{"id":217413,"date":"2025-05-21T20:35:07","date_gmt":"2025-05-21T20:35:07","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=217413"},"modified":"2025-05-21T20:35:09","modified_gmt":"2025-05-21T20:35:09","slug":"what-is-the-largest-16-bit-binary-value-that-can-be-represented-by","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/21\/what-is-the-largest-16-bit-binary-value-that-can-be-represented-by\/","title":{"rendered":"What is the largest 16-bit binary value that can be represented by"},"content":{"rendered":"\n

What is the largest 16-bit binary value that can be represented by:<\/p>\n\n\n\n

(a) Unsigned number
(b) Signed magnitude
(c) Signed two\u2019s complement<\/p>\n\n\n\n

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

Here are the correct answers for the largest 16-bit binary values under each representation:<\/p>\n\n\n\n

\n\n\n\n

(a) Unsigned Number:<\/strong><\/p>\n\n\n\n

Answer:<\/strong> 1111111111111111<\/code> (binary) = 65,535<\/strong> (decimal)<\/p>\n\n\n\n

\n\n\n\n

(b) Signed Magnitude:<\/strong><\/p>\n\n\n\n

Answer:<\/strong> 0111111111111111<\/code> (binary) = 32,767<\/strong> (decimal)<\/p>\n\n\n\n

\n\n\n\n

(c) Signed Two\u2019s Complement:<\/strong><\/p>\n\n\n\n

Answer:<\/strong> 0111111111111111<\/code> (binary) = 32,767<\/strong> (decimal)<\/p>\n\n\n\n

\n\n\n\n

\u2705 Explanation (300+ words):<\/h3>\n\n\n\n

The number of bits (in this case, 16 bits) determines how many binary values can be represented. Each of the three number formats interprets the same 16-bit binary sequence differently:<\/p>\n\n\n\n

\n\n\n\n

(a) Unsigned Number:<\/strong><\/h4>\n\n\n\n

In an unsigned representation<\/strong>, all 16 bits are used to represent the magnitude of the number. There is no sign bit (i.e., no bit is used to indicate positive or negative).<\/p>\n\n\n\n

    \n
  • The smallest unsigned value is 0000000000000000<\/code> = 0.<\/li>\n\n\n\n
  • The largest unsigned value is when all bits are 1s: 1111111111111111<\/code>.<\/li>\n\n\n\n
  • This binary number is equal to: $$
    2^{16} – 1 = 65,535
    $$<\/li>\n<\/ul>\n\n\n\n

    So, the largest 16-bit unsigned<\/strong> binary number is 65,535<\/strong>.<\/p>\n\n\n\n

    \n\n\n\n

    (b) Signed Magnitude:<\/strong><\/h4>\n\n\n\n

    In signed magnitude<\/strong> representation, the first bit is the sign bit<\/strong>:<\/p>\n\n\n\n

      \n
    • 0<\/code> indicates a positive number.<\/li>\n\n\n\n
    • 1<\/code> indicates a negative number.<\/li>\n\n\n\n
    • The remaining 15 bits represent the magnitude.<\/li>\n<\/ul>\n\n\n\n

      The largest positive<\/strong> number in signed magnitude is:<\/p>\n\n\n\n

        \n
      • 0<\/code> followed by 15 1<\/code>s: 0111111111111111<\/code><\/li>\n\n\n\n
      • This represents: $$
        2^{15} – 1 = 32,767
        $$<\/li>\n<\/ul>\n\n\n\n

        So, the largest 16-bit signed magnitude<\/strong> number is 32,767<\/strong>.<\/p>\n\n\n\n

        \n\n\n\n

        (c) Signed Two\u2019s Complement:<\/strong><\/h4>\n\n\n\n

        In two\u2019s complement<\/strong> representation:<\/p>\n\n\n\n

          \n
        • The first bit is still the sign bit<\/strong>, but the negative numbers are represented differently (using inversion and addition of 1).<\/li>\n\n\n\n
        • The range for a 16-bit two\u2019s complement number is: $$
          -2^{15} \\text{ to } 2^{15} – 1
          $$ That is: $$
          -32,768 \\text{ to } 32,767
          $$<\/li>\n\n\n\n
        • The largest number is when the sign bit is 0 and the remaining bits are all 1s: 0111111111111111<\/code> = 32,767<\/strong><\/li>\n<\/ul>\n\n\n\n
          \n\n\n\n

          \ud83d\udccc Summary Table:<\/h3>\n\n\n\n
          Representation<\/th>Largest 16-bit Value<\/th>Decimal Equivalent<\/th><\/tr><\/thead>
          Unsigned<\/td>1111111111111111<\/td>65,535<\/td><\/tr>
          Signed Magnitude<\/td>0111111111111111<\/td>32,767<\/td><\/tr>
          Signed Two\u2019s Complement<\/td>0111111111111111<\/td>32,767<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

          Each format has a different range because of how it uses the bits, particularly the most significant bit (MSB).<\/p>\n","protected":false},"excerpt":{"rendered":"

          What is the largest 16-bit binary value that can be represented by: (a) Unsigned number(b) Signed magnitude(c) Signed two\u2019s complement The Correct Answer and Explanation is: Here are the correct answers for the largest 16-bit binary values under each representation: (a) Unsigned Number: Answer: 1111111111111111 (binary) = 65,535 (decimal) (b) Signed Magnitude: Answer: 0111111111111111 (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-217413","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/217413","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=217413"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/217413\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=217413"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=217413"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=217413"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}