# Multiplexers

Multiplexer(MUX) is a device that allows digital signals from several sources to be routed onto a single line of output. It has several input lines and a single output line. It has also data selector lines which specifies which input signal has to be switched to the output line. n data selector lines are required for routing 2n input lines.

## 4-input Multiplexer

A 4-input multiplexer has two data-selector lines a combination of which are used to select any of the four data-input lines.

Logic symbol of a 4-input MUX is shown in figure.

If a binary 0 is applied to the data-selector lines, the data on input D0 appear on the data-output line. If a binary 1 is applied to the data-selector lines, the data on input D1 appear on the data-output line. If a binary 2 is applied to the data-selector lines, the data on input D2 appear on the data-output line. If a binary 3 is applied to the data-selector lines, the data on input D0 appear on the data-output line.

This operation is given in the table.

Data Selector Output
S1 S0 Y
0 0 $$D_0$$
0 1 $$D_1$$
1 0 $$D_2$$
1 1 $$D_3$$

From the table it is clear that

$$Y \; is \; D_0 \; only \; if \; S_1=0 \; and \; S_0=0 \; : \; Y=D_0 \overline S_1 \overline S_0.$$ $$Y \; is \; D_0 \; only \; if \; S_1=0 \; and \; S_0=1 \; : \; Y=D_1 \overline S_1 S_0.$$ $$Y \; is \; D_0 \; only \; if \; S_1=1 \; and \; S_0=0 \; : \; Y=D_2 S_1 \overline S_0.$$ $$Y \; is \; D_0 \; only \; if \; S_1=1 \; and \; S_0=1 \; : \; Y=D_3 S_1 S_0.$$

The total expression for the data output is

$$Y=D_0 \overline S_1 \overline S_0+D_1 \overline S_1 S_0+D_2 S_1 \overline S_0+D_3 S_1 S_0$$

This can be implemented using four 3-input AND gates, a 4-input OR gate, and two inverters as shown in the figure.