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2.7.5 NOR Gate
The NOR gate is the complement of the OR gate. It produces high output (1) only when all the inputs are low (0). In all
other cases, low output (0) is produced.
The symbol and truth table of NOR gate are shown below.
A (A+B)' A (A+B+C)'
B
B C
Symbol of NOR gate Symbol
A B (A+B)' A B C (A+B+C)'
0 0 1 0 0 0 1
0 1 0 0 0 1 0
1 0 0 0 1 0 0
1 1 0 0 1 1 0
Truth table of two variables NOR gate 1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 0
Truth table of three variables NOR gate
NOR gate can be demonstrated with the following logic circuit using OR and NOT gate.
A (A+B) (A+B)'
B
NOR gate is a universal gate as it can be used to represent the fundamental gates AND, OR, and NOT.
Representing NOT gate using NOR gate only:
When a single Boolean variable passes through the NOR gate, it gets complemented as shown in the circuit given
below.
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]
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Propositional Logic, Hardware Implementation, Arithmetic Operations 57

