Page 68 - Computer science 868 Class 12
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2.2 UNIVERSAL GATES
Two more logic gates are obtained when AND and OR gates are inverted. They are named NAND and NOR respectively.
They are also called Universal gates because any digital circuit can be implemented using NAND and NOR only.
2.2.1 NAND Gate
NAND is the complement of AND gate. It produces low output (0) only when all inputs are high (1). In all other cases,
high output (1) 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 1 0 0 1 1
1 0 1 0 1 0 1
1 1 0 0 1 1 1
Truth table of two variables NAND gate 1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 0
Symbol of NAND gate Truth table of three variables AND gate
NAND gate can be demonstrated with the following logic circuit using AND and NOT gate
A
A.B (A.B)'
B
NAND gate is a Universal gate as it can be used to represent the fundamental gates AND,OR, NOT.
Representing NOT gate using NAND gate only:
When a single boolean variable passes through the NAND gate it gets complemented as shown in the circuit below:
Output across NAND gate
A A' = (A.A)'
A
= A' [Idempotent Law]
Representing AND gate using NAND gate only:
Two NAND gates in series is equivalent to AND gate as shown below in the logic circuit diagram:
Output across NAND gate 1 = (A.B)'
A (A.B)' A.B
1 1 2 Output of NAND gate 2 = ((A.B)')'
B = A.B [Involution law]
Representing OR gate using NAND gate only:
OR operation is achieved by passing complemented input through the NAND gate as shown in the logic circuit diagram.
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