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GATE CSE 2022 Q41: IEEE-754 single precision values in three registers

Question

Consider three floating point numbers AA, BB and CC stored in registers RAR_A, RBR_B and RCR_C, respectively as per IEEE-754 single precision floating point format. The 32-bit content stored in these registers (in hexadecimal form) are as follows.

RAR_A = 0xC1400000RBR_B = 0x42100000RCR_C = 0x41400000

Which one of the following is FALSE?

Try it: multiple choice: exactly one correct option

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Answer: B (official GATE 2022 final answer key)

Concept used: Decode sign (1 bit), biased exponent (8 bits, bias 127) and mantissa (23 bits with hidden 1).

First step: 0x41400000 has sign 0, exponent 130−127=3130 - 127 = 3 and mantissa 1.121.1_2, so C=1.5×23C = 1.5 \times 2^3; decode A and B the same way.

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Source: official GATE 2022 CS question paper and final answer key, organised by IIT Kharagpur. Question paper · Answer key

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