Question

Which of the following doesn't represent exclusive NOR of X and Y?

Answer 1

Answer:

Explanation:

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

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.

Answer : (D)