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Answer the following.
Given the Boolean function F(A,B,C,D) = Σ(2, 3, 6, 7, 8, 10, 12, 14, 15). Reduce the above…
Given the Boolean function $F(A,B,C,D) = \Sigma(2, 3, 6, 7, 8, 10, 12, 14, 15)$.
(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: (8, 10, 12, 14) → AD'; (2, 3, 6, 7) → A'C; (6, 7, 14, 15) → BC
Reduced expression: F = AD' + A'C + BC
Quad (8, 10, 12, 14) gives AD'. Quad (2, 3, 6, 7) gives A'C. Quad (6, 7, 14, 15) gives BC. There is no octet.
Answer (b)
Logic gate diagram for $F = AD' + A'C + BC$: three 2-input AND gates feeding one 3-input OR gate.