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Answer the following.
Given the Boolean function F(A,B,C,D) = π(0, 1, 2, 4, 5, 8, 10, 11, 14, 15). Reduce the above…
Given the Boolean function $F(A,B,C,D) = \pi(0, 1, 2, 4, 5, 8, 10, 11, 14, 15)$.
(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: (10, 11, 14, 15) → (A' + C'); (0, 1, 4, 5) → (A + C); (0, 2, 8, 10) → (B + D)
Reduced expression: F = (A' + C')(A + C)(B + D)
Quad (10, 11, 14, 15) gives (A' + C'). Quad (0, 1, 4, 5) gives (A + C). Quad (0, 2, 8, 10) gives (B + D). There is no octet.
Answer (b)
Logic gate diagram for $F = (A' + C')(A + C)(B + D)$: three 2-input OR gates feeding one 3-input AND gate.