ITPEC FE Subject A October 2025 Question 1

IEEE 754 Floating Point — parse a 32-bit binary representation.

Parse 0 10000010 11000000000000000000000:

• •S = 0 → positive
• •E = 10000010 = 128 + 2 = 130
• •F = 11000000000000000000000 → 2⁻¹ + 2⁻² = 0.5 + 0.25 = 0.75

Value = (-1)⁰ × 2^(130−127) × (1 + 0.75) = 1 × 8 × 1.75 = 14.0

Why not others:
- (a) 0.1875 — would require a negative exponent (E < 127)
- (b) 0.4375 — would require a negative exponent (E < 127)
- (c) 6.0 — would be 2² × 1.5 (E=129, F=0.5)

Key rule: Formula is (-1)^S × 2^(E−127) × (1+F) for 32-bit floats. Convert E from binary, compute F as sum of 2^(−i) for each set bit.

AI-generated — may contain errors