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A Boolean digital circuit is composed using two 4-input multiplexers (M1 and M2) and one 2-input multiplexer (M3) as shown in the figure. X0-X7 are the inputs of the multiplexers M1 and M2 and could be connected to either 0 or 1. The select lines of the multiplexers are connected to Boolean variables A, B and C as shown. Which one of the following set of values of (X0, X1, X2, X3, X4, X5, X6, X7) will realise the Boolean function A + A̅.C̅ + A.B.C?
- (1, 1, 0, 0, 1, 1, 1, 0)
- (1, 1, 0, 0, 1, 1, 0, 1)
- (1, 1, 0, 1, 1, 1, 0, 0)
- (0, 0, 1, 1, 0, 1, 1, 1)
Correct answer: (1, 1, 0, 0, 1, 1, 1, 0)
Solution
The correct option (1, 1, 0, 0, 1, 1, 1, 0) satisfies the Boolean function A + A̅.C̅ + A.B.C by ensuring that for all combinations of A, B, and C, the output evaluates to true when A is true or when A is false and both B and C are false.
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