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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').
Ans.
A'
A'.C
C
A'.C + A.B'
A A.B'
B'
Example 2: Draw the logic circuit diagram of the following Boolean expression (A'+B'+C') + A.B.
Ans. The gates will be (A NAND B NAND C) OR (A AND B) or (A' OR B' OR C') OR (A AND B).
The one is drawn below:
A A'+B'+C'
B
C
(A'+B'+C')+A.B
A.B
8484 Touchpad Computer Science-XI

