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GATE CSE 2025 Session 1 Q25: Sign-extended 2's complement forms of −6

Question

The number −6-6 can be represented as 1010 in 4-bit 2's complement representation. Which of the following is/are CORRECT 2's complement representation(s) of −6-6?

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Answer: B, D (official GATE 2025 final answer key)

Concept used: Sign extension: widen a 2's complement number by copying the sign bit.

First step: The sign bit of 1010 is 1, so every new high-order bit must be 1.

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Source: official GATE 2025 Session 1 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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