F(A,B,C,D) = π (0, 1, 2, 3, 4, 6, 9, 11, 13) Reduce the Boolean function F(A,B,C,D) = π (0, 1, 2, 3, 4, 6, 9, 11, 13) by using 4-variable Karnaugh map…

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Reduce the following using a Karnaugh map.

F(A,B,C,D) = π (0, 1, 2, 3, 4, 6, 9, 11, 13) Reduce the Boolean function F(A,B,C,D) = π (0, 1, 2…

$F(A,B,C,D) = \pi (0, 1, 2, 3, 4, 6, 9, 11, 13)$

(a)[4]

Reduce the Boolean function $F(A,B,C,D) = \pi (0, 1, 2, 3, 4, 6, 9, 11, 13)$ by using 4-variable Karnaugh map, showing the various groups (i.e. octal, quads and pairs).

(b)[1]

Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs.

Draw: logic gate diagram for the reduced expression

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Answer

Answer (a)

Groups: (9, 13) → (A' + C + D'); (0, 2, 4, 6) → (A + D); (1, 3, 9, 11) → (B + D')

Reduced expression: F = (A' + C + D').(A + D).(B + D')

Maxterms (0s) grouped: quad (0, 2, 4, 6) gives (A + D), quad (1, 3, 9, 11) gives (B + D'), pair (9, 13) gives (A' + C + D').

Answer (b)

Logic gate diagram for $F(A,B,C,D) = (A+D) \cdot (B+D') \cdot (A'+C+D')$: three OR gates feeding one AND gate.