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Question 25.SG.Q.6: In the circuit shown in the following figure, X is given by ......

In the circuit shown in the following figure, X is given by

(a) X = A\bar B\bar C + \bar AB\bar C + \bar A\bar BC + ABC

(b) X = AB + BC + AC

(c) X = \bar A\bar B + \bar B\bar C + \bar A\bar C

(d) X = \bar A\bar B + \bar B\bar C + \bar A\bar C

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Let the output of the first MUX be Y. Therefore,

Y = \bar AB + A\bar B = A ⊕ B

X = \bar YC + Y\bar C = Y ⊕ C

Thus,

X = A ⊕ B ⊕ C = \bar A\bar BC + \bar AB\bar C + A\bar B\bar C + ABC

Ans. (a)

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