The NAND gate is a universal gate that can be used to build all basic logic gates. It is constructed by connecting a NOT gate to the output of an AND gate. In its truth table, the NAND gate output is 0 only when both inputs are 1, and 1 for all other combinations. Circuits for AND, OR, NOT, NOR, half adder, and full adder can all be made using only NAND gates, demonstrating its universal properties for building digital logic functions.

1. NAND GATE

2. SYMBOL OF NAND GATE
 A Negated AND is called a
NOT-AND or NAND gate.
 NAND gate is obtained by
connecting a NOT gate in
the output of an AND gate.
 The output of the AND gate
is inverted by the NOT gate
 The output is given by the
Boolean equation A.B

3. TRUTH TABLE
 When A = 0 and B = 0,
then Y = A.B = 1
 When A = 0 and B = 1,
then Y = A.B = 1
 When A = 1 and B = 0,
then Y = A.B = 1
 When A = 1 and B = 1,
then Y = A.B = 0

4. NAND – UNIVERSAL GATE
A NAND gate is known as a universal
gate because
It can be used to realize all the three basic
logic functions of an OR gate, AND gate
and NOT gate.
Thus in digital circuits, NAND gate
serves as a building block.

5. AND GATE
An AND gate can be produced by using
two NAND gates

6. OR GATE
An OR gate can be produced by using
three NAND gates

7. NOT GATE
If the two inputs of a NAND gate are
connected together, then we get a NOT
gate.

8. NOR GATE
If the output of an OR gate is connected
to a NOT gate, then we get NOR gate.

9. EX-OR GATE
The circuit for EX-OR gate using
NAND gate is shown.
It needs four NAND gates.

10. APPLICATION

11. HALF ADDER
 NAND gate can be used to
construct half adder
circuit.
 The half adder circuit
using NAND gate is
shown.
 The half adder has two
inputs and two outputs.
 A half adder computes the
sum of two bits and produces
the correct carry bit.

12. FULLADDER
 NAND gate can be used to
construct full adder circuit.
 The full adder circuit
using NAND gate is
shown.
 The full adder has three
inputs and two outputs.

13. THANK YOU