Question

Reduce the Boolean function F(A,B,C,D) = π (0,1,2,3,7,8,9,10,11,12,13,15) by using 4-variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs).

Answer 1

To reduce F(A, B, C, D) = π(0, 1, 2, 3, 7, 8, 9, 10, 11, 12, 13, 15) using a 4-variable K-map:

K-map Mapping (POS):

Fill cells 0, 1, 2, 3, 7, 8, 9, 10, 11, 12, 13, 15 with 0.

	CD (00)	CD (01)	CD (11)	CD (10)
AB (00)	0	0	0	0
AB (01)	4	5	0	6
AB (11)	0	0	0	14
AB (10)	0	0	0	0

Octet (Cells 0,1,3,2 & 8,9,11,10): Top and bottom rows combined. ⇒ B
Quad 1 (Cells 8,9,12,13): Bottom-left square. ⇒ (A′ + C)

Quad 2 (Cells 3,7,15,11): Third column vertical group. ⇒ (C′ + D)

F(A, B, C, D) = B.(A′ + C).(C′ + D′)