{"id":194628,"date":"2025-02-24T10:13:29","date_gmt":"2025-02-24T10:13:29","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=194628"},"modified":"2025-02-24T10:13:35","modified_gmt":"2025-02-24T10:13:35","slug":"convert-each-decimal-fraction-to-binary-using-the-sum-of-weights-method","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/24\/convert-each-decimal-fraction-to-binary-using-the-sum-of-weights-method\/","title":{"rendered":"Convert each decimal fraction to binary using the sum-of-weights method"},"content":{"rendered":"\n<p>Convert each decimal fraction to binary using the sum-of-weights method:<\/p>\n\n\n\n<p>(a) 0.26<\/p>\n\n\n\n<p>(b) 0.762<\/p>\n\n\n\n<p>(c) 0.0975<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To convert each decimal fraction to binary using the <strong>sum-of-weights<\/strong> method, we follow these steps:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Steps for Conversion:<\/strong><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Multiply the decimal fraction by 2.<\/li>\n\n\n\n<li>Note the <strong>integer part<\/strong> (0 or 1); this is the next binary digit.<\/li>\n\n\n\n<li>Retain the <strong>fractional part<\/strong> and repeat step 1 until the fraction reaches 0 or a repeating cycle is noticed.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>(a) 0.26 in Binary<\/strong><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>0.26\u00d72=0.520.26 \\times 2 = 0.52 \u2192 Integer: 0<\/li>\n\n\n\n<li>0.52\u00d72=1.040.52 \\times 2 = 1.04 \u2192 Integer: 1<\/li>\n\n\n\n<li>0.04\u00d72=0.080.04 \\times 2 = 0.08 \u2192 Integer: 0<\/li>\n\n\n\n<li>0.08\u00d72=0.160.08 \\times 2 = 0.16 \u2192 Integer: 0<\/li>\n\n\n\n<li>0.16\u00d72=0.320.16 \\times 2 = 0.32 \u2192 Integer: 0<\/li>\n\n\n\n<li>0.32\u00d72=0.640.32 \\times 2 = 0.64 \u2192 Integer: 0<\/li>\n\n\n\n<li>0.64\u00d72=1.280.64 \\times 2 = 1.28 \u2192 Integer: 1<\/li>\n\n\n\n<li>0.28\u00d72=0.560.28 \\times 2 = 0.56 \u2192 Integer: 0<\/li>\n\n\n\n<li>0.56\u00d72=1.120.56 \\times 2 = 1.12 \u2192 Integer: 1<\/li>\n<\/ol>\n\n\n\n<p><strong>Binary Representation:<\/strong> <strong>0.0100001101\u2026<\/strong> (approximated)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>(b) 0.762 in Binary<\/strong><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>0.762\u00d72=1.5240.762 \\times 2 = 1.524 \u2192 Integer: 1<\/li>\n\n\n\n<li>0.524\u00d72=1.0480.524 \\times 2 = 1.048 \u2192 Integer: 1<\/li>\n\n\n\n<li>0.048\u00d72=0.0960.048 \\times 2 = 0.096 \u2192 Integer: 0<\/li>\n\n\n\n<li>0.096\u00d72=0.1920.096 \\times 2 = 0.192 \u2192 Integer: 0<\/li>\n\n\n\n<li>0.192\u00d72=0.3840.192 \\times 2 = 0.384 \u2192 Integer: 0<\/li>\n\n\n\n<li>0.384\u00d72=0.7680.384 \\times 2 = 0.768 \u2192 Integer: 0<\/li>\n\n\n\n<li>0.768\u00d72=1.5360.768 \\times 2 = 1.536 \u2192 Integer: 1<\/li>\n\n\n\n<li>0.536\u00d72=1.0720.536 \\times 2 = 1.072 \u2192 Integer: 1<\/li>\n<\/ol>\n\n\n\n<p><strong>Binary Representation:<\/strong> <strong>0.11000011\u2026<\/strong> (approximated)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>(c) 0.0975 in Binary<\/strong><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>0.0975\u00d72=0.1950.0975 \\times 2 = 0.195 \u2192 Integer: 0<\/li>\n\n\n\n<li>0.195\u00d72=0.390.195 \\times 2 = 0.39 \u2192 Integer: 0<\/li>\n\n\n\n<li>0.39\u00d72=0.780.39 \\times 2 = 0.78 \u2192 Integer: 0<\/li>\n\n\n\n<li>0.78\u00d72=1.560.78 \\times 2 = 1.56 \u2192 Integer: 1<\/li>\n\n\n\n<li>0.56\u00d72=1.120.56 \\times 2 = 1.12 \u2192 Integer: 1<\/li>\n\n\n\n<li>0.12\u00d72=0.240.12 \\times 2 = 0.24 \u2192 Integer: 0<\/li>\n\n\n\n<li>0.24\u00d72=0.480.24 \\times 2 = 0.48 \u2192 Integer: 0<\/li>\n\n\n\n<li>0.48\u00d72=0.960.48 \\times 2 = 0.96 \u2192 Integer: 0<\/li>\n\n\n\n<li>0.96\u00d72=1.920.96 \\times 2 = 1.92 \u2192 Integer: 1<\/li>\n<\/ol>\n\n\n\n<p><strong>Binary Representation:<\/strong> <strong>0.0001100110\u2026<\/strong> (approximated)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation:<\/strong><\/h3>\n\n\n\n<p>The sum-of-weights method represents decimal fractions as sums of negative powers of two. Each binary digit corresponds to a fraction of 1\/2,1\/4,1\/8,&#8230;1\/2, 1\/4, 1\/8, &#8230;. This method efficiently represents fractions in binary, but some decimal numbers have repeating patterns in binary, similar to how 1\/31\/3 repeats in decimal (0.333&#8230;).<\/p>\n\n\n\n<p>Now, I&#8217;ll generate an image illustrating these conversions.<\/p>\n\n\n\n<p>Here is the mathematical illustration showing the step-by-step conversion of decimal fractions to binary using the sum-of-weights method. Let me know if you need any modifications or explanations!<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/02\/image-1391.png\" alt=\"\" class=\"wp-image-194629\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Convert each decimal fraction to binary using the sum-of-weights method: (a) 0.26 (b) 0.762 (c) 0.0975 The Correct Answer and Explanation is : To convert each decimal fraction to binary using the sum-of-weights method, we follow these steps: Steps for Conversion: (a) 0.26 in Binary Binary Representation: 0.0100001101\u2026 (approximated) (b) 0.762 in Binary Binary Representation: [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-194628","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194628","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=194628"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/194628\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=194628"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=194628"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=194628"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}