How to implement Boolean functions using multiplexer?

Implementation of functions using MUX

Implementation of Boolean function using multiplexers (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

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
Boolean function

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
Boolean function implementation using MUX
4 variable function using 8 to 1 line MUX
4 variable function using 8 to 1 line MUX

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
4 to 1 line MUX using 2 to 1 line MUX

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
4 to 1 line mux working
16 to 1 line multiplexer
16 to 1 line multiplexer

How to design a 3-input majority function using mux?

3 input majority function using MUX
3 input majority function using MUX

 

Implementation of the three-input majority function using a 4-to-1 multiplexer. (a)
Implementation of the three-input majority function
using a 4-to-1 multiplexer.
(a)

How to design a 3 input XOR gate using MUX?

3 input XOR gate using MUX
3 input XOR gate using MUX
Three-input XOR implemented with a 4-to-1 multiplexer
Three-input XOR implemented with a 4-to-1 multiplexer

Also read here

https://eevibes.com/digital-logic-design/what-are-the-universal-shift-registers-and-their-applications/

 

What are the universal shift registers and their applications?

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