{"id":264717,"date":"2025-07-21T15:48:57","date_gmt":"2025-07-21T15:48:57","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=264717"},"modified":"2025-07-21T15:48:59","modified_gmt":"2025-07-21T15:48:59","slug":"convert-the-following-binary-numbers-to-decimal-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/21\/convert-the-following-binary-numbers-to-decimal-2\/","title":{"rendered":"Convert the following binary numbers to decimal"},"content":{"rendered":"\n<p>Convert the following binary numbers to decimal. <\/p>\n\n\n\n<p>a) 10100 b) 110110<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Let&#8217;s convert the binary numbers into decimal.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">a) Binary number: 10100<\/h3>\n\n\n\n<p>To convert a binary number to decimal, we multiply each digit of the binary number by 2 raised to the power of its position, starting from 0 on the rightmost side.<\/p>\n\n\n\n<p>For <strong>10100<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The rightmost digit is at position 0, the next at position 1, and so on.<\/li>\n\n\n\n<li>We multiply each binary digit (0 or 1) by 2 raised to the power of its position:<\/li>\n<\/ul>\n\n\n\n<p>1\u00d724=161 \\times 2^4 = 16 0\u00d723=00 \\times 2^3 = 0 1\u00d722=41 \\times 2^2 = 4 0\u00d721=00 \\times 2^1 = 0 0\u00d720=00 \\times 2^0 = 0<\/p>\n\n\n\n<p>Now, add all the results together: 16+0+4+0+0=2016 + 0 + 4 + 0 + 0 = 20<\/p>\n\n\n\n<p>So, the decimal equivalent of <strong>10100<\/strong> is <strong>20<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">b) Binary number: 110110<\/h3>\n\n\n\n<p>For <strong>110110<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Similarly, each digit is multiplied by 2 raised to the power of its position, starting from the rightmost digit.<\/li>\n<\/ul>\n\n\n\n<p>1\u00d725=321 \\times 2^5 = 32 1\u00d724=161 \\times 2^4 = 16 0\u00d723=00 \\times 2^3 = 0 1\u00d722=41 \\times 2^2 = 4 1\u00d721=21 \\times 2^1 = 2 0\u00d720=00 \\times 2^0 = 0<\/p>\n\n\n\n<p>Now, add all the results together: 32+16+0+4+2+0=5432 + 16 + 0 + 4 + 2 + 0 = 54<\/p>\n\n\n\n<p>So, the decimal equivalent of <strong>110110<\/strong> is <strong>54<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Summary:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>a)<\/strong> The decimal equivalent of <strong>10100<\/strong> is <strong>20<\/strong>.<\/li>\n\n\n\n<li><strong>b)<\/strong> The decimal equivalent of <strong>110110<\/strong> is <strong>54<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>This method is based on the binary number system, where each place value is a power of 2, starting from 202^0 on the rightmost side.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Convert the following binary numbers to decimal. a) 10100 b) 110110 The correct answer and explanation is: Let&#8217;s convert the binary numbers into decimal. a) Binary number: 10100 To convert a binary number to decimal, we multiply each digit of the binary number by 2 raised to the power of its position, starting from 0 [&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 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