GATE | GATE CS 2013 | Question 65

Which one of the following expressions does NOT represent exclusive NOR of x and y?
(A) xy+x’y’
(B) x⊕y’
(C) x’⊕y
(D) x’⊕y’

Answer: (D)

Explanation: By Definition of XNOR, $x\odot y = x' y' + xy$
So Option-A is correct.
Also by Definition of XOR, $x\oplus y = x' y + xy'$
Option-B is $x\oplus y' = x' y' + x(y')' = x' y' + xy = x\odot y$
So Option-B is also correct.
Option-C is $x' \oplus y = (x')' y + x' y' = x' y' + xy = x\odot y$
Option-C is also correct.
Option-D x’⊕y’ = x”y’ + x’y” = xy’ + x’y = x⊕y ≠ x⊙y