Page 69 - Computer science 868 Class 12
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A
1 Output of NAND gate 1 = A'
A A' Output of NAND gate 2 = B'
(A+B)
3 Output of NAND gate 3
B' = (A'.B')'
B = A"+B" [De Morgan’s Law]
2 = A+B [Involution Law]
B
2.2.2 NOR Gate
NOR is the complement of the OR gate. It produces high output (1) only when all inputs are low (0). In all other cases,
low output (0) is produced.
The symbol and truth table are shown below:
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 variable NOR gates
Symbol of 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, 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 below:
Output across NOR gate is
A A' (A+A)'
A = A' [Idempotent Law]
Representing OR gate using NOR gate only:
Two NOR gates in series is equivalent to OR gate as 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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Computer Hardware 67

