Consider IEEE-754 single precision numbers: RA = 0xC1400000 (A), RB = 0x42100000 (B), RC = 0x4140000

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GATE-CS is a competitive examination conducted in India. This question is from the 2022 GATE-CS Digital Logic paper.

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Question

Consider IEEE-754 single precision numbers: RA = 0xC1400000 (A), RB = 0x42100000 (B), RC = 0x41400000 (C). Which one of the following is FALSE?

Accepted Answer

Correct Answer: (B) C = A + B is FALSEConcept -- IEEE-754 Single Precision Decoding (from Patterson and Hennessy, Computer Organization and Design):Decode RA = 0xC1400000: Sign=1(neg), Exp=10000010=130, Bias=127, exp=3. Mantissa=1.1=1.5. A = -1.5 * 2^3 = -12.Decode RB = 0x42100000: Sign=0(pos), Exp=10000100=132, Bias=127, exp=5. Mantissa=10001=1.00010 wait: 0x42100000 = 0 10000100 00100000..0. Mantissa=1.001. B = 1.001 * 2^5 = 1.125 * 32 = 36.Decode RC = 0x41400000: Sign=0(pos), Exp=10000010=130, Bias=127, exp=3. Mantissa=1.1=1.5. C = 1.5 * 2^3 = 12.Check options: (A) A+C = -12+12 = 0. TRUE (so A is not false). (B) C = A+B: 12 = -12+36 = 24. FALSE! 12 != 24. (B) is FALSE. (C) B = C+3: 36 = 12+3 = 15? Not 36. Wait: B-C = 36-12=24, not 3. Recalculate B. 0x42100000: binary 0 10000100 00100000000000000000000. Exp=132-127=5. Mantissa=1.00100...=1.125. B=1.125*32=36. C-A=12-(-12)=24. So B=C*3=36 and C=A+B means 12=-12+36=24 which is false. (B) is the false statement.

Consider IEEE-754 single precision numbers: RA = 0xC1400000 (A), RB = 0x42100000 (B), RC = 0x41400000 (C). Which one of the following is FALSE?

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Consider IEEE-754 single precision numbers: RA = 0xC1400000 (A), RB = 0x42100000 (B), RC = 0x41400000 (C). Which one of the following is FALSE?

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