# GATE | GATE-CS-2006 | Question 38

Consider a Boolean function f (w, x, y, z). suppose that exactly one of its inputs is allowed to change at a time. If the function happens to be true for two input vectors i1 = (w1, x1, y1, z1) and i2 = (w2, x2, y2, z2) we would like the function to remain true as the input changes from i1 to i2 (i1 and i2 differ in exactly one bit position), without becoming false momentarily. Let f (w, x, y, z) = ∑(5,7,11,12,13,15). Which of the following cube
covers of f will ensure that the required property is satisfied?

(A) w’xz, wxy’, xy’z, xyz,wyz
(B) wxy,w’xz,wyz
(C) wx(yz)’, xz, wx’yz
(D) wzy, wyz, wxz, w’xz, xy’z, xyz

Explanation:
We construct the K – Map as : After simplification of this K – Map we get answer as : w’xz, wxy’, xy’z, xyz, wyz

Thus, option (A) is the answer.

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