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Representing AND gate using NOR gate only:
AND operation is achieved by passing complemented input through the NOR gate as shown in the logic circuit diagram
given below.
A A'
1 Output in NOR gate 1 is A'
A
3 A.B Output in NOR gate 2 is B'
Output in NOR gate 3 is (A'+B')'
B B' = (A')'.('B')' [De Morgan’s Law]
2
B = A.B [Involution Law]
3.7.6 XOR Gate
The XOR gate is a digital logical gate that produces 1 (high) as output for an odd number of 1 (high) as input. It is
pronounced as exclusive OR gate. An encircled plus sign (⊕) is used to show the XOR operation.
The symbol and truth table of the XOR gate are given below.
A B A⊕B A A⊕B
0 0 0 B
0 1 1 Symbol of XOR gate
1 0 1
1 1 0 The Boolean expression of a two
variables XOR gate is A'.B+A.B'
Truth table of two variables XOR gate
The logic circuit diagram of the two variable XOR gate is as follows:
A A.B'
B'
A'.B + A.B'
A'
A'.B
B
The truth table of the three variables 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
Boolean expression of the three
1 0 1 0
variable XOR gate is A'.B'.C + A'.B.C'
1 1 0 0
+ A.B'.C'+A.B.C.
1 1 1 1
8282 Touchpad Computer Science-XI

