### Implementation of Boolean Function using Multiplexer

Here you would see how to design a Combinational Logic Circuit using Multiplexer step by step with the help of an example - Implementation of Boolean Function using Multiplexer

## Implementation of Boolean Function using Multiplexer

Combinational logic circuits can be designed using Multiplexers (MUX). Standard ICs like 74152 (8:1 MUX), 74150 (16:1 MUX) etc are available in market. Combinational logic design using Multiplexer provide many advantages like reduction of IC package count, simplified logic design, no requirement of logic expression simplification in the circuit etc.

### Example: Implement the following Boolean function using 8:1 MUX

F (A, B, C, D) = Σm (0, 1, 3, 4, 8, 9, 15)

Solution: Following are the steps to implement the given Boolean Function using 8:1 MUX:

Step 1: To find number of select lines and input lines of the MUX

For n variable Boolean function, the number of select lines would be (n-1).

As we know that for an 8:1 MUX the number of select lines would be 3. In this case there are four variables A, B, C & D.

i.e., n = 4

Therefore, Number of select lines would be

n-1 = 3.

The variables B, C and D would be used as select lines.

And the remaining variable i.e., A, which is the MSB, would be taken as the input variable.

Step 2: Formation of Implementation Table

Implementation Table: Write the MSB i.e. A and A/ at the left side of the table column wise and the other variables i.e., B, C, D at the top of the table row wise sequentially as shown below:

Write numbers from 0 to 15 in the cells of the Implementation table.

Encircle the numbers or minterms given in the question.

If both the numbers in a column are encircled, then put ‘1’ against the corresponding input line ‘I’.

If both the numbers in a column are not encircled, then put ‘0’ against the corresponding input line ‘I’.

If only one number is encircled in a particular column, then write its corresponding MSB i.e., A or A/ against its input line ‘I’.

Step 3: Draw the circuit to implement the given Boolean Function using 8:1 MUX

In this way you can implement a combinational logic circuit using Multiplexer.