Question

Reduce the Boolean function F(P, Q, R, S) = ∑(0, 1, 2, 5, 7, 8, 9, 10, 13, 15) by using 4-variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs).

Answer 1

A 4-variable K-map has 16 cells

PQ\RS	00	01	11	10
00	1	1	0	1
01	1	0	0	1
11	1	0	1	0
10	0	1	0	1

By grouping the ones, we get:

Quad covering (P'Q') → Covers minterms {0, 1, 2, 5}

Quad covering (RS') → Covers minterms {8, 9, 10, 13}

Pair covering (Q'R') → Covers minterms {7, 15}

So the simplified expression F = P'Q' +RS' + Q'R'