{"id":252070,"date":"2025-07-11T06:33:43","date_gmt":"2025-07-11T06:33:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=252070"},"modified":"2025-07-11T06:33:45","modified_gmt":"2025-07-11T06:33:45","slug":"divide-10001111-by-1011-and-compare-the-result-as-obtained-in-decimal-system","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/11\/divide-10001111-by-1011-and-compare-the-result-as-obtained-in-decimal-system\/","title":{"rendered":"Divide 10001111 by 1011 and compare the result as obtained in decimal system"},"content":{"rendered":"\n

Divide 10001111 by 1011 and compare the result as obtained in decimal system<\/p>\n\n\n\n

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

Let’s divide the binary numbers 10001111<\/strong> by 1011<\/strong> and compare the result with the decimal system.<\/p>\n\n\n\n

Step 1: Convert Binary Numbers to Decimal<\/h3>\n\n\n\n
    \n
  • The binary number 10001111<\/strong> can be converted to decimal as follows: 100011112=(1\u00d727)+(0\u00d726)+(0\u00d725)+(0\u00d724)+(1\u00d723)+(1\u00d722)+(1\u00d721)+(1\u00d720)10001111_2 = (1 \\times 2^7) + (0 \\times 2^6) + (0 \\times 2^5) + (0 \\times 2^4) + (1 \\times 2^3) + (1 \\times 2^2) + (1 \\times 2^1) + (1 \\times 2^0)100011112\u200b=(1\u00d727)+(0\u00d726)+(0\u00d725)+(0\u00d724)+(1\u00d723)+(1\u00d722)+(1\u00d721)+(1\u00d720) 100011112=128+8+4+2+1=1431010001111_2 = 128 + 8 + 4 + 2 + 1 = 143_{10}100011112\u200b=128+8+4+2+1=14310\u200b<\/li>\n\n\n\n
  • The binary number 1011<\/strong> can be converted to decimal as follows: 10112=(1\u00d723)+(0\u00d722)+(1\u00d721)+(1\u00d720)1011_2 = (1 \\times 2^3) + (0 \\times 2^2) + (1 \\times 2^1) + (1 \\times 2^0)10112\u200b=(1\u00d723)+(0\u00d722)+(1\u00d721)+(1\u00d720) 10112=8+2+1=11101011_2 = 8 + 2 + 1 = 11_{10}10112\u200b=8+2+1=1110\u200b<\/li>\n<\/ul>\n\n\n\n

    Step 2: Perform the Division in Decimal<\/h3>\n\n\n\n

    Now, divide the decimal equivalents: 14311=13\\frac{143}{11} = 1311143\u200b=13<\/p>\n\n\n\n

    Step 3: Convert the Result Back to Binary<\/h3>\n\n\n\n

    The quotient is 13<\/strong> in decimal. We can convert 13<\/strong> to binary: 1310=(1\u00d723)+(0\u00d722)+(0\u00d721)+(1\u00d720)=1101213_{10} = (1 \\times 2^3) + (0 \\times 2^2) + (0 \\times 2^1) + (1 \\times 2^0) = 1101_21310\u200b=(1\u00d723)+(0\u00d722)+(0\u00d721)+(1\u00d720)=11012\u200b<\/p>\n\n\n\n

    Conclusion<\/h3>\n\n\n\n
      \n
    • Binary Division<\/strong>: 10001111 \u00f7 1011<\/strong> results in 1101<\/strong> in binary.<\/li>\n\n\n\n
    • Decimal Division<\/strong>: The result of dividing 143 by 11<\/strong> gives 13<\/strong> in decimal, which confirms that the binary result 1101<\/strong> corresponds to the decimal result 13<\/strong>.<\/li>\n<\/ul>\n\n\n\n

      Both methods give the same result, and the comparison shows that the binary division accurately represents the decimal operation. The key takeaway is the consistency between the two systems, with binary numbers directly corresponding to their decimal equivalents.<\/p>\n\n\n\n

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

      Divide 10001111 by 1011 and compare the result as obtained in decimal system The Correct Answer and Explanation is: Let’s divide the binary numbers 10001111 by 1011 and compare the result with the decimal system. Step 1: Convert Binary Numbers to Decimal Step 2: Perform the Division in Decimal Now, divide the decimal equivalents: 14311=13\\frac{143}{11} […]<\/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-252070","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/252070","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=252070"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/252070\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=252070"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=252070"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=252070"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}