Page 58 - computer science (868) class 11
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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
Truth table of three variables NAND gate
The NAND gate can be demonstrated with the following logic circuit using AND and NOT gate.
A A.B (A.B)'
B
The NAND gate is a universal gate as it can be used to represent the fundamental gates AND, OR, and 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 in series are equivalent to AND gate as shown in the logic circuit diagram given below.
Output across NAND gate 1 = (A.B)'
A (A.B)' A.B
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
given below.
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')'
= A"+B" [De Morgan’s Law]
B
2 = A+B [Involution Law]
B
5656 Touchpad Computer Science-XI

