The number –6 can be represented as 1010 in 4-bit 2's complement representation. Which of the follow

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Question

The number –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?

Accepted Answer

Correct Answer: (B) and (D)Concept — Sign Extension in 2's Complement: To extend a 2's complement number to a wider bit width while preserving its value, the sign bit (MSB) is replicated (copied) into all the newly added bit positions on the left. This is called sign extension.Given: −6 in 4-bit 2's complement = 1010. The sign bit = 1 (negative number).Extending to 8 bits: Replicate the sign bit (1) into the 4 new leftmost positions:1010 → 1111 1010Verification: 1111 1010 in 8-bit 2's complement = −(0000 0110) = −6. ✓ → Option B is correct.Extending to 16 bits: Replicate the sign bit (1) into the 12 new leftmost positions:1010 → 1111 1111 1111 1010Verification: This is −6 in 16-bit 2's complement. ✓ → Option D is correct.Why Options A and C are wrong:Option A (1000 1010): The leading 4 bits are 1000, not 1111. The sign bit (1) is placed only in the MSB position, while the other 3 new bits are 0. This does not correspond to −6; this represents −118 in 8-bit 2's complement.Option C (1000 0000 0000 1010): Similarly, only the MSB is 1 and the rest of the extension bits are 0. This does not represent −6.Key rule: For sign extension of a negative number in 2's complement, fill ALL new high-order bits with 1, not just the MSB.

The number –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?

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The number –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?

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Frequently Asked Questions