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The symbol and truth table of AND gate are shown below.
A A . B A A . B . C
B
B C
Symbol of AND gate
A B A.B A B C A.B.C
0 0 0 0 0 0 0
0 1 0 0 0 1 0
1 0 0 0 1 0 0
1 1 1 0 1 1 0
Truth table of two variables AND gate 1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 1
Truth table of three variables AND gate
3.7.3 OR Gate
A logical gate that results in inclusive disjunction is called an OR gate. The OR gate is a binary gate. It produces high
output (1) when any one input is high (1). Only when all the inputs are low, 0 is produced as an output. The OR
operation is represented by a plus (+). The symbol and truth table of OR gate are shown below.
A A+B A A+B+C
B
B C
Symbol of OR gate Symbol
A B A+B A B C A+B+C
0 0 0 0 0 0 0
0 1 1 0 0 1 1
1 0 1 0 1 0 1
1 1 1 0 1 1 1
Truth table of two variables OR gate 1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 1
Truth table of three variables OR gate
Two more logic gates are obtained when AND and OR gates are inverted. They are named as NAND and NOR gates
respectively. They are also called universal gates because any digital circuit can be implemented using NAND and NOR
gates only.
3.7.4 NAND Gate
The NAND gate is the complement of AND gate. It produces low output (0) only when all the inputs are high (1). In all
other cases, high output (1) is produced. The symbol and truth table of NAND gate are shown below.
A
A A . B B A.B.C
B C
Symbol of NAND gate Symbol
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Propositional Logic, Hardware Implementation, Arithmetic Operations 79

