Three Variable Function using an 8:1 Multiplexer

Let's start this tutorial with a basic introduction of 8:1 multiplexer before moving on to cover how a three variable logic function can be implemented using an 8:1 multiplexer.

Introduction to 8:1 Multiplexer

A multiplexer (or MUX) is a digital logic circuit that accepts multiple data inputs and allows only one of them at a time to pass through the output line. Hence, multiplexer is also known as data selector. In other words, a multiplexer is a digital circuit which

Based on the number of input data lines, there are several types of multiplexers. But, this article is meant for explaining the implementation of a logic function in three variables using an 8:1 multiplexer. So, let us discuss the basics of 8:1 multiplexer only.

A 8:1 multiplexer is one which has eight input data lines, i.e., I₀, I₁, I₂,…I₇, three select lines, i.e. S₀, S₁, and S₂, and one output line Y. The block diagram of the 8:1 mux is shown in Figure 1.

The logic level applied to the three select lines decides which data input passes through the output channel of the multiplexer. The operation of the 8:1 multiplexer can be understood with the help of its truth table which is given below.

Select Lines			Output
S2	S1	S0	Y
0	0	0	I0
0	0	1	I1
0	1	0	I2
0	1	1	I3
1	0	0	I4
1	0	1	I5
1	1	0	I6
1	1	1	I7

Now, let us discuss the realization of a three-variable logic function using an 8:1 multiplexer with the help of an example.

Example

Implement the following logical function using an 8:1 multiplexer.

$$\mathrm{F\lgroup A,B,C\rgroup=\sum m\lgroup 0,1,2,5,7\rgroup }$$

Solution

The truth table of the 8:1 multiplexer for the given logic function is as follows −

Select Lines			Output
S2	S1	S0	Y
0	0	0	1
0	0	1	1
0	1	0	1
0	1	1	0
1	0	0	0
1	0	1	1
1	1	0	0
1	1	1	1

Using this truth table, we can draw the logic block diagram to realize the function F using an 8:1 MUX which is shown in Figure 2.

Here, the inputs A, B, and C are applied to the select lines S₂, S₁, and S0 respectively. From the truth table, it is clear that the function F = 1, when ABC = 000, 001, 010, 101, 111. Thus, we connect logic 1 to the data input lines I₀, I₁, I₂, I₅, and I₇, and the logic 0 is connected to all other data input lines, i.e. I₃, I₄, and I₆.

Conclusion

In this way, we can easily implement a given 3-variable Boolean function using an 8:1 multiplexer. To excel in the implementation of a three-variable Boolean using 8:1 MUX, try to solve the following tutorial problems.

Q1.Implement the following Boolean function using 8-to-1 MUX.

$$\mathrm{F\lgroup X,Y,Z\rgroup=\sum m\lgroup 0,2,5,7\rgroup }$$

Q2.Implement the following three variable logic function using an 8:1 multiplexer.

$$\mathrm{F\lgroup A,B,C\rgroup=\sum m\lgroup 0,1,3,4,6\rgroup }$$