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 = (w\’ + z\’ )( x\’ + z )
(B) f = w\’z\’ + w\’x\’ + yz
(C) f = y\’z\’ + x\’y\’ + wz
(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\’y\’ + wz.
Option (C) is correct.
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