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## Circuit Implementation Using Multiplexers

### What is a multiplexer?

It quite often happens, in the design of large-scale digital systems, that a single line is required to carry two or more different digital signals. Of course, only one signal at a time can be placed on the one line. What is required is a device that will allow us to select, at different instants, the signal we wish to place on this common line. Such a circuit is referred to as a Multiplexer.

A multiplexer performs the function of selecting the input on any one of 'n' input lines and feeding this input to one output line.

Multiplexers are used as one method of reducing the number of integrated circuit packages required by a particular circuit design. This in turn reduces the cost of the system.

Assume that we have four lines, C0, C1, C2 and C3, which are to be multiplexed on a single line, Output (f). The four input lines are also known as the Data Inputs. Since there are four inputs, we will need two additional inputs to the multiplexer, known as the Select Inputs, to select which of the C inputs is to appear at the output. Call these select lines A and B.

The gate implementation of a 4-line to 1-line multiplexer is shown below:

The circuit symbol for the above multiplexer is:

Design multiplexer implementations for the following functions using the numerical method.

The simulation should be used to check the workings.