![Implementation of Functions using Multiplexer](https://eevibes.com/wp-content/uploads/2022/12/Implementation-of-Functions-using-Multiplexer.png)
Table of Contents
Implementation of Functions using Multiplexer
Implementation of Boolean function using multiplexer (MUX) is very simple. If you want to implement a Boolean function of n variables, you need a multiplexers that has (n-1) select lines. The purpose of select lines in a multiplexer is to choose which input to be forwarded to output lines. For
2n input lines, you will always have n select lines and a single output line.
Procedure of Functions Implementation using MUX
In order to implement a Boolean function using mux follow the following procedure:
Use the first (n-1) variables of functions as select lines of multiplexer
. The remaining variable of function is used as data line or data input. For example if you want to implement a 3 variable function
F(A,B,C)
then A and B will be used as select lines
C can take four possible values (C or C’ or 1 or 0). This variable will be used as data input to the MUX.
Example
Implement the following Boolean function using MUX.
![Boolean function](https://eevibes.com/wp-content/uploads/2022/01/Boolean-function.png)
Solution:
First make the truth table as shown below
Select n-1 variables for select lines of MUX (ABC). This will help us to decide to use 8 to 1 line MUX.
Use the last variable (D) for representing it in terms of function as shown in the table
![Boolean function implementation using MUX](https://eevibes.com/wp-content/uploads/2022/01/Boolean-function-implementation-using-MUX.png)
![4 variable function using 8 to 1 line MUX](https://eevibes.com/wp-content/uploads/2022/01/4-variable-function-using-8-to-1-line-MUX.png)
How to design a 4 to 1 line MUX using 2 to 1 line MUX?
![4 to 1 line MUX using 2 to 1 line MUX](https://eevibes.com/wp-content/uploads/2022/01/4-to-1-line-MUX-using-2-to-1-line-MUX.png)
The above figure shows the design of 4 to 1 line MUX using 2 to 1 line MUX. The working of this circuit is explained as follows. When 01 is selected, w1 should be forwarded to the output line.
![4 to 1 line mux working](https://eevibes.com/wp-content/uploads/2022/01/4-to-1-line-mux-working.png)
![16 to 1 line multiplexer](https://eevibes.com/wp-content/uploads/2022/01/16-to-1-line-multiplexer.png)
How to design a 3-input majority function using mux?
![3 input majority function using MUX](https://eevibes.com/wp-content/uploads/2022/01/3-input-XOR-gate-using-MUX.png)
![Implementation of the three-input majority function using a 4-to-1 multiplexer. (a)](https://eevibes.com/wp-content/uploads/2022/01/Implementation-of-the-three-input-majority-function.png)
using a 4-to-1 multiplexer.
(a)
How to design a 3 input XOR gate using MUX?
![3 input XOR gate using MUX](https://eevibes.com/wp-content/uploads/2022/01/3-input-XOR-gate-using-MUX-1.png)
![Three-input XOR implemented with a 4-to-1 multiplexer](https://eevibes.com/wp-content/uploads/2022/01/Three-input-XOR-implemented-with-a-4-to-1-multiplexer.png)
4.32 Implement the following Boolean function with a multiplexer (a)
F(A, B, C, D) =Σ(0, 2, 5, 8, 10, 14)
(b) F(A, B, C, D) =∏(2,6,11)
Solution (a):
Solution (b):
Also read here
What are the universal shift registers and their applications?