The GATE Grind

GATE 2014 EC (EC2) – Question 26

Digital Circuits · Combinatorial Circuits · 1 mark · Multiple choice

A half-subtractor has inputs X,Y and difference N = X − Y. Find borrow M and difference N.

  1. $M=X\oplus Y,\ N=XY$
  2. $M=XY,\ N=X\oplus Y$
  3. $M=\overline XY,\ N=X\oplus Y$
  4. $M=X\overline Y,\ N=\overline{X\oplus Y}$

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Correct answer: (C) $M=\overline XY,\ N=X\oplus Y$

Explanation

Subtracting Y from X produces a borrow only for X=0,Y=1, so M=X̄Y. The one-bit difference is1whenever the inputs differ, giving N=X XOR Y. Thus **M=X̄Y,N=X XOR Y,C**. The borrow direction follows the specified subtraction X−Y.