Multiplexer

Introduction to Multiplexer(MUX)

Multiplexer:-

1. It is a combinational circuit.

The basic design unit of MUX is : $2^{n} \rightarrow 1$

It means in a $2^{n} \rightarrow 1$ MUX, there are

$2^{n}$ input lines
$n$ select lines // Select lines are used to select the inputs.
1 output

2. A multiplexor is a functionally complete combinational circuit. for example, a 4*1 MUX can represent any Boolean function of two variable.

3. To implement an n variable boolean function you need $2^{n}\rightarrow 1$ MUX, in normal case.

Implementing 4*1 MUX

${\color{Red} f= S_{1}'S_{0}'I_{0} +S_{1}'S_{0}I_{1} +S_{1}S_{1}'I_{2}+ S_{1}S_{0}I_{3}}$

Sometimes you need $2^{n-1}\rightarrow 1$ to implement an n variable boolean function, but you need some additional circuit to implement this.

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Multiplexer:
A multiplexer is a combinational circuit that selects one of several input signals and forwards the selected input into a single output line.
A multiplexer of 2ⁿ inputs has n select lines, which are used to select which input line to send to the output.
The block diagram of a 4x1 multiplexer is as below:

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