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Question
Given the Boolean function F(A, B, C, D) = ∑(2, 3, 6, 7, 8, 10, 12, 14, 15).
- Reduce the above expression by using 4- variable Karnaugh map, showing the various groups (i.e., octal, quads and pairs.
- Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs.
Solution
(a) Karnuagh Map
Quad1 (m2, m3, m6, m7) = AC'
Quad1 (m6, m7, m14, m15) = AD
Pair1 (m8, m12) = A'B'C
Pair2 (m10, m14) = AB'C
Reduced expression : AC’ + AD + A'B'C + AB'C
(b) Logic circuit diagram of the reduced expression
F = AC' + AD + A'B'C + AB'C
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