{"id":44358,"date":"2025-06-30T15:17:56","date_gmt":"2025-06-30T15:17:56","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=44358"},"modified":"2025-06-30T15:17:57","modified_gmt":"2025-06-30T15:17:57","slug":"select-the-correct-answer-that-corresponds-to-the-floating-point-representation-of-the-decimal-number","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/select-the-correct-answer-that-corresponds-to-the-floating-point-representation-of-the-decimal-number\/","title":{"rendered":"Select the correct answer that corresponds to the floating-point representation of the decimal number"},"content":{"rendered":"\n

Select the correct answer that corresponds to the floating-point representation of the decimal number: -8.625 Select one: a. \u2022 S=1 \u2022 E=10000010 \u2022 Fraction=1110101 b. \u2022 S=0 \u2022 E=10000010 \u2022 Fraction=000101 c. \u2022 S=0 \u2022 E=00000010 \u2022 Fraction=110101 d. \u2022 S=1 \u2022 E=10000010 \u2022 Fraction=000101<\/p>\n\n\n\n

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

To represent the decimal number -8.625 in IEEE 754 single-precision floating-point format, we need to go through a series of steps. The IEEE 754 single-precision format consists of:<\/p>\n\n\n\n

    \n
  1. 1 sign bit (S)<\/strong><\/li>\n\n\n\n
  2. 8 exponent bits (E)<\/strong><\/li>\n\n\n\n
  3. 23 fraction (mantissa) bits<\/strong><\/li>\n<\/ol>\n\n\n\n

    Step 1: Convert the decimal to binary<\/h3>\n\n\n\n

    First, let’s convert the absolute value of the number, 8.625, into binary.<\/p>\n\n\n\n

      \n
    • Integer part (8)<\/strong>:
      Convert 8 to binary:
      8 = 1000\u2082<\/li>\n\n\n\n
    • Fractional part (0.625)<\/strong>:
      Multiply the fractional part by 2 repeatedly until you reach 0 or a repeating pattern:
      0.625 \u00d7 2 = 1.25 \u2192 Take the integer part (1).
      0.25 \u00d7 2 = 0.5 \u2192 Take the integer part (0).
      0.5 \u00d7 2 = 1.0 \u2192 Take the integer part (1).
      So, the fractional part is 0.101\u2082.<\/li>\n<\/ul>\n\n\n\n

      Thus, the binary representation of 8.625 is:
      1000.101\u2082<\/strong>.<\/p>\n\n\n\n

      Step 2: Normalize the binary number<\/h3>\n\n\n\n

      In normalized scientific notation, the binary number should be expressed as a number between 1 and 2. This is done by shifting the binary point.<\/p>\n\n\n\n

      For 1000.101\u2082<\/strong>, we shift the binary point three places to the left to get:
      1.000101 \u00d7 2\u00b3<\/strong>.<\/p>\n\n\n\n

      Step 3: Determine the exponent and bias<\/h3>\n\n\n\n

      In IEEE 754 single-precision, the exponent is stored with a bias of 127. So, the exponent for 2\u00b3 is:
      Exponent = 3 + 127 = 130.<\/p>\n\n\n\n

      In binary, 130 is:
      10000010\u2082<\/strong>.<\/p>\n\n\n\n

      Step 4: Determine the fraction (mantissa)<\/h3>\n\n\n\n

      The mantissa is the part of the number after the binary point in the normalized form, but without the leading 1 (since it is implied). So, for 1.000101<\/strong>, the mantissa is:
      000101<\/strong>.<\/p>\n\n\n\n

      Step 5: Sign bit<\/h3>\n\n\n\n

      Since the original number is negative (-8.625), the sign bit (S) will be 1.<\/p>\n\n\n\n

      Putting it all together:<\/h3>\n\n\n\n
        \n
      • Sign bit (S)<\/strong> = 1 (since the number is negative)<\/li>\n\n\n\n
      • Exponent (E)<\/strong> = 10000010\u2082 (which is 130 in decimal)<\/li>\n\n\n\n
      • Fraction (Mantissa)<\/strong> = 000101 (just the bits after the leading 1)<\/li>\n<\/ul>\n\n\n\n

        Thus, the correct IEEE 754 representation is:
        S = 1, E = 10000010, Fraction = 000101<\/strong>.<\/p>\n\n\n\n

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

        The correct answer is d. S=1, E=10000010, Fraction=000101<\/strong>.<\/p>\n\n\n\n

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

        Select the correct answer that corresponds to the floating-point representation of the decimal number: -8.625 Select one: a. \u2022 S=1 \u2022 E=10000010 \u2022 Fraction=1110101 b. \u2022 S=0 \u2022 E=10000010 \u2022 Fraction=000101 c. \u2022 S=0 \u2022 E=00000010 \u2022 Fraction=110101 d. \u2022 S=1 \u2022 E=10000010 \u2022 Fraction=000101 The Correct Answer and Explanation is: To represent the decimal […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-44358","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44358","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=44358"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44358\/revisions"}],"predecessor-version":[{"id":44364,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44358\/revisions\/44364"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=44358"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=44358"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=44358"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}