Question

Given the following truth table, driven a Sum of Product (SOP) and Product of Sum (POS) form of Boolean expression from it :

x	y	z	G(x,y,z)
0	0	0	0
0	0	1	1
0	1	0	1
0	1	1	0
1	0	0	0
1	0	1	1
1	1	0	0
1	1	1	1

Answer 1

The desired Canonical Sum-of-Product form is as following;

G = ∑(1, 2, 5, 7) = X’Y’Z + X’YZ’ + XY’Z + XYZ

The desired Canonical Product-of-Sum form is as following;

G = π(0, 3, 4, 6) = (X + Y + Z)(X + Y’ + Z’)(X’ + Y + Z)(X’ + Y’ + Z)