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Computer Architectures - Digital Circuits - 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.

 

a2

a1

a0

d7

d6

d5

d4

d3

d2

d1

d0

|

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:

 

a2

a1

a0

d7

d6

d5

d4

d3

d2

d1

d0

|

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:

 


 

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