NAND Gate

Logic Gates are one of the most important topics in electronics, especially digital electronics. The concept of logic gates relies on the concept of Boolean functions. Logic gates take one or multiple binary values as input and return one binary value as output after doing the logical calculation on them. There are several kinds of GATEs available in Digital Electronics, some of them are known as basic gates, and some of them are known as universal gates.

A NAND gate falls under the category of Universal gates because the NAND gate can implement any Boolean function without the help of basic gates and also calculate the results of logical inputs without the help of any other logic gate.

What is NAND Gate?

Logic gates are small digital switching circuit that determines the output of two or more inputted Boolean functions in Binary format. Logical 1 means True or High in nature, whereas Logical 0 means False or Low in nature. Based on different logical operations, the output differs. There can be many inputs in a logic gate but there will be only one output. Each logic gate has its own Truth Table which represents all the combinations of input and output.

NAND gate, also known as Not-AND gate, does the exact opposite or complement of the AND gate.

Operation of AND Gate

NAND Gate takes Boolean values as input and returns:

• Returns 1, if all the inputs are 0 or alternative (meaning one is 0, and the other is 1 or vice versa).
• Returns 0, if all inputs are 1

The Boolean expression of NAND Gate is as follows –

Say we have two inputs, A and B and the output is called X, then the expression is –

X = (A . B)’

Types of NAND Gates

There are two types of NAND gates, based on the number of inputs

• 2-Input NAND Gate
• 3-Input NAND Gate

2-Input NAND Gate

It is the simplest form of NAND gate which takes two inputs and returns the output. There are 2² = 4 combinations of input and output.

Three-Input NAND Gate

As the name suggests, it has three inputs and only one output. There are 2³ = 8 combinations of input and output.

Symbol of AND Gate

Given Below is the Symbol of NAND gate, A and B represent the two inputs. The NAND gate performs the logical NAND operation on the inputs. The output is represented by the line extending from the bottom of the NAND gate symbol.

The truth table of the Two-Input NAND gate is as follows –

NAND Gate

Truth Table of AND Gate

In the given truth table, it returns 1, if all the inputs are 0 or alternative (meaning one is 0, and the other is 1 or vice versa). otherwise returns 0, if all inputs are 1.

3 Input NAND Gate

NAND Gate in Terms of Transistor

The NAND gate is one of the main building blocks of Digital Logic Circuits. Its operation can also be explained via the concept of transistors. Transistors are a type of semiconductor device that are mainly used to amplify or switch electronic signals.

NAND gate in terms of Transistor

Working of the Circuit

Here in the above diagram, there are two transistors named Q1 and Q2, which are connected in a series configuration. The collector terminal of Q1 is connected with Vcc and also with the output terminal. The emitter of Q1 is connected with the collector of Q2, which makes the connection in a series configuration. The emitter of Q2 is connected with the ground which completes the entire circuit.

Lets take an case when the inputs A and B are 0. In this case, transistor will act like a switch and terminates the connection between collector and emitter. When 5V supply is ON, it reaches the collector terminal directly of the first transistor. The collector terminal is connected with output, so 5V supply directly goes to the output. Hence the output will be HIGH.

Applications of NAND Gate

• Universal Gate: NAND gate is called Universal Gate because all the basic logic gates can be formed using them.
• Used to store data: NAND gates are used to create elements like Flip-Flops and Latches, which is a key component to storing data.
• Arithmetic Logic: NAND gates are extensively used in the Arithmetic and Logic Units (ALUs) of a computing device to perform operations like addition, subtraction, etc.
• Used in Decoder and Encoder: NAND gates are also used in Decoder and Encoder circuits to convert a binary code into a set of digital signals and vice versa.
• Used in Multiplexers and Demultiplexers: NAND gates are used in Multiplexers to decide which route a signal should take to reach a single output. The demultiplexer does the exact opposite of this.
• Clock Generators: NAND gates used in Clock generators to generate clock signals which synchronize various operation in Digital Circuit.
• Logical Operations: NAND gates are also used to implement various logical operations.

Advantages of NAND Gate

• It is a Universal Gate: NAND gate is a Universal Gate, so it can be used to construct any basic logic gate without using any other Gate. Also, it can solve complex Logical Problems.
• Simplify Logical Expressions: Using only the NAND gate, we can simplify any complex logical circuits and represent them in a simpler manner.
• Low Components Needed: NAND gate can represent any other logic gate, we can utilize NAND gates to solve complex logical expressions, and as a result, a small number of NAND gates are required.
• Less Power Consumption: Implementing logical functions using a NAND gate consumes way less power than other gates.

Disadvantages of NAND Gate

• Lack of Flexibility: Although NAND is a Universal Gate, implementing all logic circuits using a NAND gate might not always yield the most optimized result.
• Speed: In some cases using the NAND gate might result in a propagation delay, those logical expressions might need some dedicated Gates to resolve.

Solved Example of NAND Gate

Implement the given circuit using NAND gate.

We have 4 inputs named as A, B, C and D. Here we are going to perform the functionality of NAND Gate by using 2 AND gate and 1 OR gate.

And in the resultant section, we will use 2 NAND Gates and 1 OR gate to know the difference between the functionality of AND ate and NAND gate.

Circuit Diagram

Solution:

Converting the AND and OR gate into NAND gate and keeping the Boolean expression same.

Implement the given circuit using NAND gate

As the result, we are getting output : A’B’ + C’D’

NAND Gate – FAQs

Why is NAND Gate called Universal Gate?

NAND Gate is called Universal Gate because it can be used to form any other basic logic gates like AND OR NOT without taking the help of another gate.

How is a NAND gate different from an AND gate?

When we inverse the output of the AND gate we get the NAND gate. Means that the result of the AND gate will just be reversed in case of NAND gate. It is short form of NOT-AND gate.

How Logical NOT operation is achieved in NAND gate?

The logical NOT operation is performed on the output of the AND gate. The NAND gate is a combination of AND and NOT gate, where two or more input enters the AND get and yields a single output which is then fed into the NOT gate which yields the complement of the output.