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Question 25.SG.Q.11: The Boolean function realized by the logic circuit shown in ......

The Boolean function realized by the logic circuit shown in the following figure is

(a) F = ∑ m (0, 1, 3, 5, 9, 10, 14)

(b) F = ∑ m (2, 3, 5, 7, 8, 12, 13)

(c) F = ∑ m (1, 2, 4, 5, 11, 14, 15)

(d) F = ∑ m (2, 3, 5, 7, 8, 9, 12)

1079457-25.11
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\begin{aligned} F(A, B, C, D)= & \bar{A} \bar{B} C+\bar{A} B D+A \bar{B} \bar{C}+A B(\bar{C} \bar{D}) \\ = & \bar{A} \bar{B} C(D+\bar{D})+\bar{A} B(C+\bar{C}) D \\ & +A \bar{B} \bar{C}(D+\bar{D})+A B \bar{C} \bar{D} \end{aligned}

which gives

F = ∑m(2,3,5,7,8,9,12)

Ans. (d)

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