A multiplexer is a combinatorial circuit that is given a certain
number (usually a power of two) data inputs, let us say
2^{n}, 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.
a_{2} 
a_{1} 
a_{0} 
d_{7} 
d_{6} 
d_{5} 
d_{4} 
d_{3} 
d_{2} 
d_{1} 
d_{0} 
 
x 
 
 
 
 
 
 
 
 
 
 
 
 
 
0 
0 
0 
 
 
 
 
 
 
 
0 
 
0 
0 
0 
0 
 
 
 
 
 
 
 
1 
 
1 
0 
0 
1 
 
 
 
 
 
 
0 
 
 
0 
0 
0 
1 
 
 
 
 
 
 
1 
 
 
1 
0 
1 
0 
 
 
 
 
 
0 
 
 
 
0 
0 
1 
0 
 
 
 
 
 
1 
 
 
 
1 
0 
1 
1 
 
 
 
 
0 
 
 
 
 
0 
0 
1 
1 
 
 
 
 
1 
 
 
 
 
1 
1 
0 
0 
 
 
 
0 
 
 
 
 
 
0 
1 
0 
0 
 
 
 
1 
 
 
 
 
 
1 
1 
0 
1 
 
 
0 
 
 
 
 
 
 
0 
1 
0 
1 
 
 
1 
 
 
 
 
 
 
1 
1 
1 
0 
 
0 
 
 
 
 
 
 
 
0 
1 
1 
0 
 
1 
 
 
 
 
 
 
 
1 
1 
1 
1 
0 
 
 
 
 
 
 
 
 
0 
1 
1 
1 
1 
 
 
 
 
 
 
 
 
1 
We can abbreviate this table even more by using a letter to
indicate the value of the selected input, like this:
a_{2} 
a_{1} 
a_{0} 
d_{7} 
d_{6} 
d_{5} 
d_{4} 
d_{3} 
d_{2} 
d_{1} 
d_{0} 
 
x 
 
 
 
 
 
 
 
 
 
 
 
 
 
0 
0 
0 
 
 
 
 
 
 
 
c 
 
c 
0 
0 
1 
 
 
 
 
 
 
c 
 
 
c 
0 
1 
0 
 
 
 
 
 
c 
 
 
 
c 
0 
1 
1 
 
 
 
 
c 
 
 
 
 
c 
1 
0 
0 
 
 
 
c 
 
 
 
 
 
c 
1 
0 
1 
 
 
c 
 
 
 
 
 
 
c 
1 
1 
0 
 
c 
 
 
 
 
 
 
 
c 
1 
1 
1 
c 
 
 
 
 
 
 
 
 
c 
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:
