GATE | GATE CS Mock 2018 | Set 2 | Question 63

Given f(x, y, w, z) = Σm(0, 1, 2, 3, 7, 8, 10) + Σd(5, 6, 11, 15), where d represents the don’t-care condition in Karnaugh maps. Which of the following is a minimum sum of products (SOP) form of f(x, y, w, z)?
(A) f = y’z’ + x’y’ + wz
(B) f = w’z’ + w’x’ + yz
(C) f = y’z’+x’z
(D) f = (y’ + z’ )( w’ + z )


Answer: (C)

Explanation: Given f(x, y, w, z) = Σm(0,1,2,3,7,8,10) + Σd(5,6,11,15), note that the order of variables are x, y, w, z but not w, x, y, z.
K-map of given function is :


The minimized sum of products is f = y’z’+x’z.

Note that y’z’ + x’y’ + wz is also correct SOP, but it is minimized.



Option (C) is correct.

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