Page 81 - ComputerScience_Class_11

Output across NOR gate is
A A' (A+A)'

A = A' [Idempotent law]

Representing OR gate using NOR gate only:
Two NOR in series are equivalent to OR gates shown below in the logic circuit diagram.

Output in NOR gate 1 is (A+B)'
A (A+B)' (A+B)
1 2 Output in NOR gate 2 is ((A+B)'}'
B = (A+B) [Involution Law]

Representing AND gate using NOR gate only:

The 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:

Truth table of a two-variable XOR gate A A⊕B
A B A⊕B B
0 0 0 Symbol of XOR gate
0 1 1
1 0 1 The Boolean expression of a two
1 1 0 variables XOR gate is A'.B+A.B'

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

Propositional Logic, Hardware Implementation, Arithmetic Operations 79