gate 2017

Question

Given f(w, x, y, z) = Σ_m(0,1,2,3,7,8,10) + Σ_d(5,6,11,15), where d represents the don’t-care condition in Karnaugh maps. Which of the following is a minimum product-of-sums(POS) form of f(w,x,y,z)?

a:    f = (w' + z' )( x' + z )

B:  f = (w' + z ) ( x + z )

C:  f = ( w + z ) ( x ' + z )

D:  f = ( w + z' ) ( x' + z )

Answer 1

1	1	1	1
0	X	1	X
0	0	X	0
1	0	X	1

f'=wz+xz'

f = (w' + z' )( x' + z )