Combination of Logic Gates
NAND gate From “AND” and “NOT” gate,
Fig. 49
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

NOR gate From “OR” and “NOT” gate,
Fig. 50
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

XOR gate From NOT, AND and OR gate, known as exclusive OR gate.
Fig. 51
The logic gate which gives high output (i.e., 1) if either input A or input B but not both are high (i.e., 1) is called exclusive OR gate or the XOR gate.
It may be noted that if both the inputs of the XOR gate are high, then the output is low (i.e., 0).
Boolean expression and truth table: Y = A ⊕ B =
A

B

Y

0

0

0

0

1

1

1

0

1

1

1

0

Exclusive NOR (XNOR) gate
XOR + NOT XNOR
Fig. 52
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 such as the OR, AND, and NOT can be constructed from the NAND gates.
Construction of the NOT gate from the NAND gate When both the inputs (A and B) of the NAND gate are joined together, then it works as the NOT gate (Fig. 53).
Fig. 53
Truth table and logic symbol:
Input

Output

A = B

Y

0

1

1

0

Construction of the AND gate from the NAND gate When the output of the NAND gate is given to the input of the NOT gate (made from the NAND gate), then the resultant logic gate works as the AND gate (Fig. 54).
Fig. 54
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

Construction of the OR gate by the NAND gate When the outputs of two NOT gates (obtained from the NAND gate) is given to the inputs of the NAND gate, the resultant logic gate works as the OR gate (Fig. 55).
Fig. 55
Truth table and logic symbol:
A

B

A

B

Y

0

0

1

1

0

0

1

1

0

1

1

0

0

1

1

1

1

0

0

1
