Correct : b

To solve this, we need to decode each of the three IEEE 754 single precision hex values into their actual decimal numbers. IEEE 754 single precision uses 32 bits structured as: 1 sign bit + 8 exponent bits + 23 mantissa bits. The exponent is stored with a bias of 127, meaning the actual exponent = stored exponent − 127. The value formula is:
Value = (−1)^sign × 1.mantissa × 2^{(exponent − 127)}
Decoding RX = 0xC1100000:
Converting to binary: 1100 0001 0001 0000 0000 0000 0000 0000
Sign bit = 1 (negative)
Exponent bits = 10000010 = 130 → actual exponent = 130 − 127 = 3
Mantissa bits = 00100000... = 0.001 → full mantissa = 1.001
Value = −1 × 1.001 × 2³ = −1001 (binary) = −9
So X = −9.
Decoding RY = 0x40C00000:
Converting to binary: 0100 0000 1100 0000 0000 0000 0000 0000
Sign bit = 0 (positive)
Exponent bits = 10000001 = 129 → actual exponent = 129 − 127 = 2
Mantissa bits = 10000000... = 0.1 → full mantissa = 1.1
Value = +1 × 1.1 × 2² = 110 (binary) = 6
So Y = 6.
Decoding RZ = 0x41400000:
Converting to binary: 0100 0001 0100 0000 0000 0000 0000 0000
Sign bit = 0 (positive)
Exponent bits = 10000010 = 130 → actual exponent = 130 − 127 = 3
Mantissa bits = 10000000... = 0.1 → full mantissa = 1.1
Value = +1 × 1.1 × 2³ = 1100 (binary) = 12
So Z = 12.
Now let''s verify all four options with X = −9, Y = 6, Z = 12:
Option A — 4(X+Y)+Z: 4(−9+6)+12 = 4(−3)+12 = −12+12 = 0 ✓ — this actually holds too, but let''s check the official key.
Option B — 2Y−Z: 2(6)−12 = 12−12 = 0 ✓ — correct.
Option C — 4X+3Z: 4(−9)+3(12) = −36+36 = 0 ✓ — this also holds.
Option D — X+Y+Z: −9+6+12 = 9 ≠ 0 ✗ — incorrect.