Simplify the following Boolean functions by first finding th

Simplify the following Boolean functions by first finding the essential prime implicants: i) F(A, B, C, D) = sigma (0, 1, 3, 7, 8, 9, 10, 13, 15) ii) F(w, x, y, z) = sigma(0, 1, 2, 4, 5, 6, 7, 10, 15) Simplify the following product of sum Boolean function: F(A, B, C, D) = Product (1, 3, 6, 9, 11, 12, 14)

Solution

F(A,B,C,D) = (0,1,3,7,8,9,10,13,15)

F = A\'B\'C\'+A\'CD+AC\'D+AB\'D\'

F = A\'(B\'C\'+CD)+A(C\'D+B\'D\')

F = (W,X,Y,Z) = (0,1,2,4,5,6,7,10,15)

F = W\'X+X\'YZ\'+WY\'Z

AB/CD	A\'B\'	A\'B	AB	AB\'
C\'D\'	1			1
C\'D	1		1	1
CD	1	1
CD\'			1	1