Discussion
Which Boolean expression describes the output ‘X’ in the arrangement given below :
Answer: B
The expression is X = a · (b + c). Reading the diagram from the left: the third input is C-bar, which passes through a NOT gate, so the signal that leaves the NOT gate is C. That signal and B go to the OR gate, which gives (b + c). The output of the OR gate and the input A go to the AND gate, so
\[ X = a \cdot (b + c) \]
The option a + (b · c) would need an AND on the first stage and an OR on the last, which is the reverse of the arrangement, and (a · b) + c would put a and b together. The expression a + b + c would be a single OR gate of the three inputs. The answer is X = a · (b + c).
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