The GATE Grind

GATE 2018 CS – Question 14

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

Let $\oplus$ and $\odot$ denote the Exclusive OR and Exclusive NOR operations, respectively. Which one of the following is NOT CORRECT?

  1. $\overline{P\oplus Q}=P\odot Q$
  2. $\bar P\oplus Q=P\odot Q$
  3. $\bar P\oplus\bar Q=P\oplus Q$
  4. $(P\oplus\bar P)\oplus Q=(P\odot\bar P)\odot\bar Q$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (D) $(P\oplus\bar P)\oplus Q=(P\odot\bar P)\odot\bar Q$

Explanation

$P\oplus\bar P=1$, so the left side is $1\oplus Q=\bar Q$. On the right, $P\odot\bar P=0$ and $0\odot\bar Q=Q$. So the two sides are $\bar Q$ and $Q$, which are not equal. A, B and C are standard XOR/XNOR identities.