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Number Representation and Arithmetic

GATE CSE 2012 · Q7

MCQ1 markMedium

Time

The decimal value 0.5 in IEEE single precision floating point representation has

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Solution

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Official answer: B) fraction bits of 000...000 and exponent value of -1

Number Representation and Arithmetic

In IEEE 754 single-precision format:

  1. The binary representation of the decimal number 0.50.5 is (0.1)2(0.1)_2.

  2. Normalized scientific notation is:

    0.5=1.02×2−10.5 = 1.0_2 \times 2^{-1}
  3. The actual exponent value is −1-1 (stored as a biased exponent E=−1+127=126E = -1 + 127 = 126).

  4. The significand has an implicit leading 11, so the stored fraction (mantissa) bits after the binary point are 000…000000\dots000.

Thus, the representation has fraction bits of 000…000000\dots000 and an exponent value of −1-1, which corresponds to option (B).

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This Number Representation and Arithmetic previous year question is Q7 of the GATE CSE 2012 paper. Find more GATE CSE PYQs on Number Representation and Arithmetic in Digital Logic, or browse all GATE CSE PYQs.

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Number Representation and Arithmetic in GATE CSE

Number Representation and Arithmetic has 33 GATE CSE PYQs across 20 papers from 2012 to 2026. 13 of them are 1-mark MCQs like this one, and it is the only one in GATE CSE 2012.

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The decimal value 0.5 in IEEE single precision floating point representation has

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.