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A, B, C and D are input bits, and Y is the out put bit in the XOR gate circuit of the figure given below. Which of the following statements about the sum S of A, B, C, D and Y is correct?
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- S is always either zero or odd
- S is always either zero or even
- S = 1 only if the sum of A, B, C and D is even
- S = 1 only if the sum of A, B, C and D is odd
Correct Option: D
Y = A ⊕ B ⊕ C ⊕ D
= ABCD + ABCD + ABCD + ABCD + ABCD + ABCD + ABCD + ABCD
S = Y + A + B + C + D
Drawing K-map for Y, 
When sum of A, B, C, D is odd, Y = 1
and, S = 0, CY = 0 or 1
when sum of A, B, C, D is even, Y = 0
and, S = 0, CY = 0 or 1
Hence, S is always either zero or even.
