Project ForgeComputer Organization & Architecture
Memory Hierarchy & Floating Point
GATE 2017
Hard
Given the following binary number in 32-bit (single precision) IEEE-754 format:
0011 1110 0110 1101 0000 0000 0000 0000
The decimal value closest to this floating-point number is
- A1.45 × 10¹
- B1.45 × 10⁻¹
- 2.27 × 10⁻¹
- D2.27 × 10¹
Explanation
Sign=0 (positive). Exponent (next 8 bits) = 01111100₂ = 124, so actual exponent = 124−127 = −3. Mantissa (next 23 bits) = 11011010...0 → fraction = 0.8515625, so the significand is 1.8515625. Value = 1.8515625 × 2⁻³ = 1.8515625/8 ≈ 0.23145, which is closest to 2.27×10⁻¹ among the given options.
Source: GATE CS 2017 (Session 2) (2017)
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