Page 71 - Computer science 868 Class 12
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Applications of the XOR gate:
• Used in half and full adders. • Used in pseudo-random number generation.
2.2.4 XNOR Gate
The XNOR gate is the digital logic gate that produces 0 (low) as output for an odd number of 1 (high) as input. It
is pronounced as exclusive NOR gate. It is the complement of the XOR gate. An encircled dot sign ⊙ is used to
represent the XNOR operation.
The symbol and truth table of the XNOR gate is given below:
A B A⊙B
0 0 1 A A⊙B
0 1 0 B
1 0 0
1 1 1 The Boolean expression of the two
Truth table of 2 variable XNOR gate variable XNOR gate is A'.B' + A.B.
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 variable XNOR gate, Boolean expression and logic circuit diagram is as follows:
A B C A⊙B⊙C A' A'.B'.C'
B'
0 0 0 1 C'
0 0 1 0 A'.B'.C' + A'.B.C + A.B.C'
0 1 0 0 A' A'.B.C
B
0 1 1 1 C
1 0 0 0
A A.B'.C
1 0 1 1 B'
1 1 0 1 C
1 1 1 0 A A.B.C'
B
Boolean expression of the three variable XNOR C'
gate is A'.B'.C'+A'.B.C+A.B'.C+A.B.C'.
Example 1: Draw the logic circuit diagram of the following Boolean expression A'.C + A.B'.
Ans. The gates will be (A' AND C) OR (A AND B').
A' A'.C
C
A'.C + A.B'
A A.B'
B'
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Computer Hardware 69

