# Design a multiplexer circuit

• Engineering
Homework Helper

## 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:

## 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.

gneill
Mentor
Looks okay. You might have considered using a Karnaugh Map approach which would yield the two terms by inspection.

NascentOxygen
Staff Emeritus
How did you fill in the P and Q columns?

Homework Helper
How did you fill in the P and Q columns?

When ##C = 0##, the value of ##Q## does not matter and the value of ##X## depends only on ##A##.

Similarly when ##C = 1##, the value of ##P## does not matter and the value of ##X## depends only on ##B##.

This gives half a column of ##Q##s and ##P##s that do not matter. I could have filled those in with a ##d## or ##-##, but that was the problem statement provided and they seemed to have used a ##0##.

NascentOxygen
Staff Emeritus
This question is a bit puzzling. It's as though that table belongs to some other question and accidently got mixed in here.

The task is wholly described in just these lines:

Design a multiplexer circuit given the data such that:

When C=0, the output X=A.
When C=1, the output X=B.

The table with signals P and Q is either a mistake or a red herring, IMO.