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GATE 2020 EC – Question 48

Digital Circuits · Number Representations · 2 marks · Multiple choice

P, Q, and R are the decimal integers corresponding to the 4-bit binary number 1100 considered in signed magnitude, 1's complement, and 2's complement representations, respectively. The 6-bit 2's complement representation of $(P+Q+R)$ is

  1. 110101
  2. 110010
  3. 111101
  4. 111001

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Correct answer: (A) 110101

Explanation

In signed magnitude 1100 is $-4$ (sign bit 1, magnitude 100). In 1's complement, 1100 is $-(0011)_2=-3$. In 2's complement, 1100 is $-(0100)_2=-4$. So $P+Q+R=-4-3-4=-11$, whose 6-bit 2's complement is $64-11=53=110101$.