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## Homework Statement

Design a multiplexer circuit given the data such that:

When ##C = 0##, the output ##X = A##.

When ##C = 1##, the output ##X = B##.

The truth table is displayed below:

## Homework Equations

## The Attempt at a Solution

I wanted to make sure I understood this and I wasn't overlooking anything.

Looking at the ##A##, ##C## and ##P## columns, I deduced I needed a term of the form ##A \cdot \bar C##.

Looking at the ##B##, ##C## and ##Q## columns, I deduced I needed a term of the form ##B \cdot C##.

Looking at the ##P##, ##Q## and ##X## columns, I see I need a gate that satisfies ##\bar P \cdot Q + P \cdot \bar Q + P \cdot Q##.

That last expression can be simplified to:

##\bar P \cdot Q + P \cdot \bar Q + P \cdot Q = \bar P \cdot Q + P(\bar Q + Q) = \bar P \cdot Q + P = Q + P##

So from what I can gather, ##Q + P = B \cdot C + A \cdot \bar C##.

Hence ##X = Q + P = B \cdot C + A \cdot \bar C##.

Thank you.