Project ForgeThree floating point numbers X, Y, and Z are stored in three registers RX, RY, and RZ, respectively in IEEE 754 single precision format as given below in hexadecimal: RX = 0xC1100000, RY = 0x40C00000, and RZ = 0x41400000. Which of the following option(s) is/are CORRECT?
- 4(X+Y) + Z = 0
- 2Y − Z = 0
- 4X + 3Z = 0
- DX + Y + Z = 0
Explanation
Decoding: RX=0xC1100000 → sign=1, exponent=130(unbiased3), mantissa=0.125 → X=−(1.125)×2³=−9. RY=0x40C00000 → sign=0, exponent=129(unbiased2), mantissa=0.5 → Y=1.5×2²=6. RZ=0x41400000 → sign=0, exponent=130(unbiased3), mantissa=0.5 → Z=1.5×2³=12. Checking: 4(−9+6)+12=4(−3)+12=0 ✓. 2(6)−12=0 ✓. 4(−9)+3(12)=−36+36=0 ✓. But −9+6+12=9≠0 (D false).
Source: GATE CS 2025 (Session 2 / CS2) (2025)
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