(1) The 'NAND' gate: From 'AND' and 'NOT' gate
Boolean expression and truth table: 
|
A
|
B
|
Y¢ = A × B
|
Y
|
|
0
|
0
|
0
|
1
|
|
0
|
1
|
0
|
1
|
|
1
|
0
|
0
|
1
|
|
1
|
1
|
1
|
0
|
(2) The 'NOR' gate: From 'OR' and 'NOT' gate
Boolean expression and truth table: 
|
A
|
B
|
Y¢ = A + B
|
Y
|
|
0
|
0
|
0
|
1
|
|
0
|
1
|
1
|
0
|
|
1
|
0
|
1
|
0
|
|
1
|
1
|
1
|
0
|
(3) The 'XOR' gate: From 'NOT', 'AND' and 'OR' gate. Called as exclusive OR gate.
It may be noted that if both the inputs of the XOR gate is 1, then the output is 0.
Boolean expression and truth table: Y = A Å B = 
|
A
|
B
|
Y
|
|
0
|
0
|
0
|
|
0
|
1
|
1
|
|
1
|
0
|
1
|
|
1
|
1
|
0
|
(4) The exclusive nor (XNOR) gate: XOR + NOT XNOR
Boolean expression: Y = A ¤ B =
Logic Gates Using 'NAND' Gate
The NAND gate is the building block of the digital electronics. All the logic gates like the OR, the AND and the NOT can be constructed from the NAND gates.
(1) Construction of the ' NOT' gate circuit from the ' NAND' gate
(i) When both the inputs (A and B) of the NAND gate are joined together then it works as the NOT gate.
(ii) Truth table and logic symbol
|
Input
|
Output
|
|
A = B
|
Y
|
|
0
|
1
|
|
1
|
0
|
(2) Construction of the 'AND' gate from the 'NAND' gate:
(i) When the output of the NAND gate is given to the input of the NOT gate (made from the NAND gate), then the final logic circuit behaves as the AND gate
(ii) Truth table and logic symbol
|
A
|
B
|
Y¢
|
Y
|
|
0
|
0
|
1
|
0
|
|
0
|
1
|
1
|
0
|
|
1
|
0
|
1
|
0
|
|
1
|
1
|
0
|
1
|
(3) Construction of the 'OR' gate by the 'NAND' gate
(i) When the outputs of two NOT gates (obtained from the NAND gate) is given to the inputs of the NAND gate, the final logic circuit behaves as the OR gate
(ii) Truth table and logic symbol
|
A
|
B
|
|
|
Y
|
|
0
|
0
|
1
|
1
|
0
|
|
0
|
1
|
1
|
0
|
1
|
|
1
|
0
|
0
|
1
|
1
|
|
1
|
1
|
0
|
0
|
1
|
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