Universal Logic Gate: NAND Gate and NOR Gate as Universal Gate

Last Updated on December 2, 2023 by Electricalvolt

Nand Gate and NOR Gate are universal logic gates. In this article, we will discuss universal logic gates in digital electronics and the implementation of basic logic gates (AND, OR, and NOT) using universal logic gates. So, let’s begin with the basic definition of the universal logic gate.

In digital electronics, the logic gates are classified into two major categories, namely, basic logic gates and universal logic gates. There are three basic logic gates, namely AND gate, OR gate, and NOT gate.

What is a Universal Gate?

In digital electronics, a universal logic gate is one that can be used to implement any logical function without using any other type of logic gate.

In digital electronics, there are two types of universal logic gates, namely, NAND gate and NOR gate. These are called universal logic gates because they can perform all three basic logic operations, i.e., AND, OR, and NOT. Therefore, we can realize any logical function using only NAND gates or only NOR gates.

Let us now discuss the NAND gate and NOR gate in detail.

What is Universal NAND Gate?

A NAND gate is a universal logic gate used in digital electronic systems to implement logical functions.

The NAND gate can have two or more inputs and only one output. It is basically a combination of two basic logical functions, namely, AND and NOT, i.e.

NAND Gate = AND Gate + NOT Gate

Hence, it is also called NOTed AND gate.

The logic circuit symbols of two input and three input NAND gates are depicted in the following figure.

universal  NAND gate

Truth Table of NAND Gate

The table that describes the relationship between input variables and output variables of a logic gate is referred to as a truth table.

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

Truth table of 2-input NAND Gate

The following is the truth table of a three-input NAND gate.

Truth table of 3-input NAND Gate

From the above truth tables, it is clear that if any of the inputs of the NAND gate is low (logic 0), the output will be high (logic 1), and if all the inputs of the NAND gate are high (logic 1), the output will be low (logic 0).

Boolean Expression of NAND Gate

The Boolean expression is a logic function that describes the behavior of a logic gate for different input combinations.

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

Boolean expression of 2-input NAND Gate

The Boolean expression of a three-input NAND gate is given below,

Boolean expression of 3-input NAND Gate

What is Universal NOR Gate?

A NOR gate is a universal logic gate used in digital electronic systems to implement logical functions.

The NOR gate can have two or more inputs and only one output. It is basically a combination of two basic logical functions, namely, OR and NOT, i.e.

NOR Gate = OR Gate + NOT Gate

Hence, it is also called the NOTedOR gate.

The logic circuit symbols of two-input and three-input NOR gates are depicted in the following figure.

NOR Gate as universal gate

Truth Table of Universal Logic NOR Gate

The following is the truth table of a two-input NOR gate:

Truth table of 2-input NOR Gate

The following is the truth table of a three-input NOR gate:

truth table of 3-input NOR gate

From the above truth tables, it is clear that if any of the inputs of the NOR gate is high (logic 1), the output will be low (logic 0), and if all the inputs of the NOR gate are low (logic 0), the output will be high (logic 1).

Boolean Expression of NOR Gate

The Boolean expression of a two-input NOR gate is given below.

Boolean expression of 2-input NOR Gate

The Boolean expression of a three-input NOR gate is given below.

Boolean expression of 3-input NOR gate

After discussing the NAND and NOR gates individually, let us now discuss the implementation of basic logic gates (AND, OR, and NOT) using NAND and NOR gates.

Implementation of Basic Logic Gates using Universal Logic Gates

1. NOT Gate using NAND Gate

The following figure shows a NOT gate using a NAND gate.

NOT gate using universal NAND Gate

2. NOT Gate using NOR Gate

NOT gate using universal NOR Gate

3. AND Gate using NAND Gate

The following figure shows an AND gate using a universal NAND gate.

AND gate using universal NAND Gate

4. AND Gate using NOR Gate

The following figure shows an AND gate using a universal NOR gate.

AND Gate using universal NOR Gate

5. OR Gate using NAND Gate

The following figure shows an OR gate using a universal NAND gate.

OR Gate using universal NAND Gate

6. OR Gate using NOR Gate

The following figure shows an OR gate using NOR gate.

OR Gate using universal NOR Gate

Conclusion

Hence, this is all about universal logic gates in digital electronics. From the above discussion, it is clear that we can implement all three basic logic functions, i.e., AND, OR, and NOT, using only NAND gates or only NOR gates. That is why NAND and NOR gates are referred to as universal logic gates.

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About Ayushi

Ayushi is B.Tech in Electronics & Communication engineering from National Institute of Technology(NIT-Surat). She has 4 years of experience, and her area of interest is power electronics, digital electronics, artificial intelligence and data science.

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