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GATE CSE 2025 Session 2 Q49: Relations among three IEEE 754 single-precision values

Question

Three floating point numbers XX, YY, and ZZ are stored in three registers RXR_X, RYR_Y, and RZR_Z, respectively in IEEE 754 single precision format as given below in hexadecimal:

RXR_X = 0xC1100000, RYR_Y = 0x40C00000, and RZR_Z = 0x41400000

Which of the following option(s) is/are CORRECT?

Try it: multiple select: one or more correct options

Select one or more options
Select all correct options. No negative marking, no partial marks.
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Answer: A, B, C (official GATE 2025 final answer key)

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

First step: 0xC1100000 has sign 1, exponent 130−127=3130 - 127 = 3 and significand 1.0012=1.1251.001_2 = 1.125, so X=−9X = -9; decode YY and ZZ the same way.

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Source: official GATE 2025 Session 2 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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