{"id":199393,"date":"2025-03-11T16:20:44","date_gmt":"2025-03-11T16:20:44","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=199393"},"modified":"2025-03-11T16:20:46","modified_gmt":"2025-03-11T16:20:46","slug":"convert-the-following-binary-numbers-into-decimal","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/11\/convert-the-following-binary-numbers-into-decimal\/","title":{"rendered":"Convert the following binary numbers into decimal"},"content":{"rendered":"\n<p>Convert the following binary numbers into decimal:<\/p>\n\n\n\n<p>(a) 100001<\/p>\n\n\n\n<p>(b) 100111<\/p>\n\n\n\n<p>(c) 101010<\/p>\n\n\n\n<p>(d) 111001<\/p>\n\n\n\n<p>(e) 1100000<\/p>\n\n\n\n<p>(f) 11111101<\/p>\n\n\n\n<p>(g) 11110010<\/p>\n\n\n\n<p>(h) 11111111<\/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<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/03\/image-854-1024x635.png\" alt=\"\" class=\"wp-image-199394\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Understanding Binary to Decimal Conversion:<\/h3>\n\n\n\n<p>Binary is a base-2 number system, meaning it consists only of the digits 0 and 1. Each position in a binary number represents a power of 2, starting from (2^0) at the rightmost position.<\/p>\n\n\n\n<p>To convert binary to decimal, sum up the values of the positions where there is a 1.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conversions:<\/h3>\n\n\n\n<p>(a) <strong>100001<\/strong><br>[<br>(1 \\times 2^5) + (0 \\times 2^4) + (0 \\times 2^3) + (0 \\times 2^2) + (0 \\times 2^1) + (1 \\times 2^0) = 32 + 1 = 33<br>]<\/p>\n\n\n\n<p>(b) <strong>100111<\/strong><br>[<br>(1 \\times 2^5) + (0 \\times 2^4) + (0 \\times 2^3) + (1 \\times 2^2) + (1 \\times 2^1) + (1 \\times 2^0) = 32 + 4 + 2 + 1 = 39<br>]<\/p>\n\n\n\n<p>(c) <strong>101010<\/strong><br>[<br>(1 \\times 2^5) + (0 \\times 2^4) + (1 \\times 2^3) + (0 \\times 2^2) + (1 \\times 2^1) + (0 \\times 2^0) = 32 + 8 + 2 = 42<br>]<\/p>\n\n\n\n<p>(d) <strong>111001<\/strong><br>[<br>(1 \\times 2^5) + (1 \\times 2^4) + (1 \\times 2^3) + (0 \\times 2^2) + (0 \\times 2^1) + (1 \\times 2^0) = 32 + 16 + 8 + 1 = 57<br>]<\/p>\n\n\n\n<p>(e) <strong>1100000<\/strong><br>[<br>(1 \\times 2^6) + (1 \\times 2^5) + (0 \\times 2^4) + (0 \\times 2^3) + (0 \\times 2^2) + (0 \\times 2^1) + (0 \\times 2^0) = 64 + 32 = 96<br>]<\/p>\n\n\n\n<p>(f) <strong>11111101<\/strong><br>[<br>(1 \\times 2^7) + (1 \\times 2^6) + (1 \\times 2^5) + (1 \\times 2^4) + (1 \\times 2^3) + (1 \\times 2^2) + (0 \\times 2^1) + (1 \\times 2^0) = 253<br>]<\/p>\n\n\n\n<p>(g) <strong>11110010<\/strong><br>[<br>(1 \\times 2^7) + (1 \\times 2^6) + (1 \\times 2^5) + (1 \\times 2^4) + (0 \\times 2^3) + (0 \\times 2^2) + (1 \\times 2^1) + (0 \\times 2^0) = 242<br>]<\/p>\n\n\n\n<p>(h) <strong>11111111<\/strong><br>[<br>(1 \\times 2^7) + (1 \\times 2^6) + (1 \\times 2^5) + (1 \\times 2^4) + (1 \\times 2^3) + (1 \\times 2^2) + (1 \\times 2^1) + (1 \\times 2^0) = 255<br>]<\/p>\n\n\n\n<p>This method allows for an easy conversion of binary numbers to decimal by summing the powers of 2 where there are 1s.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Convert the following binary numbers into decimal: (a) 100001 (b) 100111 (c) 101010 (d) 111001 (e) 1100000 (f) 11111101 (g) 11110010 (h) 11111111 The correct answer and explanation is : Understanding Binary to Decimal Conversion: Binary is a base-2 number system, meaning it consists only of the digits 0 and 1. Each position in a [&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-199393","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199393","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=199393"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199393\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=199393"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=199393"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=199393"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}