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GATE 2025 CS (CS1) – Question 25

Digital Logic · Number Representation and Arithmetic · 1 mark · Multiple select

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. 1000 1010 in 8-bits
  2. 1111 1010 in 8-bits
  3. 1000 0000 0000 1010 in 16-bits
  4. 1111 1111 1111 1010 in 16-bits

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Show answer and explanation

Correct answer: (B) 1111 1010 in 8-bits; (D) 1111 1111 1111 1010 in 16-bits

Explanation

Sign extension replicates the sign bit. -6 is 1111 1010 in 8 bits and 1111 1111 1111 1010 in 16 bits. Padding with 1000... gives a different value.