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GATE ECE 2016

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Following is the K-map of a Boolean function of five variables P,Q,R,S and X. The minimum
sum-of –product (SOP) expression for the function is
 

A)  P'Q'SX'+PQ'SX'+QR'S'X+QRS'X

B)  Q'SX'+QS'X

C)  Q'SX+QS'X'

D)  Q'S+QS'

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In the above K Map , if we see :

There is no possibility of merging the cells of the 2 4*4 K Map i.e. for X = 0 and X = 1..

Only two merges of minterms will be there :

a) So the minimum product term in the K Map corresponding to X = 0 , P and R variables are varying bt Q and S are constant..So the product term will be :   Q' S X'

b) Similarly for X = 1 K map we have product term = Q S' X

Hence the minimum SOP will be : Q' S X' + Q S' X

Hence B) should be the correct answer..

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