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GATE 2012 CS (CS1) – Question 17

Digital Logic · Number Representation and Arithmetic · 1 mark · Multiple choice

The decimal number 0.5 in IEEE single precision has

  1. all-zero fraction bits and exponent value 0
  2. all-zero fraction bits and exponent value −1
  3. fraction bits 100…000 and exponent value 0
  4. no exact representation

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Show answer and explanation

Correct answer: (B) all-zero fraction bits and exponent value −1

Explanation

Normalize $0.5=1.0\times2^{-1}$. The implicit leading one leaves an all-zero fraction field and the unbiased exponent is −1. Thus B. The stored biased exponent field is 126, distinct from the exponent value asked here.

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