(i) Given the Boolean function F(A,B,C,D) = ∑(0, 1, 2, 3, 4, 6, 9, 11, 13).
(a) Reduce the above expression by using 4-variable Karnaugh map, showing the various groups (i.e. octal, quads and pairs).
(b) Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs.

(ii) Given the Boolean function F(A,B,C,D) = π(0, 1, 3, 5, 6, 7, 9, 11, 13, 14, 15). (a) Reduce the above expression by using 4-variable Karnaugh map, showing the various groups(i.e. octal, quads and pairs).
(b) Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs

Solution

(i) (a)

F(A,B,C,D) = A'D + B'D + AC'D

(b)

(ii) (a)

F(A,B,C,D) = D' . (B'+C') . (A+B+C)

(b)