GATE CS 2025 Set 1 | Question 25

MSQ · 1 mark

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?

  1. Option A: 1000 1010 in 8-bits
  2. Option B: 1111 1010 in 8-bits (correct)
  3. Option C: 1000 0000 0000 1010 in 16-bits
  4. Option D: 1111 1111 1111 1010 in 16-bits (correct)

Answer

(B), (D)

Explanation

To widen a 2’s complement number, copy its sign bit into every new position (sign extension). The sign bit of 1010 is 1, so \(-6\) is 1111 1010 in 8 bits and 1111 1111 1111 1010 in 16 bits.

  • (A) False: 1000 1010 is \(-128 + 10 = -118\).
  • (B) True: 1111 1010 is \(-128 + 122 = -6\).
  • (C) False: 1000 0000 0000 1010 is \(-32768 + 10 = -32758\).
  • (D) True: it is 1010 sign-extended to 16 bits, value \(-6\).

Answer: B, D