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Consider the multiplexer based logic circuit shown in the figure. Which one of the following Boolean functions is realized by the circuit?

Consider the multiplexer based logic circuit shown in the figure. Which one of the following Boolean functions is realized by the circuit? Correct Answer F = W ⊕ S<sub style="">1</sub> ⊕ S<sub style="">2</sub>

Concept: 

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For a 2 × 1 MUX is shown above, the output function F is expressed as:

F = S̅1 I0 + S1I1

i.e. when S1 = 0, I0 is transmitted to the output.

And when S1 = 1, I1 is transmitted to the output.

Analysis:

The given circuit is redrawn as:

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F1 = S̅1 w + S1 w̅

F1 = S1 ⊕ w

Now, the required function f will be:

F2 = F = S̅2F1 + S2F̅1

F = S2 ⊕ F1

F = S2 ⊕ S1 ⊕ w

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