Implementations of Logic Functions using gates

Implementations of Logic Functions using gates 

Example 1(3 variable POS expression):

Y=( A+B').(B+C')

 

Implementation POS expression using Logic Gates

Let us see how to implement this 3 variable POS expression using Logic Gates. First A and B are given as input to the OR gate. B is given through the NOT gate since it is the compliment B'. 

In the same way in the second OR gate B and C are given as input. C is given through the NOT gate since it is the compliment C'. The outputs of both OR gates are given as input to the AND gate to receive the final output Y=( A+B').(B+C').

Example 2 (3 variable SOP expression):

Y= AC+BC'+A'BC

 

Implementation of SOP expression using Logic Gates

The sum terms are given as the input to the AND gate. A and C are given as input to the first AND gate to get the output AC. B and inverted C are given as the input to the second AND gate to get the output BC'. 

Inverted A,B and C are given as the input third AND gate to get the output A'BC. Now all the outputs of all the three AND gates are given as the input to the OR gate to get the final output 

Y= AC+BC'+A'BC.

Example 3(Mixed Logic):

Y=A+(B+C').D

 

Implementation of Logic expression using Logic Gates

For the first OR gate B and inverted C is given as input. For the AND gate the output of first OR gate and D is given as the input. To get the final output, A and the output of the AND gate is given as the input to the OR gate.