{"id":193218,"date":"2025-02-19T07:41:09","date_gmt":"2025-02-19T07:41:09","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=193218"},"modified":"2025-02-19T07:41:11","modified_gmt":"2025-02-19T07:41:11","slug":"what-is-the-8-bit-binary-representation-of-49-in-sign-magnitude-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/19\/what-is-the-8-bit-binary-representation-of-49-in-sign-magnitude-form\/","title":{"rendered":"What is the 8-bit binary representation of -49 in sign magnitude form"},"content":{"rendered":"\n
    \n
  1. What is the 8-bit binary representation of -49 in sign magnitude form?<\/li>\n\n\n\n
  2. What is the 8-bit binary representation of -31 in excess 127 form?<\/li>\n\n\n\n
  3. What is the decimal value of 11001010 when viewed as an unsigned 8-bit integer?<\/li>\n\n\n\n
  4. What is the decimal value of 11001010 when viewed as a sign magnitude 8-bit integer?<\/li>\n\n\n\n
  5. What is the 32 bit floating point representation of 1.5 in binary and hex form?<\/li>\n\n\n\n
  6. How many bits would a complete load instruction need to have to hold a main memory address of decimal 65536<\/li>\n<\/ol>\n\n\n\n

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

    Let’s break down each of your questions step by step:<\/p>\n\n\n\n

      \n
    1. 8-bit binary representation of -49 in sign magnitude form:<\/strong><\/li>\n<\/ol>\n\n\n\n
        \n
      • Sign magnitude<\/strong> representation works by encoding the sign separately. In an 8-bit system:\n
          \n
        • First, convert 49 to binary: 49<\/code> in decimal = 00110001<\/code> in binary.<\/li>\n\n\n\n
        • Since it is negative, the first bit is set to 1 to represent the sign.<\/li>\n\n\n\n
        • Thus, the sign magnitude representation of -49 is: 10110001<\/code>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
            \n
          1. 8-bit binary representation of -31 in excess 127 form:<\/strong><\/li>\n<\/ol>\n\n\n\n
              \n
            • Excess 127<\/strong> is a form of bias representation where the number is offset by a constant value (127 in this case).<\/li>\n\n\n\n
            • First, convert 31 to binary: 31<\/code> in decimal = 00011111<\/code> in binary.<\/li>\n\n\n\n
            • Add the bias of 127 to it: 31 + 127 = 158<\/code>.<\/li>\n\n\n\n
            • Convert 158 to binary: 158<\/code> in decimal = 10011110<\/code> in binary.<\/li>\n\n\n\n
            • Therefore, the excess 127 representation of -31 is 10011110<\/code>.<\/li>\n<\/ul>\n\n\n\n
                \n
              1. Decimal value of 11001010<\/code> when viewed as an unsigned 8-bit integer:<\/strong><\/li>\n<\/ol>\n\n\n\n
                  \n
                • Treat the binary number as an unsigned 8-bit integer, where the value is simply the binary converted to decimal:\n
                    \n
                  • 11001010<\/code> in binary = 202<\/code> in decimal.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
                      \n
                    1. Decimal value of 11001010<\/code> when viewed as a sign magnitude 8-bit integer:<\/strong><\/li>\n<\/ol>\n\n\n\n
                        \n
                      • In sign magnitude form, the most significant bit represents the sign, and the remaining bits represent the magnitude:\n
                          \n
                        • The first bit is 1<\/code>, which indicates a negative number.<\/li>\n\n\n\n
                        • The magnitude part is 1001010<\/code>, which is 74<\/code> in decimal.<\/li>\n\n\n\n
                        • Therefore, the decimal value is -74<\/code>.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
                            \n
                          1. 32-bit floating point representation of 1.5 in binary and hex form:<\/strong>
                            A 32-bit IEEE 754 floating point number is divided into three parts:<\/li>\n<\/ol>\n\n\n\n
                              \n
                            • 1 bit for the sign.<\/li>\n\n\n\n
                            • 8 bits for the exponent (with a bias of 127).<\/li>\n\n\n\n
                            • 23 bits for the fraction (mantissa).<\/li>\n\n\n\n
                            • For 1.5, the normalized binary representation is 1.1<\/code> (which is 1.5<\/code> in binary).<\/li>\n\n\n\n
                            • The exponent is 0 (since 1.5 = 1.1 * 2^0<\/code>), so the exponent with bias 127 is 127 + 0 = 127<\/code>.<\/li>\n\n\n\n
                            • Convert 127 to binary: 01111111<\/code>.<\/li>\n\n\n\n
                            • The mantissa is the fractional part after the leading 1, which is .1<\/code>, so the mantissa is 10000000000000000000000<\/code> (padding with zeros to 23 bits). The final IEEE 754 representation of 1.5 is:<\/li>\n\n\n\n
                            • Binary:<\/strong> 0 01111111 10000000000000000000000<\/code><\/li>\n\n\n\n
                            • Hex:<\/strong> 0x3F800000<\/code><\/li>\n<\/ul>\n\n\n\n
                                \n
                              1. How many bits would a complete load instruction need to have to hold a main memory address of decimal 65536?<\/strong><\/li>\n<\/ol>\n\n\n\n
                                  \n
                                • To store a memory address of 65536<\/code>, we need to find how many bits are required to represent this value.<\/li>\n\n\n\n
                                • First, convert 65536<\/code> to binary:\n
                                    \n
                                  • 65536<\/code> in decimal = 10000000000000000<\/code> in binary (17 bits).<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                                  • So, the instruction that holds a memory address must have at least 17 bits<\/strong> to accommodate the address 65536<\/code>.<\/li>\n<\/ul>\n\n\n\n

                                    Let me know if you need further clarification on any part!<\/p>\n","protected":false},"excerpt":{"rendered":"

                                    The Correct Answer and Explanation is : Let’s break down each of your questions step by step: Let me know if you need further clarification on any part!<\/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-193218","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/193218","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=193218"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/193218\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=193218"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=193218"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=193218"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}