Logic NAND Gate- Symbol, Truth Table, Circuit Diagram, Working

Last Updated on October 26, 2023 by Electricalvolt

In this article, we will discuss the logic NAND gate, its definition, truth table, Boolean expression, electrical equivalent circuit, and more. So, let’s get started with the basic definition of logic NAND gate.

What is NAND Gate?

In digital electronics, a NAND gate is a type of universal logic gate using which one can implement any basic logic function. The NAND gate is basically a combination of two basic logic gates, i.e., AND and NOT, hence it is also called Noted AND gate.

The NAND gate performs the same operation as an AND gate followed by a NOT gate, i.e.

The NAND gate produces a low or logic 0 output, when all of its inputs are high or logic 1, and it produces a high or logic 1 output when any of its inputs is low or logic 0. Therefore, the NAND gate is an inversion of the AND gate in terms of operation.

Symbol of NAND Gate

The basic logic symbol of the NAND gate is shown in the following figure.

symbol of NAND Gate

Boolean Expression of NAND Gate

The Boolean expression of a two-input NAND gate is given below.

 Boolean expression of a two-input NAND gate

Where A and B are the input variables, and Y is the output variable of the given NAND gate.

The Boolean expression of a three-input NAND gate is given as follows:

Boolean expression of a three-input NAND gate

Where, A, B, and C are the input variables, and Y is the output variable of the given NAND gate.

Working of NAND Gate

The operation of a two-input NAND gate for different possible combinations of inputs is as follows:

2-Input NAND Gate

  • When A = 0 and B = 0, the output Y is 1.
  • When A = 0 and B = 1, the output Y is 1.
  • When A = 1 and B = 0, the output Y is 1.
  • When A = 1 and B = 1, the output Y is 0.

3-Input NAND Gate

The operation of a three-input NAND gate for different possible combinations of inputs is described below:

  • When A = 0, B = 0, and C = 0, the output Y is 1.
  • When A = 0, B = 0, and C = 1, the output Y is 1.
  • When A = 0, B = 1, and C = 0, the output Y is 1.
  • When A = 0, B = 1, and C = 1, the output Y is 1.
  • When A = 1, B = 0, and C = 0, the output Y is 1.
  • When A = 1, B = 0, and C = 1, the output Y is 1.
  • When A = 1, B = 1, and C = 0, the output Y is 1.
  • When A = 1, B = 1, and C = 1, the output Y is 0.

Hence, from this discussion, it is clear that the output of the NAND gate is low only when all of its inputs are high, for the rest input combinations, the output is high.

Truth Table of NAND Gate

2-Input NAND Gate

The following is the truth table of a two-input NAND gate:

InputOutput
ABY = (AB)’
001
011
101
110

3-Input NAND Gate

InputOutput
ABCY = (AB)’
0001
0011
0101
0111
1001
1011
1101
1110

Realization of NAND Gate using Basic Logic Gates

As mentioned in the introductory section, the NAND gate is a combination of basic logic gates namely, AND gate and NOT gate.

Therefore, we can realize or implement a NAND gate by connecting an AND gate and a NOT gate as shown in the following figure.

NAND gate Equivalent

Multi-Input NAND Gate

We can implement a higher order NAND gate, i.e. NAND gate having more number of inputs by using two-input NAND Gates.

For example, the realization of a six-input NAND Gate using six two-input NAND gates and a three-input NAND gate is depicted in the following figure.

Multi-Input NAND Gate

The output of this logic circuit is given as follows:

output of multi-input NAND Gate

Realization of Basic Logic Gates using NAND Gate

As we mentioned above that, the NAND gate is a universal logic gate, hence we can implement any basic logic using this NAND gate.

1. AND Gate using NAND Gate

The implementation of an AND gate using a NAND gate is shown in the following figure.

AND Gate using NAND Gate

The output of this logic circuit is equivalent to AND gate output, i.e.

2. OR Gate using NAND Gate

The implementation of an OR Gate using NAND is shown in the following figure.

OR Gate using NAND Gate

The output of this NAND logic circuit is equivalent to an OR gate output, i.e.

3. NOT Gate using NAND Gate

The implementation of a NOT gate using a NAND gate is shown in the following figure.

NOT Gate using NAND Gate

The output of this NAND logic circuit is equivalent to the NOT gate output, i.e.

NAND Gate in RTL Logic

We can construct a NAND gate using RTL or Resistor Transistor Logic. The implementation of a two-input NAND gate in resistor transistor logic is shown in the following figure.

NAND Gate in RTL Logic

When both transistor T1 and T2 conducts we get low output( A=1, B=1, then Y=0). If any of the transistors is not conducting then we will get high output( A=1, B=0, then Y=1)

NAND Gate Integrated Circuits

NAND gates also come in the form of integrated circuits (ICs). The commonly used NAND gate ICs are listed in the following table.

Logic FamilyIC Name & Input
TTL (Transistor-Transistor Logic) Logic74LS00 (Quad 2-input)
TTL Logic74LS10 (Triple 3-input)
TTL Logic74LS20 (Dual 4-input)
TTL Logic74LS30 (Single 8-input)
CMOS (Complementary Metal Oxide Semiconductor) LogicCD4011 (Quad 2-input)
CMOS LogicCD4023 (Triple 3-input)
CMOS LogicCD4012 (Dual 4-input)

This is all about the NAND Gate, its definition, truth table, operation, Boolean expression, etc.

Please follow and like us:
About Komal

Komal is B.Tech. in Electronics & Communication engineering from National Institute of Technology(NIT-Surat). She has M.Tech. in VLSI Design from National Institute of Technolgy, Warangal. Her area of interest is PDK development and RTL Design.

Your subscription could not be saved. Please try again.
Your subscription has been successful.

Want To Learn Faster?

Get electrical, electronic, automation, and instrumentation engineering articles delivered to your inbox every week.

Leave a Comment