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Reduce the following using a Karnaugh map.
Given the Boolean function F(A, B, C, D) = Σ(0, 1, 2, 3, 4, 6, 9, 11, 13). Reduce the above…
Given the Boolean function $F(A, B, C, D) = \Sigma(0, 1, 2, 3, 4, 6, 9, 11, 13)$.
(a)[4]
Reduce the above expression 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
Must show: variables and their complements as inputs
Answer
Answer (a)
Groups: (0, 2, 4, 6) → A'D'; (1, 3, 9, 11) → B'D; (9, 13) → AC'D
Reduced expression: F = A'D' + B'D + AC'D
Two quads {0,2,4,6} = A'D' and {1,3,9,11} = B'D, and a pair {9,13} = AC'D.
Answer (b)
Logic gate diagram for $F = A'D' + B'D + AC'D$: two 2-input AND gates and one 3-input AND gate feeding a 3-input OR gate.