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+16 votes

Which one of the following expressions does **NOT** represent exclusive NOR of $x$ and $y$?

- $xy + x′ y′$
- $x\oplus y′$
- $x′\oplus y$
- $x′\oplus y′$

+20 votes

Best answer

$A$ : means both are either true OR both are false. then it will be true = ExNOR

$B$ & $C$ : whenever any one of the literal is complemented then ExOR can be turned to ExNOR and complement sign on the literal can be removed. So these two also represents ExNOR operation of $x$ and $y$.

Answer is option D. **I**t is the ExOR operation b/w the two.

+7 votes

The exclusive NOR and exclusive OR of x and y is given by the expressions

x⊙y = x.y + x'.y' (exclusive NOR or XNOR)

x⊕y = x'.y + x.y' (exclusive OR or XOR)

So (A) is automatically true.

(B) is x⊕y' which evaluates to x'.y' + x.(y')' (as per the formula above for XOR) = x'.y' + x.y which is equivalent to x⊙y.

(C) is x'⊕y which evaluates to (x')'.y + x'.y' (as per the formula above for XOR) = x.y + x'.y' which is equivalent to x⊙y.

(D) is x'⊕y' which evaluates to (x')'.y' + x'.(y')' (as per the formula above for XOR) = x.y' + x'.y which is NOT equivalent to x⊙y.

Hence D is FALSE.

x⊙y = x.y + x'.y' (exclusive NOR or XNOR)

x⊕y = x'.y + x.y' (exclusive OR or XOR)

So (A) is automatically true.

(B) is x⊕y' which evaluates to x'.y' + x.(y')' (as per the formula above for XOR) = x'.y' + x.y which is equivalent to x⊙y.

(C) is x'⊕y which evaluates to (x')'.y + x'.y' (as per the formula above for XOR) = x.y + x'.y' which is equivalent to x⊙y.

(D) is x'⊕y' which evaluates to (x')'.y' + x'.(y')' (as per the formula above for XOR) = x.y' + x'.y which is NOT equivalent to x⊙y.

Hence D is FALSE.

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