Question

Consider the following Boolean expressions:

I: x.y + x'y'

II: XOR (x', y')

III: XOR (x', y)

Which of the above expressions represents exclusive NOR operation?

1. I and II
2. I and III
3. II and III
4. I, II and III

Answer 1

Correct Answer - Option 2 : I and III

Formula:

XNOR(x, y) = x ⊙ y = x.y + x'.y' 

XOR(x,y) = x ⊕ y = x.y' + x'y

Statement I:  Represents exclusive NOR operation

x.y + x'y' = x ⊙ y

Statement II:  It does not represents exclusive NOR operation

XOR (x', y') =  x' ⊕ y' = x'.(y')' + (x')'.(y')'=   x'.y + x.y' = x ⊕ y

It does not  exclusive OR operation

Statement III:  Represents exclusive NOR operation

XOR (x', y) = x' ⊕ y = x'.y' + (x')'.y =   x'.y' + x.y = x ⊙ y

Therefore option 2 is correct.

NOTE:

⊙ → XNOR

⊕ → XOR