{"id":251431,"date":"2025-07-10T17:15:31","date_gmt":"2025-07-10T17:15:31","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=251431"},"modified":"2025-07-10T17:15:35","modified_gmt":"2025-07-10T17:15:35","slug":"convert-the-following-decimal-number-into-binary","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/10\/convert-the-following-decimal-number-into-binary\/","title":{"rendered":"Convert the following decimal number into binary."},"content":{"rendered":"\n

Convert the following decimal number into binary. please give full answer a) (128)10 b) (55)10 c) (173)10 d) (39)10 please give full answer<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To convert a decimal number into binary, we repeatedly divide the decimal number by 2, noting the quotient and the remainder at each step. The binary equivalent is obtained by reading the remainders in reverse order (starting from the last division). Let\u2019s break down the conversions step by step for each number.<\/p>\n\n\n\n

a) (128)10 to binary:<\/h3>\n\n\n\n
    \n
  1. Divide 128 by 2: quotient = 64, remainder = 0<\/li>\n\n\n\n
  2. Divide 64 by 2: quotient = 32, remainder = 0<\/li>\n\n\n\n
  3. Divide 32 by 2: quotient = 16, remainder = 0<\/li>\n\n\n\n
  4. Divide 16 by 2: quotient = 8, remainder = 0<\/li>\n\n\n\n
  5. Divide 8 by 2: quotient = 4, remainder = 0<\/li>\n\n\n\n
  6. Divide 4 by 2: quotient = 2, remainder = 0<\/li>\n\n\n\n
  7. Divide 2 by 2: quotient = 1, remainder = 0<\/li>\n\n\n\n
  8. Divide 1 by 2: quotient = 0, remainder = 1<\/li>\n<\/ol>\n\n\n\n

    Reading the remainders from bottom to top gives the binary representation:
    (128)10 = (10000000)2<\/strong><\/p>\n\n\n\n

    b) (55)10 to binary:<\/h3>\n\n\n\n
      \n
    1. Divide 55 by 2: quotient = 27, remainder = 1<\/li>\n\n\n\n
    2. Divide 27 by 2: quotient = 13, remainder = 1<\/li>\n\n\n\n
    3. Divide 13 by 2: quotient = 6, remainder = 1<\/li>\n\n\n\n
    4. Divide 6 by 2: quotient = 3, remainder = 0<\/li>\n\n\n\n
    5. Divide 3 by 2: quotient = 1, remainder = 1<\/li>\n\n\n\n
    6. Divide 1 by 2: quotient = 0, remainder = 1<\/li>\n<\/ol>\n\n\n\n

      Reading the remainders from bottom to top gives the binary representation:
      (55)10 = (110111)2<\/strong><\/p>\n\n\n\n

      c) (173)10 to binary:<\/h3>\n\n\n\n
        \n
      1. Divide 173 by 2: quotient = 86, remainder = 1<\/li>\n\n\n\n
      2. Divide 86 by 2: quotient = 43, remainder = 0<\/li>\n\n\n\n
      3. Divide 43 by 2: quotient = 21, remainder = 1<\/li>\n\n\n\n
      4. Divide 21 by 2: quotient = 10, remainder = 1<\/li>\n\n\n\n
      5. Divide 10 by 2: quotient = 5, remainder = 0<\/li>\n\n\n\n
      6. Divide 5 by 2: quotient = 2, remainder = 1<\/li>\n\n\n\n
      7. Divide 2 by 2: quotient = 1, remainder = 0<\/li>\n\n\n\n
      8. Divide 1 by 2: quotient = 0, remainder = 1<\/li>\n<\/ol>\n\n\n\n

        Reading the remainders from bottom to top gives the binary representation:
        (173)10 = (10101101)2<\/strong><\/p>\n\n\n\n

        d) (39)10 to binary:<\/h3>\n\n\n\n
          \n
        1. Divide 39 by 2: quotient = 19, remainder = 1<\/li>\n\n\n\n
        2. Divide 19 by 2: quotient = 9, remainder = 1<\/li>\n\n\n\n
        3. Divide 9 by 2: quotient = 4, remainder = 1<\/li>\n\n\n\n
        4. Divide 4 by 2: quotient = 2, remainder = 0<\/li>\n\n\n\n
        5. Divide 2 by 2: quotient = 1, remainder = 0<\/li>\n\n\n\n
        6. Divide 1 by 2: quotient = 0, remainder = 1<\/li>\n<\/ol>\n\n\n\n

          Reading the remainders from bottom to top gives the binary representation:
          (39)10 = (100111)2<\/strong><\/p>\n\n\n\n

          Summary of Results:<\/h3>\n\n\n\n
            \n
          • (128)10 = (10000000)2<\/li>\n\n\n\n
          • (55)10 = (110111)2<\/li>\n\n\n\n
          • (173)10 = (10101101)2<\/li>\n\n\n\n
          • (39)10 = (100111)2<\/li>\n<\/ul>\n\n\n\n

            Each binary number corresponds to the decimal value provided, following the steps of division and collection of remainders.<\/p>\n\n\n\n

            \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

            Convert the following decimal number into binary. please give full answer a) (128)10 b) (55)10 c) (173)10 d) (39)10 please give full answer The Correct Answer and Explanation is: To convert a decimal number into binary, we repeatedly divide the decimal number by 2, noting the quotient and the remainder at each step. The binary […]<\/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-251431","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/251431","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=251431"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/251431\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=251431"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=251431"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=251431"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}