Page 70 - Computer science 868 Class 12
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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.
A A' Output in NOR gate 1 is A'
1
A A.B Output in NOR gate 2 is B'
3 3 Output in NOR gate 3 is (A'+B')'
= (A')'.('B')' [De Morgan’s Law]
B B'
2 = A.B [Involution Law]
B
2.2.3 XOR Gate
The XOR gate is a digital logic 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 is given below:
A B A⊕B
A A⊕B
0 0 0
0 1 1 B
1 0 1
1 1 0 The Boolean expression of a two
variable XOR gate is A'.B+A.B'
Truth table of 2 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 variable XOR gate, Boolean expression and logic circuit diagram is as follows:
A'
A B C A⊕B⊕C B' A'.B'.C
0 0 0 0 C
0 0 1 1 A' A'.B'.C + A'.B.C' +
A.B'.C' + A.B.C
0 1 0 1 B A'.B.C'
0 1 1 0 C'
1 0 0 1 A A.B'.C'
1 0 1 0 B'
C'
1 1 0 0
1 1 1 1 A A.B.C
B
Boolean expression of the three variable C
XOR gate is A'.B'.C +A'.B.C'+A.B'.C'+A.B.C.
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