{"id":66,"date":"2023-06-11T19:18:07","date_gmt":"2023-06-11T19:18:07","guid":{"rendered":"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/?page_id=66"},"modified":"2023-09-01T16:34:39","modified_gmt":"2023-09-01T16:34:39","slug":"binary-numbers","status":"publish","type":"page","link":"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/binary-numbers\/","title":{"rendered":"Binary Numbers"},"content":{"rendered":"<div class=\"responsive-tabs\">\n<h2 class=\"tabtitle\">Introduction<\/h2>\n<div class=\"tabcontent\">\n\n<h3>What is binary?<\/h3>\n<p>Binary is a base 2 number system, meaning that all numbers and other data can only represented using ones and zeros. All modern computer systems store data and programs in binary.<\/p>\n<div id=\"attachment_2161\" style=\"width: 539px\" class=\"wp-caption alignnone\"><a href=\"https:\/\/learnlearn.uk\/alevelcs\/wp-content\/uploads\/sites\/20\/2020\/09\/binary.png\"><img aria-describedby=\"caption-attachment-2161\" decoding=\"async\" loading=\"lazy\" class=\"size-full wp-image-2161\" src=\"https:\/\/learnlearn.uk\/alevelcs\/wp-content\/uploads\/sites\/20\/2020\/09\/binary.png\" alt=\"\" width=\"529\" height=\"352\" \/><\/a><p id=\"caption-attachment-2161\" class=\"wp-caption-text\">This stream of ones and zeros could represent any form of data &#8211; text, graphics, video, sound<\/p><\/div>\n\n<\/div><h2 class=\"tabtitle\">Why binary?<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Why do computers use binary?<\/h3>\n<p>There are a number of advantages to using binary in computer systems:<\/p>\n<p><strong>Key Advantages<\/strong><\/p>\n<ul>\n<li>Binary data can be transmitted easily and reliably.<\/li>\n<li>Binary data can be stored and read very easily and reliably.<\/li>\n<li>Computers use circuits that can only be on one of 2 states &#8211; on or off, these work very well with binary calculations.<\/li>\n<li>The input voltage in to computers is not very stable, so only a system that use voltage\/no voltage would be reliable.<\/li>\n<\/ul>\n<p>Take a look at the following video for more detailed information.<\/p>\n<div class=\"nv-iframe-embed\">\n<div class=\"container-lazyload preview-lazyload container-youtube js-lazyload--not-loaded\"><a href=\"https:\/\/www.youtube.com\/watch?v=k-5jpns0uTA\" class=\"lazy-load-youtube preview-lazyload preview-youtube\" data-video-title=\"Why do computers use binary?\" title=\"Play video &quot;Why do computers use binary?&quot;\">https:\/\/www.youtube.com\/watch?v=k-5jpns0uTA<\/a><noscript>Video can&#8217;t be loaded because JavaScript is disabled: <a href=\"https:\/\/www.youtube.com\/watch?v=k-5jpns0uTA\" title=\"Why do computers use binary?\">Why do computers use binary? (https:\/\/www.youtube.com\/watch?v=k-5jpns0uTA)<\/a><\/noscript><\/div>\n<\/div>\n<p><em>YouTube blocked at school? <a href=\"https:\/\/drive.google.com\/file\/d\/1Qgm0NwsVEJMnFllOT4lH8qO2160KnhBv\/view?usp=sharing\">Watch the Google Drive version instead.<\/a><\/em><\/p>\n<h3><\/h3>\n\n<\/div><h2 class=\"tabtitle\">Bits, Bytes, Nibbles<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Bits, Bytes &amp; Nibbles<\/h3>\n<p><strong>Bit \u00a0 \u2013 e.g. 0<\/strong><\/p>\n<p>Each individual 1 or 0 is known as a\u00a0<strong>bit<\/strong>.<\/p>\n<p>Here are three bits \u2013 110<\/p>\n<p><strong>Byte \u2013 e.g. 11001100<\/strong><\/p>\n<p>Each group of 8 bits is known as a\u00a0<strong>Byte<\/strong><\/p>\n<p>Here\u00a0is a<strong>\u00a0stream<\/strong>\u00a0of Bytes:<\/p>\n<p>01010011 01101011 01111001 01110010 01101001 01101101 00100000 01101001 01110011 00100000 01100001 01110111 01100101 01110011 01101111 01101101 01100101 00100001<\/p>\n<p><strong>Nibble \u2013 e.g. 1111<\/strong><\/p>\n<p>A nibble is\u00a0<strong>4 bits<\/strong>, or half a<strong>\u00a0Byte<\/strong>.<\/p>\n<p>Here is a nibble \u2013 1101<\/p>\n\n<\/div><h2 class=\"tabtitle\">Denary to Binary<\/h2>\n<div class=\"tabcontent\">\n\n<h3><strong>Decimal to Binary Conversion<\/strong><\/h3>\n<p>Let&#8217;s suppose we are trying to find the binary for the <strong>decimal number 75.<\/strong><\/p>\n<h3>Step 1 &#8211; Write the 128 to 1 numbers<\/h3>\n<p>Starting on the right hand side, write down the numbers 1, 2,4,8 etc, doubling each time until you reach 128.<\/p>\n<p><strong>Remember smallest number at the right hand side!!!<\/strong><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65\" src=\"https:\/\/learnlearn.uk\/binary\/wp-content\/uploads\/sites\/11\/2017\/01\/step-1.png\" alt=\"step-1\" width=\"967\" height=\"91\" \/><\/p>\n<p>&nbsp;<\/p>\n<h3>Step 2 &#8211; Cross out the unused numbers<\/h3>\n<p>Keeping only the numbers that you need to add up to your decimal number, cross out all other numbers.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-66\" src=\"https:\/\/learnlearn.uk\/binary\/wp-content\/uploads\/sites\/11\/2017\/01\/step2.png\" alt=\"step2\" width=\"928\" height=\"172\" \/><\/p>\n<p>&nbsp;<\/p>\n<h3>Step 3 &#8211; Write the ones or zeros<\/h3>\n<p>Under each number write a 1 if there is a number and a zero if you crossed out the number. Put the numbers all together and you have your binary number!<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-67\" src=\"https:\/\/learnlearn.uk\/binary\/wp-content\/uploads\/sites\/11\/2017\/01\/step-3.png\" alt=\"step-3\" width=\"962\" height=\"252\" \/><\/p>\n\n<\/div><h2 class=\"tabtitle\">Binary to Denary<\/h2>\n<div class=\"tabcontent\">\n\n<h3><strong>Binary to decimal Conversion<\/strong><\/h3>\n<p>Let&#8217;s suppose we are trying to find the\u00a0decimal for the <strong>binary number 01101011.<\/strong><\/p>\n<h3>Step 1 &#8211; Write the 128 to 1 numbers<\/h3>\n<p>Starting on the right hand side, write down the numbers 1, 2,4,8 etc, doubling each time until you reach 128.<\/p>\n<p><strong>Remember smallest number at the right hand side!!!<\/strong><\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-65\" src=\"https:\/\/learnlearn.uk\/binary\/wp-content\/uploads\/sites\/11\/2017\/01\/step-1.png\" alt=\"step-1\" width=\"967\" height=\"91\" \/><\/p>\n<h3>Step 2 &#8211; Write the ones and zeros below the numbers<\/h3>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-70\" src=\"https:\/\/learnlearn.uk\/binary\/wp-content\/uploads\/sites\/11\/2017\/01\/binarytodecstep1.png\" alt=\"binarytodecstep2\" width=\"949\" height=\"124\" \/><\/p>\n<h3>Step 3 &#8211; Add up all the numbers with 1s below them to find your decimal number<\/h3>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-71\" src=\"https:\/\/learnlearn.uk\/binary\/wp-content\/uploads\/sites\/11\/2017\/01\/bintodecstep3.png\" alt=\"bintodecstep3\" width=\"958\" height=\"237\" \/><\/p>\n\n<\/div><h2 class=\"tabtitle\">Practice<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Practice<\/h3>\n<p>Practice converting denary to binary with the great little game.<\/p>\n<p><iframe loading=\"lazy\" src=\"https:\/\/games.penjee.com\/binary-bonanza\/game.php\" width=\"900\" height=\"600\" frameborder=\"no\" scrolling=\"no\" data-mce-fragment=\"1\"><\/iframe><\/p>\n\n<\/div><h2 class=\"tabtitle\">Resources<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Practice<\/h3>\n<p><a href=\"https:\/\/www.worksheetworks.com\/math\/numbers\/systems.html\">Conversion worksheets generator<\/a><\/p>\n<p><a href=\"https:\/\/games.penjee.com\/binary-bonanza\/game.php\">Binary Conversion Fun Game<\/a><\/p>\n<p><a href=\"https:\/\/docs.google.com\/document\/d\/1LycktRhGqVuvCTt4wAIfvo3v3qszzJtIeT3qpsXArXs\/edit\">Binary Worksheet<\/a><\/p>\n<p><a href=\"https:\/\/create.kahoot.it\/share\/b2c7696f-8f61-44ae-90ec-0480f4395313\">Binary Kahoot<\/a><\/p>\n<p><a href=\"https:\/\/docs.google.com\/presentation\/d\/1Xrpp76_zuCQf3QfO3GnRe4QTdtIe3OwpA7C116bbkl8\/edit?usp=sharing\">Why do computers use binary? &#8211; Teacher Presentation<\/a><\/p>\n<p><strong>Exam Questions<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>What is binary? Binary is a base 2 number system, meaning that all numbers and other data can only represented using ones and zeros. All modern computer systems store data and programs in binary. Why do computers use binary? There are a number of advantages to using binary in computer systems: Key Advantages Binary data&hellip;&nbsp;<a href=\"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/binary-numbers\/\" class=\"\" rel=\"bookmark\">Read More &raquo;<span class=\"screen-reader-text\">Binary Numbers<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"neve_meta_sidebar":"","neve_meta_container":"","neve_meta_enable_content_width":"off","neve_meta_content_width":100,"neve_meta_title_alignment":"","neve_meta_author_avatar":"","neve_post_elements_order":"","neve_meta_disable_header":"","neve_meta_disable_footer":"","neve_meta_disable_title":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.6 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Binary Numbers - Edexcel iGCSE Computer Science<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/binary-numbers\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Binary Numbers - Edexcel iGCSE Computer Science\" \/>\n<meta property=\"og:description\" content=\"What is binary? Binary is a base 2 number system, meaning that all numbers and other data can only represented using ones and zeros. All modern computer systems store data and programs in binary. Why do computers use binary? There are a number of advantages to using binary in computer systems: Key Advantages Binary data&hellip;&nbsp;Read More &raquo;Binary Numbers\" \/>\n<meta property=\"og:url\" content=\"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/binary-numbers\/\" \/>\n<meta property=\"og:site_name\" content=\"Edexcel iGCSE Computer Science\" \/>\n<meta property=\"article:modified_time\" content=\"2023-09-01T16:34:39+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/learnlearn.uk\/alevelcs\/wp-content\/uploads\/sites\/20\/2020\/09\/binary.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Estimated reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"4 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/binary-numbers\/\",\"url\":\"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/binary-numbers\/\",\"name\":\"Binary Numbers - Edexcel iGCSE Computer Science\",\"isPartOf\":{\"@id\":\"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/#website\"},\"datePublished\":\"2023-06-11T19:18:07+00:00\",\"dateModified\":\"2023-09-01T16:34:39+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/binary-numbers\/#breadcrumb\"},\"inLanguage\":\"en-GB\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/binary-numbers\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/binary-numbers\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Binary Numbers\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/#website\",\"url\":\"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/\",\"name\":\"Edexcel iGCSE Computer Science\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-GB\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Binary Numbers - Edexcel iGCSE Computer Science","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/binary-numbers\/","og_locale":"en_GB","og_type":"article","og_title":"Binary Numbers - Edexcel iGCSE Computer Science","og_description":"What is binary? Binary is a base 2 number system, meaning that all numbers and other data can only represented using ones and zeros. All modern computer systems store data and programs in binary. Why do computers use binary? There are a number of advantages to using binary in computer systems: Key Advantages Binary data&hellip;&nbsp;Read More &raquo;Binary Numbers","og_url":"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/binary-numbers\/","og_site_name":"Edexcel iGCSE Computer Science","article_modified_time":"2023-09-01T16:34:39+00:00","og_image":[{"url":"https:\/\/learnlearn.uk\/alevelcs\/wp-content\/uploads\/sites\/20\/2020\/09\/binary.png"}],"twitter_card":"summary_large_image","twitter_misc":{"Estimated reading time":"4 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/binary-numbers\/","url":"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/binary-numbers\/","name":"Binary Numbers - Edexcel iGCSE Computer Science","isPartOf":{"@id":"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/#website"},"datePublished":"2023-06-11T19:18:07+00:00","dateModified":"2023-09-01T16:34:39+00:00","breadcrumb":{"@id":"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/binary-numbers\/#breadcrumb"},"inLanguage":"en-GB","potentialAction":[{"@type":"ReadAction","target":["https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/binary-numbers\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/binary-numbers\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/"},{"@type":"ListItem","position":2,"name":"Binary Numbers"}]},{"@type":"WebSite","@id":"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/#website","url":"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/","name":"Edexcel iGCSE Computer Science","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-GB"}]}},"rttpg_featured_image_url":null,"rttpg_author":{"display_name":"learnlearnadmin","author_link":"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/author\/learnlearnadmin\/"},"rttpg_comment":0,"rttpg_category":null,"rttpg_excerpt":"What is binary? Binary is a base 2 number system, meaning that all numbers and other data can only represented using ones and zeros. All modern computer systems store data and programs in binary. Why do computers use binary? There are a number of advantages to using binary in computer systems: Key Advantages Binary data&hellip;&nbsp;Read&hellip;","_links":{"self":[{"href":"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/wp-json\/wp\/v2\/pages\/66"}],"collection":[{"href":"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/wp-json\/wp\/v2\/comments?post=66"}],"version-history":[{"count":2,"href":"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/wp-json\/wp\/v2\/pages\/66\/revisions"}],"predecessor-version":[{"id":455,"href":"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/wp-json\/wp\/v2\/pages\/66\/revisions\/455"}],"wp:attachment":[{"href":"https:\/\/learnlearn.uk\/edexcel-igcse-computer-science\/wp-json\/wp\/v2\/media?parent=66"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}