{"id":264379,"date":"2025-07-21T15:47:13","date_gmt":"2025-07-21T15:47:13","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=264379"},"modified":"2025-07-21T15:47:15","modified_gmt":"2025-07-21T15:47:15","slug":"convert-the-following-binary-numbers-to-decimal","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/21\/convert-the-following-binary-numbers-to-decimal\/","title":{"rendered":"Convert the following binary numbers to decimal"},"content":{"rendered":"\n

Convert the following binary numbers to decimal. 1. 1100 2. 10100 3. 10011 4. 10101 5. 11100<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Let’s convert the binary numbers to decimal:<\/p>\n\n\n\n

    \n
  1. 1100<\/strong>
    To convert from binary to decimal, each digit represents a power of 2, starting from the rightmost digit (the least significant bit). So:<\/li>\n<\/ol>\n\n\n\n

    11002=1\u00d723+1\u00d722+0\u00d721+0\u00d7201100_2 = 1 \\times 2^3 + 1 \\times 2^2 + 0 \\times 2^1 + 0 \\times 2^0 =1\u00d78+1\u00d74+0\u00d72+0\u00d71=8+4+0+0=12= 1 \\times 8 + 1 \\times 4 + 0 \\times 2 + 0 \\times 1 = 8 + 4 + 0 + 0 = 12<\/p>\n\n\n\n

    So, 1100 in binary equals 12<\/strong> in decimal.<\/p>\n\n\n\n

      \n
    1. 10100<\/strong>
      Now for 10100:<\/li>\n<\/ol>\n\n\n\n

      101002=1\u00d724+0\u00d723+1\u00d722+0\u00d721+0\u00d72010100_2 = 1 \\times 2^4 + 0 \\times 2^3 + 1 \\times 2^2 + 0 \\times 2^1 + 0 \\times 2^0 =1\u00d716+0\u00d78+1\u00d74+0\u00d72+0\u00d71=16+0+4+0+0=20= 1 \\times 16 + 0 \\times 8 + 1 \\times 4 + 0 \\times 2 + 0 \\times 1 = 16 + 0 + 4 + 0 + 0 = 20<\/p>\n\n\n\n

      So, 10100 in binary equals 20<\/strong> in decimal.<\/p>\n\n\n\n

        \n
      1. 10011<\/strong>
        For 10011:<\/li>\n<\/ol>\n\n\n\n

        100112=1\u00d724+0\u00d723+0\u00d722+1\u00d721+1\u00d72010011_2 = 1 \\times 2^4 + 0 \\times 2^3 + 0 \\times 2^2 + 1 \\times 2^1 + 1 \\times 2^0 =1\u00d716+0\u00d78+0\u00d74+1\u00d72+1\u00d71=16+0+0+2+1=19= 1 \\times 16 + 0 \\times 8 + 0 \\times 4 + 1 \\times 2 + 1 \\times 1 = 16 + 0 + 0 + 2 + 1 = 19<\/p>\n\n\n\n

        So, 10011 in binary equals 19<\/strong> in decimal.<\/p>\n\n\n\n

          \n
        1. 10101<\/strong>
          For 10101:<\/li>\n<\/ol>\n\n\n\n

          101012=1\u00d724+0\u00d723+1\u00d722+0\u00d721+1\u00d72010101_2 = 1 \\times 2^4 + 0 \\times 2^3 + 1 \\times 2^2 + 0 \\times 2^1 + 1 \\times 2^0 =1\u00d716+0\u00d78+1\u00d74+0\u00d72+1\u00d71=16+0+4+0+1=21= 1 \\times 16 + 0 \\times 8 + 1 \\times 4 + 0 \\times 2 + 1 \\times 1 = 16 + 0 + 4 + 0 + 1 = 21<\/p>\n\n\n\n

          So, 10101 in binary equals 21<\/strong> in decimal.<\/p>\n\n\n\n

            \n
          1. 11100<\/strong>
            For 11100:<\/li>\n<\/ol>\n\n\n\n

            111002=1\u00d724+1\u00d723+1\u00d722+0\u00d721+0\u00d72011100_2 = 1 \\times 2^4 + 1 \\times 2^3 + 1 \\times 2^2 + 0 \\times 2^1 + 0 \\times 2^0 =1\u00d716+1\u00d78+1\u00d74+0\u00d72+0\u00d71=16+8+4+0+0=28= 1 \\times 16 + 1 \\times 8 + 1 \\times 4 + 0 \\times 2 + 0 \\times 1 = 16 + 8 + 4 + 0 + 0 = 28<\/p>\n\n\n\n

            So, 11100 in binary equals 28<\/strong> in decimal.<\/p>\n\n\n\n

            Summary of results:<\/h3>\n\n\n\n
              \n
            1. 1100 in binary = 12<\/strong> in decimal<\/li>\n\n\n\n
            2. 10100 in binary = 20<\/strong> in decimal<\/li>\n\n\n\n
            3. 10011 in binary = 19<\/strong> in decimal<\/li>\n\n\n\n
            4. 10101 in binary = 21<\/strong> in decimal<\/li>\n\n\n\n
            5. 11100 in binary = 28<\/strong> in decimal<\/li>\n<\/ol>\n\n\n\n

              The process of converting from binary to decimal involves understanding that each binary digit (bit) represents a power of 2. By multiplying each bit by the corresponding power of 2 and summing the results, the binary number can be converted to decimal.<\/p>\n","protected":false},"excerpt":{"rendered":"

              Convert the following binary numbers to decimal. 1. 1100 2. 10100 3. 10011 4. 10101 5. 11100 The correct answer and explanation is: Let’s convert the binary numbers to decimal: 11002=1\u00d723+1\u00d722+0\u00d721+0\u00d7201100_2 = 1 \\times 2^3 + 1 \\times 2^2 + 0 \\times 2^1 + 0 \\times 2^0 =1\u00d78+1\u00d74+0\u00d72+0\u00d71=8+4+0+0=12= 1 \\times 8 + 1 \\times 4 […]<\/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-264379","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/264379","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=264379"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/264379\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=264379"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=264379"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=264379"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}