What is Multiplexer? Explain with its truth table.

A Multiplexer, also known as a Mux, is a combinational circuit that selects binary information from one of many input lines and directs it to a single output line. The selection of a particular input line is controlled by a set of selection lines. Depending on the number of input lines, the selection line takes up the binary form. For instance, if there are 8 input lines, the selection line should be of 3 bits (2^3 = 8).

The multiplexer is a data selector which gates one out of several inputs to a single output. It allows digital information from several sources to be routed from one node to another. The selection of the input is controlled by the select lines.

The simplest example of a multiplexer is a 2-to-1 multiplexer, which consists of 2 input lines, 1 output line, and 1 select line. The truth table for a 2-to-1 Mux is as follows:

Select Line (S)	Input Line D0	Input Line D1	Output (Y)
0	X	0	X
0	X	1	X
1	0	X	X
1	1	X	X

In the above table, X denotes 'don't care' condition. The output Y is equal to D0 when the select line S=0 and Y is equal to D1 when the select line S=1.

The logic equation for the above truth table can be written as:

Y = S'.D0 + S.D1

Where '.' denotes the AND operation and '+' denotes the OR operation. The ' denotes the NOT operation.

This equation shows that when S=0, the first term becomes 1 and the output Y = D0. When S=1, the second term becomes 1 and the output Y = D1. This is how a multiplexer works.

Multiplexers are used in various digital applications like data routing, data compression, etc. They are also used in constructing other digital logic circuits.