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GATE 2024 CS (CS2) – Question 14

Computer Organization and Architecture · Number Representation and Floating Point Arithmetic · 1 mark · Multiple choice

The format of a single-precision floating-point number as per the IEEE 754 standard is Sign (1 bit), Exponent (8 bits), Mantissa (23 bits). Choose the largest floating-point number among the following options. (A) Sign 0, Exponent 0111 1111, Mantissa all 1s (B) Sign 0, Exponent 1111 1110, Mantissa all 1s (C) Sign 0, Exponent 1111 1111, Mantissa all 1s (D) Sign 0, Exponent 0111 1111, Mantissa all 0s

  1. 0 | 0111 1111 | 1111 1111 1111 1111 1111 111
  2. 0 | 1111 1110 | 1111 1111 1111 1111 1111 111
  3. 0 | 1111 1111 | 1111 1111 1111 1111 1111 111
  4. 0 | 0111 1111 | 0000 0000 0000 0000 0000 000

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Show answer and explanation

Correct answer: (B) 0 | 1111 1110 | 1111 1111 1111 1111 1111 111

Explanation

Exponent 1111 1111 with non-zero mantissa is NaN, not a number. The largest finite value has exponent 1111 1110 with all-ones mantissa.