Page 82 - ComputerScience_Class_11

The truth table of the three-variable XOR gate, Boolean expression and logic circuit diagram are as follows:

A B C A⊕B⊕C
0 0 0 0

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

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

Applications of the XOR gate:
• Used in half and full adders.
• Used in pseudo-random number generation.

3.7.7 XNOR Gate
The XNOR gate is a digital logical 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
show the XNOR operation.
The symbol and truth table of the XNOR gate are given below:

Truth table of a two-variable XNOR gate
A A⊙B
A B A⊙B
B
0 0 1
Symbol of XNOR gate
0 1 0

1 0 0 The Boolean expression of the two
variable XNOR gate is A'.B' + A.B.
1 1 1

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