Consider the following minterm expression for F(P,Q,R,S):
F(P,Q,R,S) = sum(0, 2, 5, 7, 8, 10, 13, 15)
The minterms 2, 7,...

Question

Consider the following minterm expression for F(P,Q,R,S):
F(P,Q,R,S) = sum(0, 2, 5, 7, 8, 10, 13, 15)
The minterms 2, 7, 8 and 13 are 'do not care' terms. The minimal sum-of-products form for F is
A. Q'S' + QS
B. Q'S' + QS + PQ'S + P'QS'
C. Q'S' + QRS + QR'S'
D. PR + RS + PS

Accepted Answer

The minimal SOP is Q'S' + QS (Option A). We have a 4-variable Boolean function F with minterms at positions 0,2,5,7,8,10,13,15. Minterms 2,7,8,13 are don't-care terms (we can treat them as 0 or 1 to get the simplest expression). Using a K-map we find the largest possible groupings.

Consider the following minterm expression for F(P,Q,R,S): F(P,Q,R,S) = sum(0, 2, 5, 7, 8, 10, 13, 15) The minterms 2, 7, 8 and 13 are 'do not care' terms. The minimal sum-of-products form for F is A. Q'S' + QS B. Q'S' + QS + PQ'S + P'QS' C. Q'S' + QRS + QR'S' D. PR + RS + PS