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 Function 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 the multiplexer.
The remaining variable of the function is used as a 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.
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 an 8-to-1 line MUX.
Use the last variable (D) for representing it in terms of function as shown in the table.
How to design a 4-to-1 line MUX using a 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.
How to design a 3-input majority function using mux?
using a 4-to-1 multiplexer.
(a)
How to design a 3-input XOR gate using MUX?
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):
Here is the video solution that explains step by step how we can implement a function if it is given as the sum of products or the product of sums. Both arts have been explained in detail. Dont forget to subscribe and share.
Solution (b):
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