{"id":858,"date":"2020-09-10T01:18:26","date_gmt":"2020-09-10T01:18:26","guid":{"rendered":"http:\/\/learnlearn.uk\/alevelcs\/?page_id=858"},"modified":"2021-04-27T07:51:00","modified_gmt":"2021-04-27T07:51:00","slug":"hexadecimal-number-system","status":"publish","type":"page","link":"https:\/\/learnlearn.uk\/alevelcs\/hexadecimal-number-system\/","title":{"rendered":"Hexadecimal Number System"},"content":{"rendered":"<div class=\"responsive-tabs\">\n<h2 class=\"tabtitle\">Intro<\/h2>\n<div class=\"tabcontent\">\n\n<h3>What is Hexadecimal?<\/h3>\n<p>In the normal human counting system we use a base 10 number system, meaning that the each extra digit increases in powers of 10 each time:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-951 size-full\" src=\"https:\/\/learnlearn.uk\/gcsecs\/wp-content\/uploads\/sites\/8\/2018\/01\/denary-example.png?_t=1598666746\" alt=\"\" width=\"818\" height=\"190\" \/><\/p>\n<p>Hexadecimal is a Base 16 number system, meaning that increases in powers of 16, with each digit being one of 16 different combinations.<\/p>\n<p>The hexadecimal number consists of:<\/p>\n<ul>\n<li>0 = 0<\/li>\n<li>1 = 1<\/li>\n<li>2 =2<\/li>\n<li>3 = 3<\/li>\n<li>4 = 4<\/li>\n<li>5 = 5<\/li>\n<li>6 = 6<\/li>\n<li>7 =7<\/li>\n<li>8 = 8<\/li>\n<li>9 = 9<\/li>\n<li>A = 10<\/li>\n<li>B = 11<\/li>\n<li>C = 12<\/li>\n<li>D = 13<\/li>\n<li>E = 14<\/li>\n<li>F = 15<\/li>\n<\/ul>\n<p><strong>Why do we use a to f instead of 11 to 15?<\/strong><\/p>\n<p>We can&#8217;t use 11 to 15 because we wouldn&#8217;t know what number it represented. The Digits <strong>13\u00a0<\/strong> could be 13 or it could be 19\u00a0 (1 * 16 + 3), this is because denary numbers greater than 9 use 2 digits instead of one digit.<\/p>\n<p>&nbsp;<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-952\" src=\"https:\/\/learnlearn.uk\/gcsecs\/wp-content\/uploads\/sites\/8\/2018\/01\/hex-example.png\" alt=\"\" width=\"682\" height=\"226\" \/><\/p>\n<h3>Why do we use it hexadecimal?<\/h3>\n<p>Given how confusing hexadecimal is you might be forgiven for wondering why we bother using it at all. Well it has a couple of advantages:<\/p>\n<p>Large numbers can be represented in a smaller number of digits, making them easier and more accurately read by humans.<\/p>\n<p>Binary is very difficult for humans to read (especially larger numbers) but computers work in binary, so any usage where you need to be able to inspect and edit the binary directly (such as in machine code\/ assembly language) humans can work in hexadecimal, which is close to the binary representation, but easier for us to read.<\/p>\n<p>The reason Hexadecimal works so well with binary is because of the similarity between the number systems.<\/p>\n<p>binary base 2 &#8211;&gt; 2 to the power of 4 is 16,\u00a0 so ever 4 binary digits are equal to one hexadecimal digit. This makes conversion really easy!!!!<\/p>\n\n<\/div><h2 class=\"tabtitle\">Binary &gt; Hex<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Binary to Hexadecimal Conversion<\/h3>\n<p>&nbsp;<\/p>\n<h3>Hexadecimal to Binary Conversion<\/h3>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n\n<\/div><h2 class=\"tabtitle\">Denary &gt; Hex<\/h2>\n<div class=\"tabcontent\">\n\n<p>Denary to Hexadecimal Conversion<\/p>\n<p>&nbsp;<\/p>\n<p>Hexadecimal to Denary Conversion<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n\n<\/div><h2 class=\"tabtitle\">HTML\/CSS<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Hexadecimal in HTML &amp; CSS<\/h3>\n<p><a href=\"https:\/\/www.csfieldguide.org.nz\/en\/interactives\/rgb-mixer\/\">RGB Color Mixer<\/a><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n\n<\/div><h2 class=\"tabtitle\">MAC<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Media Access Control Addresses<\/h3>\n<p><a href=\"https:\/\/learnlearn.uk\/alevelcs\/wp-content\/uploads\/sites\/20\/2020\/09\/cie-hexadecimal-mac-address-and-ipv6-address.png\"><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-907\" src=\"https:\/\/learnlearn.uk\/alevelcs\/wp-content\/uploads\/sites\/20\/2020\/09\/cie-hexadecimal-mac-address-and-ipv6-address.png\" alt=\"\" width=\"813\" height=\"351\" srcset=\"https:\/\/learnlearn.uk\/alevelcs\/wp-content\/uploads\/sites\/20\/2020\/09\/cie-hexadecimal-mac-address-and-ipv6-address.png 813w, https:\/\/learnlearn.uk\/alevelcs\/wp-content\/uploads\/sites\/20\/2020\/09\/cie-hexadecimal-mac-address-and-ipv6-address-300x130.png 300w, https:\/\/learnlearn.uk\/alevelcs\/wp-content\/uploads\/sites\/20\/2020\/09\/cie-hexadecimal-mac-address-and-ipv6-address-768x332.png 768w\" sizes=\"(max-width: 813px) 100vw, 813px\" \/><\/a><\/p>\n\n<\/div><h2 class=\"tabtitle\">Assembly\/MC<\/h2>\n<div class=\"tabcontent\">\n\n<h3>Assembly Language &amp; Machine Code<\/h3>\n<p><a href=\"https:\/\/learnlearn.uk\/alevelcs\/wp-content\/uploads\/sites\/20\/2020\/09\/hexadecimal-machine-code.png\"><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-908\" src=\"https:\/\/learnlearn.uk\/alevelcs\/wp-content\/uploads\/sites\/20\/2020\/09\/hexadecimal-machine-code.png\" alt=\"\" width=\"660\" height=\"301\" srcset=\"https:\/\/learnlearn.uk\/alevelcs\/wp-content\/uploads\/sites\/20\/2020\/09\/hexadecimal-machine-code.png 660w, https:\/\/learnlearn.uk\/alevelcs\/wp-content\/uploads\/sites\/20\/2020\/09\/hexadecimal-machine-code-300x137.png 300w\" sizes=\"(max-width: 660px) 100vw, 660px\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n\n<\/div><h2 class=\"tabtitle\">Resources<\/h2>\n<div class=\"tabcontent\">\n\n<p><a href=\"https:\/\/docs.google.com\/document\/d\/1k0P9dwEFyHvPPpHanMkG_cUW_fYVDUHeprUJO5hUGj8\/edit?usp=sharing\">General Worksheet with exam style questions<\/a><\/p>\n<p><a href=\"https:\/\/www.worksheetworks.com\/math\/numbers\/systems.html\">Worksheet with With explanations<\/a><\/p>\n<p><a href=\"https:\/\/www.saddleback.edu\/faculty\/msierakowski\/binhex_worksheet.pdf\">Test sheet<\/a><\/p>\n<p><a href=\"https:\/\/www.worksheetworks.com\/math\/numbers\/systems.html\">Worksheet generator<\/a><\/p>\n<p><a href=\"http:\/\/www.hexinvaders.com\/\">Hex Invaders Game<\/a><\/p>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>What is Hexadecimal? In the normal human counting system we use a base 10 number system, meaning that the each extra digit increases in powers of 10 each time: Hexadecimal is a Base 16 number system, meaning that increases in powers of 16, with each digit being one of 16 different combinations. The hexadecimal number&hellip;&nbsp;<a href=\"https:\/\/learnlearn.uk\/alevelcs\/hexadecimal-number-system\/\" class=\"\" rel=\"bookmark\">Read More &raquo;<span class=\"screen-reader-text\">Hexadecimal Number System<\/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":"on","neve_meta_content_width":77,"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>Hexadecimal Number System - A Level 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\/alevelcs\/hexadecimal-number-system\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Hexadecimal Number System - A Level Computer Science\" \/>\n<meta property=\"og:description\" content=\"What is Hexadecimal? 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In the normal human counting system we use a base 10 number system, meaning that the each extra digit increases in powers of 10 each time: Hexadecimal is a Base 16 number system, meaning that increases in powers of 16, with each digit being one of 16 different combinations. 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In the normal human counting system we use a base 10 number system, meaning that the each extra digit increases in powers of 10 each time: Hexadecimal is a Base 16 number system, meaning that increases in powers of 16, with each digit being one of 16 different combinations. The hexadecimal number&hellip;&nbsp;Read&hellip;","_links":{"self":[{"href":"https:\/\/learnlearn.uk\/alevelcs\/wp-json\/wp\/v2\/pages\/858"}],"collection":[{"href":"https:\/\/learnlearn.uk\/alevelcs\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/learnlearn.uk\/alevelcs\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/learnlearn.uk\/alevelcs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/learnlearn.uk\/alevelcs\/wp-json\/wp\/v2\/comments?post=858"}],"version-history":[{"count":6,"href":"https:\/\/learnlearn.uk\/alevelcs\/wp-json\/wp\/v2\/pages\/858\/revisions"}],"predecessor-version":[{"id":2038,"href":"https:\/\/learnlearn.uk\/alevelcs\/wp-json\/wp\/v2\/pages\/858\/revisions\/2038"}],"wp:attachment":[{"href":"https:\/\/learnlearn.uk\/alevelcs\/wp-json\/wp\/v2\/media?parent=858"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}