The GATE Grind

GATE 2016 CS – Question 16

Digital Logic · Boolean Algebra and Minimization · 1 mark · Multiple choice

Consider the Boolean operator $\#$ with the following properties: $x \# 0 = x$, $x \# 1 = \bar{x}$, $x \# x = 0$ and $x \# \bar{x} = 1$. Then $x \# y$ is equivalent to

  1. $x\bar{y} + \bar{x}y$
  2. $x\bar{y} + \bar{x}\bar{y}$
  3. $\bar{x}y + xy$
  4. $xy + \bar{x}\bar{y}$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $x\bar{y} + \bar{x}y$

Explanation

The properties match exclusive-OR. $x \oplus 0 = x$, $x \oplus 1 = \bar{x}$, $x \oplus x = 0$ and $x \oplus \bar{x} = 1$. Exclusive-OR is written $x\bar{y} + \bar{x}y$.