{"id":185220,"date":"2025-01-22T08:52:47","date_gmt":"2025-01-22T08:52:47","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=185220"},"modified":"2025-01-22T08:52:49","modified_gmt":"2025-01-22T08:52:49","slug":"perform-the-following-octal-additions","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/22\/perform-the-following-octal-additions\/","title":{"rendered":"Perform the following octal additions"},"content":{"rendered":"\n

Perform the following octal additions. a. 770 + 665 b. 101 + 707 c. 202 + 667<\/p>\n\n\n\n

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

Octal Addition Solutions<\/h3>\n\n\n\n

a. 7708+6658770_{8} + 665_{8}<\/h4>\n\n\n\n
    \n
  1. Add the digits from right to left:
    • Units place: 0+5=50 + 5 = 5.<\/li>
    • Tens place: 7+6=15107 + 6 = 15_{10}. In octal, 151015_{10} becomes 17817_{8}. Write 77 and carry 11.<\/li>
    • Hundreds place: 7+6+1=14107 + 6 + 1 = 14_{10}. In octal, 141014_{10} becomes 16816_{8}. Write 66 and carry 11.<\/li><\/ul>Final result: 165581655_{8}.<\/li>\n<\/ol>\n\n\n\n
      \n\n\n\n

      b. 1018+7078101_{8} + 707_{8}<\/h4>\n\n\n\n
        \n
      1. Add the digits from right to left:
        • Units place: 1+7=8101 + 7 = 8_{10}. In octal, 8108_{10} becomes 10810_{8}. Write 00 and carry 11.<\/li>
        • Tens place: 0+0+1=10 + 0 + 1 = 1.<\/li>
        • Hundreds place: 1+7=10101 + 7 = 10_{10}. In octal, 101010_{10} becomes 12812_{8}. Write 22 and carry 11.<\/li><\/ul>Final result: 121081210_{8}.<\/li>\n<\/ol>\n\n\n\n
          \n\n\n\n

          c. 2028+6678202_{8} + 667_{8}<\/h4>\n\n\n\n
            \n
          1. Add the digits from right to left:
            • Units place: 2+7=9102 + 7 = 9_{10}. In octal, 9109_{10} becomes 11811_{8}. Write 11 and carry 11.<\/li>
            • Tens place: 0+6+1=70 + 6 + 1 = 7.<\/li>
            • Hundreds place: 2+6=8102 + 6 = 8_{10}. In octal, 8108_{10} becomes 10810_{8}. Write 00 and carry 11.<\/li><\/ul>Final result: 107181071_{8}.<\/li>\n<\/ol>\n\n\n\n
              \n\n\n\n

              Explanation<\/h3>\n\n\n\n

              Octal addition works similarly to decimal addition but is based on base 88. If a sum exceeds 77, it “wraps around” (like in decimal with 1010), and the remainder is written, while the quotient becomes a carry for the next higher place.<\/p>\n\n\n\n

                \n
              1. Convert to Decimal (Optional):<\/strong> For verification, converting octal numbers to decimal simplifies checking correctness.<\/li>\n\n\n\n
              2. Carry Over:<\/strong> The key difference from decimal arithmetic is that the carry occurs at 88, not 1010.<\/li>\n<\/ol>\n\n\n\n

                Benefits of Octal<\/h4>\n\n\n\n

                Octal representation is often used in computing systems as a shorthand for binary, grouping bits in sets of three, simplifying human interaction with binary data.<\/p>\n","protected":false},"excerpt":{"rendered":"

                Perform the following octal additions. a. 770 + 665 b. 101 + 707 c. 202 + 667 The Correct Answer and Explanation is : Octal Addition Solutions a. 7708+6658770_{8} + 665_{8} b. 1018+7078101_{8} + 707_{8} c. 2028+6678202_{8} + 667_{8} Explanation Octal addition works similarly to decimal addition but is based on base 88. If a […]<\/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-185220","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185220","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=185220"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/185220\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=185220"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=185220"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=185220"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}