Multiplexer

A multiplexer is a combinatorial circuit that is given a certain number (usually a power of two) data inputs, let us say 2ⁿ, and n address inputs used as a binary number to select one of the data inputs. The multiplexer has a single output, which has the same value as the selected data input.

In other words, the multiplexer works like the input selector of a home music system. Only one input is selected at a time, and the selected input is transmitted to the single output. While on the music system, the selection of the input is made manually, the multiplexer chooses its input based on a binary number, the address input.

The truth table for a multiplexer is huge for all but the smallest values of n. We therefore use an abbreviated version of the truth table in which some inputs are replaced by `-' to indicate that the input value does not matter.

Here is such an abbreviated truth table for n = 3. The full truth table would have 2^{(3 + 23)} = 2048 rows.

We can abbreviate this table even more by using a letter to indicate the value of the selected input, like this:

The same way we can simplify the truth table for the multiplexer, we can also simplify the corresponding circuit. Indeed, our simple design method would yield a very large circuit. The simplified circuit looks like this: