GATE | GATE-CS-2016 (Set 1) | Question 16

Consider the Boolean operator # with the following properties: x#0 = x, x#1 = x’, x#x = 0 and x#x’ = 1 Then x#y is equivalent to

(A) x’y + xy’
(B) xy’ + (xy)
(C) x’y + xy
(D) xy + (xy)’


Answer: (A)

Explanation: The function # basically represents XOR.

Following are true with XOR.
1) XOR of x with 0 is x itself.
2) XOR of x with 1 is complement of x.
3) XOR of x with x is 0.
4) XOR of x with x’ is 1.

XOR is represented as x’y + y’x.

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