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GATE 2014 CS (CS2) – Question 55

Computer Organization and Architecture · Number Representation and Floating Point Arithmetic · 2 marks · Multiple choice

IEEE-754 single precision uses 1 sign bit, 8 biased-exponent bits and 23 fraction bits. Float X = −14.25. Find its hexadecimal representation.

  1. C1640000H
  2. 416C0000H
  3. 41640000H
  4. C16C0000H

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Correct answer: (A) C1640000H

Explanation

14.25=1110.01₂=1.11001₂×2³. Sign is1; biased exponent is127+3=130=10000010₂; fraction starts11001followed by18zeros. The resulting bit pattern is **C1640000H,A**. The leading normalised1 is implicit.