{"id":225922,"date":"2025-06-04T18:29:00","date_gmt":"2025-06-04T18:29:00","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=225922"},"modified":"2025-06-04T18:29:03","modified_gmt":"2025-06-04T18:29:03","slug":"when-we-perform-subtraction-on-7-and-1-the-answer-in-2s-complement-form-is","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/04\/when-we-perform-subtraction-on-7-and-1-the-answer-in-2s-complement-form-is\/","title":{"rendered":"When we perform subtraction on -7 and 1, the answer in 2’s complement form is"},"content":{"rendered":"\n

When we perform subtraction on -7 and 1, the answer in 2’s complement form is _<\/em><\/strong> a) 1010 b) 1110 c) 0110 d) 1000 In radix binary, 1101 multiplied by 1011 is a) 10001111 b) 10101010 c) 11110000 d) 11001100<\/p>\n\n\n\n

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

Answer:<\/strong><\/h3>\n\n\n\n

1. Subtraction of -7 and 1 in 2’s complement form<\/strong>
Correct option: b) 1110<\/strong><\/p>\n\n\n\n

2. Binary multiplication of 1101 and 1011<\/strong>
Correct option: a) 10001111<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation:<\/strong><\/h3>\n\n\n\n

1. Subtraction in 2’s Complement: -7 – 1<\/strong><\/h4>\n\n\n\n

We are performing the operation -7 \u2013 1<\/strong>, which is equivalent to -7 + (-1)<\/strong>.<\/p>\n\n\n\n

To compute this in 2’s complement form, let’s assume a 4-bit<\/strong> system for simplicity.<\/p>\n\n\n\n

Step 1: Represent -7 in 2\u2019s complement (4-bit)<\/strong><\/p>\n\n\n\n

    \n
  • 7 in binary = 0111<\/code><\/li>\n\n\n\n
  • Invert the bits: 1000<\/code><\/li>\n\n\n\n
  • Add 1: 1001<\/code> \u2192 So, -7 = 1001<\/strong><\/li>\n<\/ul>\n\n\n\n

    Step 2: Represent -1 in 2\u2019s complement (4-bit)<\/strong><\/p>\n\n\n\n

      \n
    • 1 in binary = 0001<\/code><\/li>\n\n\n\n
    • Invert the bits: 1110<\/code><\/li>\n\n\n\n
    • Add 1: 1111<\/code> \u2192 So, -1 = 1111<\/strong><\/li>\n<\/ul>\n\n\n\n

      Step 3: Add -7 and -1<\/strong><\/p>\n\n\n\n

        1001  (-7)\n+ 1111  (-1)\n-------\n 11000\n<\/code><\/pre>\n\n\n\n
      The result is 11000<\/code>. In 4-bit representation, we drop the leftmost carry bit, resulting in 1000<\/strong>.<\/p>\n\n\n\n
      However, the question asks for -7 \u2013 1<\/strong>, which is -8<\/strong>. Let’s check the 2’s complement of -8:<\/p>\n\n\n\n
        \n
      • 8 in binary = 1000<\/code><\/li>\n\n\n\n
      • Invert: 0111<\/code><\/li>\n\n\n\n
      • Add 1: 1000<\/code> (already in 2’s complement form)<\/li>\n<\/ul>\n\n\n\n
        Thus, the correct result in 4-bit 2’s complement<\/strong> is: 1000<\/strong><\/p>\n\n\n\n
        So option d) 1000<\/strong> is correct (not b).
        \ud83d\uded1 Correction: The correct answer is d) 1000, not b) 1110.<\/strong><\/p>\n\n\n\n
        \n\n\n\n
        2. Binary Multiplication: 1101 \u00d7 1011<\/strong><\/h4>\n\n\n\n
        1101 (13 in decimal)<\/strong>
        \u00d7 1011 (11 in decimal)<\/strong>
        = 13 \u00d7 11 = 143<\/strong><\/p>\n\n\n\n
        Now convert 143 to binary:<\/p>\n\n\n\n
        143 \u00f7 2 = 71 R1
        71 \u00f7 2 = 35 R1
        35 \u00f7 2 = 17 R1
        17 \u00f7 2 = 8 R1
        8 \u00f7 2 = 4 R0
        4 \u00f7 2 = 2 R0
        2 \u00f7 2 = 1 R0
        1 \u00f7 2 = 0 R1
        Reading in reverse: 10001111<\/strong><\/p>\n\n\n\n
        \u2705 Hence, the correct answer is a) 10001111<\/strong>.<\/p>\n\n\n\n
        \n\n\n\n
        Summary<\/strong><\/h3>\n\n\n\n
          \n
        • -7 \u2013 1 in 2’s complement (4-bit) = 1000<\/strong> \u2192 Correct option: d)<\/strong><\/li>\n\n\n\n
        • 1101 \u00d7 1011 = 10001111 (143 in binary)<\/strong> \u2192 Correct option: a)<\/strong><\/li>\n<\/ul>\n\n\n\n
          \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
          When we perform subtraction on -7 and 1, the answer in 2’s complement form is _ a) 1010 b) 1110 c) 0110 d) 1000 In radix binary, 1101 multiplied by 1011 is a) 10001111 b) 10101010 c) 11110000 d) 11001100 The correct Answer and Explanation is: Answer: 1. Subtraction of -7 and 1 in 2’s […]<\/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-225922","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225922","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=225922"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/225922\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=225922"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=225922"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=225922"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}