0 </td></tr> <tr> <td>23</td> <td><b>10111</b></td> <td>16+0+4+2+1 </td></tr> <tr> <td>24</td> <td><b>11000</b></td> <td>16+8+0+0+0 </td></tr> <tr> <td>25</td> <td><b>11001</b></td> <td>16+8+0+0+1 </td></tr> <tr> <td>26</td> <td><b>11010</b></td> <td>16+8+0+2+0 </td></tr> <tr> <td>27</td> <td><b>11011</b></td> <td>16+8+0+2+1 </td></tr> <tr> <td>28</td> <td><b>11100</b></td> <td>16+8+4+0+0 </td></tr> <tr> <td>29</td> <td><b>11101</b></td> <td>16+8+4+0+1 </td></tr> <tr> <td>30</td> <td><b>11110</b></td> <td>16+8+4+2+0 </td></tr> </tbody></table> <p>Example: 10110011 </p> <ul><li>The place value of the last 1 (rightmost position) is 1.</li> <li>The place value of the 1 before that is 2.</li> <li>The place value of the 0 before that is 4.</li> <li>The place value of the 0 before that is 8.</li> <li>The place value of the 1 before that is 16.</li> <li>The place value of the 1 before that is 32.</li> <li>The place value of the 0 before that is 64.</li> <li>The place value of the 1 before that is 128.</li></ul> <p>Adding together all the place values that have 1s, it would be 1+2+16+32+128 = 179. For convenience, binary digits (bits, for short) are usually grouped together in two groups of 4 bits. This is 8 bits, or a <a href="/wiki/Byte" title="Byte">byte</a>, and is written using the <a href="/wiki/Hexadecimal_numeral_system" class="mw-redirect" title="Hexadecimal numeral system">hexadecimal numeral system</a>. This would be shown as 1011 0011 = B3. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Binary_arithmetic">Binary arithmetic</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binary_number&veaction=edit&section=1" title="Change section: Binary arithmetic" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Binary_number&action=edit&section=1" title="Edit section's source code: Binary arithmetic"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Arithmetic" title="Arithmetic">Arithmetic</a> is a way of adding together two or more <a href="/wiki/Binary" title="Binary">binary</a> numbers. There are four <a href="/wiki/Rules" class="mw-redirect mw-disambig" title="Rules">rules</a> in binary arithmetic. They are: </p><p><i>0</i> + <i>0</i> = <i>0</i> <br /><i>1</i> + <i>0</i> = <i>1</i> <br /><i>1</i> + <i>1</i> = <i>10</i> (2) <br /><i>1</i> + <i>1</i> + <i>1</i> = <i>11</i> (3) </p><p>This is because in binary there are only two digits; 0 and 1. Because of this, the number two and three have to be represented in some other way. This is how the binary value for three is calculated: </p> <table class="wikitable"> <tbody><tr> <th>Column </th> <th>Decimal Value </th> <th>Binary </th></tr> <tr> <td>1 </td> <td>2 </td> <td>1 </td></tr> <tr> <td>2 </td> <td>1 </td> <td>1 </td></tr></tbody></table> <p>This shows that the binary value would be <i>11</i>. </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binary_number&veaction=edit&section=2" title="Change section: History" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Binary_number&action=edit&section=2" title="Edit section's source code: History"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Leibniz_binary_system_1697.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Leibniz_binary_system_1697.jpg/220px-Leibniz_binary_system_1697.jpg" decoding="async" width="220" height="178" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Leibniz_binary_system_1697.jpg/330px-Leibniz_binary_system_1697.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Leibniz_binary_system_1697.jpg/440px-Leibniz_binary_system_1697.jpg 2x" data-file-width="1923" data-file-height="1554" /></a><figcaption>The binary numeral system, in a <a href="/wiki/Manuscript" title="Manuscript">manuscript</a> by <a href="/wiki/Gottfried_Wilhelm_Leibniz" class="mw-redirect" title="Gottfried Wilhelm Leibniz">Gottfried Wilhelm Leibniz</a>, 1697</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Leibniz_binary_system_1703.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Leibniz_binary_system_1703.png/220px-Leibniz_binary_system_1703.png" decoding="async" width="220" height="296" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Leibniz_binary_system_1703.png/330px-Leibniz_binary_system_1703.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Leibniz_binary_system_1703.png/440px-Leibniz_binary_system_1703.png 2x" data-file-width="727" data-file-height="979" /></a><figcaption>A page from <i>„Explication de l’Arithmétique Binaire“</i>, by Leibniz, 1703</figcaption></figure> <p>Binary is a numbering system that is a series of 1s and 0s meaning (to the computers) on and off. It is <a href="/wiki/Base_(mathematics)" title="Base (mathematics)">base</a> two and our number system (<a href="/wiki/Decimal" title="Decimal">decimal</a>) is base ten, where ten numerals are used rather than two. </p><p>In 1817 John Leslie (a Scottish mathematician) suggested that primitive societies may have evolved counting with objects (like pebbles) before they had even words to describe the total number of objects involved. The next step in the evolution of counting would have been the discovery that this pile of objects could be reduced into two piles of equal measures (leaving either 0 objects left over or just a remainder of 1). This remainder (odd = 1 or even = 0) would then be recorded and one of the piles removed whilst the second pile was then further divided into two sub piles. If you record the remainder left over after the original pile has been divided in two and continue repeating this process; of sub dividing one of the remaining piles into half and then removing one of those piles and continue by subdividing the remaining pile into two piles you will ultimately be left with just either 2 or 3 objects. If you record the remainder left over (odd = 1 or even = 0) at the end of each reduction you will eventually be left with a tally record of 1's and 0's which will be the binary representation of your original pile of objects. So instead of representing your original pile of objects with a repeating number or marks or tokens (which for large numbers could be quite long) you have reduced your pile of objects into more compact binary number. If you need to recover the original number of objects from this summarised binary number it is easy enough to do; by simply starting with the first tally mark and then doubling it and adding one if the next binary number contains a 1 and then continuing the process until the end of the binary number is reached. So binary counting may be both the oldest and the most modern method of counting. </p><p>Binary was invented by many people but the modern binary number system is credited to <a href="/wiki/Gottfried_Leibniz" title="Gottfried Leibniz">Gottfried Leibniz</a> in 1679, a <a href="/wiki/Germany" title="Germany">German</a> <a href="/wiki/Mathematician" title="Mathematician">mathematician</a>. Binary has been used in nearly everything <a href="/wiki/Electronics" title="Electronics">electronic</a>; from <a href="/wiki/Calculator" title="Calculator">calculators</a> to <a href="/wiki/Supercomputer" title="Supercomputer">supercomputers</a>. <a href="/wiki/Machine_code" title="Machine code">Machine code</a> is binary digits. </p> <div class="mw-heading mw-heading2"><h2 id="Related_pages">Related pages</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binary_number&veaction=edit&section=3" title="Change section: Related pages" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Binary_number&action=edit&section=3" title="Edit section's source code: Related pages"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Octal" title="Octal">Octal</a></li> <li><a href="/wiki/Hexadecimal" title="Hexadecimal">Hexadecimal</a></li> <li><a href="/wiki/Negative_binary_numbers" class="mw-redirect" title="Negative binary numbers">Negative binary numbers</a></li> <li><a href="/wiki/Decimal_numbers_in_binary" class="mw-redirect" title="Decimal numbers in binary">Decimal numbers in binary</a></li> <li><a href="/wiki/Truth_value" title="Truth value">Truth value</a></li></ul> <div class="boilerplate metadata plainlinks" id="stub"><span typeof="mw:File"><a href="/wiki/File:Xy_icon.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Xy_icon.svg/30px-Xy_icon.svg.png" decoding="async" width="30" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Xy_icon.svg/45px-Xy_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/Xy_icon.svg/60px-Xy_icon.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> <i>This <a href="/wiki/Wikipedia:Stub" title="Wikipedia:Stub">short article</a> about <a href="/wiki/Category:Math_stubs" title="Category:Math stubs">mathematics</a> can be made longer. You can help Wikipedia by <a class="external text" href="https://simple.wikipedia.org/w/index.php?title=Binary_number&action=edit">adding to it</a></i>.</div> <p><br /> </p> <div class="mw-heading mw-heading2"><h2 id="Translation">Translation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Binary_number&veaction=edit&section=4" title="Change section: Translation" class="mw-editsection-visualeditor"><span>change</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Binary_number&action=edit&section=4" title="Edit section's source code: Translation"><span>change source</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>You can translate binary to normal numbers using </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 10110=2^{4}+2^{2}+2^{1}=22}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>10110</mn> <mo>=</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>+</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> <mo>=</mo> <mn>22</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 10110=2^{4}+2^{2}+2^{1}=22}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9817fe67015ed3c12e4795d99922d1e7535b6bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:26.665ex; height:2.843ex;" alt="{\displaystyle 10110=2^{4}+2^{2}+2^{1}=22}"></span> </p>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://simple.wikipedia.org/w/index.php?title=Binary_number&oldid=9742877">https://simple.wikipedia.org/w/index.php?title=Binary_number&oldid=9742877</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Special:Categories" title="Special:Categories">Category</a>: <ul><li><a href="/wiki/Category:Numbering_systems" title="Category:Numbering systems">Numbering systems</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden category: <ul><li><a href="/wiki/Category:Math_stubs" title="Category:Math stubs">Math stubs</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 changed on 1 September 2024, at 17:07.</li> <li id="footer-info-copyright">Text is available under the <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike License</a> and the <a href="/wiki/Wikipedia:Text_of_the_GNU_Free_Documentation_License" title="Wikipedia:Text of the GNU Free Documentation License">GFDL</a>; additional terms may apply. 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