Page 83 - ComputerScience_Class_11

The logic circuit diagram of the two variables XNOR gate is as follows:

A A.B
B

A'.B' + A.B

A' A'.B'

B'

The truth table of the three variables XNOR gate, Boolean expression and logic circuit diagram are as follows:

A B C A⊙B⊙C
0 0 0 1
0 0 1 0
0 1 0 0
0 1 1 1

1 0 0 0
1 0 1 1 Boolean expression of the three
1 1 0 1 variable XNOR gate is
1 1 1 0 A'.B'.C' + A'.B.C + A.B'.C + A.B.C'.

A' A'.B'.C'
B'
C'

A' A'.B.C A'.B'.C' + A'.B.C + A.B'.C + A.B.C'
B
C

A A.B'.C
B'
C

A A.B.C'
B
C'

Let us give some more examples of drawing logic circuit from a Boolean expression and vice versa.
Example 1: Draw the logic circuit diagram of the following Boolean expression A'.C + A.B'.
The gates will be (A' AND C) OR (A AND B').

Answer:
A'
A'.C
C
A'.C + A.B'

A A.B'
B'

Propositional Logic, Hardware Implementation, Arithmetic Operations 81