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GATE CSE 2023 Q45: IEEE-754 product of 0xC1800000 and 0x3F5C2EF4

Question

Consider the IEEE-754 single precision floating point numbers P=0xC1800000 and Q=0x3F5C2EF4.

Which one of the following corresponds to the product of these numbers (i.e., P × Q), represented in the IEEE-754 single precision format?

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Answer: C (official GATE 2023 final answer key)

Concept used: Multiplying by a power of two changes only the sign and exponent fields, not the mantissa.

First step: Decode P: sign 1, biased exponent 0x83=1310x83 = 131, mantissa 0, so P=−24=−16P = -2^4 = -16.

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Source: official GATE 2023 CS question paper and final answer key, organised by IIT Kanpur. Question paper · Answer key

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