If you are a bit familiar with digital electronics, after reading the topic of article you would have definitely understood what we are going to discuss in this article. Here in this article logic gates are explained in very simple method. It also covers a small portion of Boolean algebra. To understand about logic gates, you ought to know about Boolean algebra.

**Related Article: How to convert numbers from Binary to Decimal and Decimal to Binary?**

## What is Boolean algebra?

As you know, all machine deals only with binary values (i.e. 0 and 1) so the branch of algebra which describes binary system is Boolean algebra. Boolean algebra is backbone of digital electronics and has contributed a lot in this field. In simple words, we can say that combination logic circuit is nothing but efficient implementation of Boolean function. With the help of Boolean algebra we are able to reduce complex function to a simpler one so ultimately hardware is reduced and circuit made is cheaper.

There are several rules in Boolean algebra which helps us to reduce the Boolean functions. Few are listed in table below:

- A+0=A
- A+1=1
- A*0=0
- A*1=A
- A+A=A
- A+A’=1
- A*A=A
- A*A’=0
- A’’=A
- A+AB=A
- A+A’B=A+B
- (A+B)(A+C)=A+BC

## What are the basic logic gates?

In simple words, it is a device which is able to implement a Boolean function. It means it performs logical operations on input and gives output. Number of input may vary but output is always one. There are three basic logical operations: AND, OR and NOT.

### AND gate:

If there are two inputs say A and B and suppose A is 0 and B is 1. After implementing AND gate we will get 0 as output. In simple words, the output is A*B. it is denoted by A.B and read as A AND B. AND gate produces high output when all inputs are high otherwise output is low. Its Boolean function is: Z=A.B

### OR gate:

If there are two inputs say A and B and suppose A is 0 and B is 1. After implementing OR gate we will get 1 as output. In simple words, the output is A+B, it is denoted by A+B and read as A OR B. OR gate produces a high output when any one of inputs is high and low output when all inputs are low. Its Boolean function is: Z=A+B

### NOT gate:

It deals only with one input. It is an inverter gate i.e. it simply changes the input it means if input is 1 we get 0 as output and vice versa. Boolean expression of NOT gate is: Z=A’

### NAND gate:

This is combination of AND gate which is followed by NOT gate. We can also say that output of NAND gate is inverse of AND gate. NAND gate produces high output when any of inputs is low.

### NOR gate:

This is combination of OR gate which is followed by NOT gate. . We can also say that output of NOR gate is inverse of OR gate. NOR gate produces a low output when any one of inputs is high otherwise output is high.

### XOR gate:

This gate is widely used in digital electronics. It is also denoted by XOR. It gives high output when inputs are not at equal logic level. It gives output on the basis of magnitude of input so it is also used as magnitude comparator.

### XNOR gate:

This is combination of XOR followed by a NOT gate. It gives high output when all inputs are at same level and gives low output when outputs are at different levels.

## Universal logic gates:

Charles Sanders Peirce proved that NOR and NAND gates when implemented in different way can reproduce the functions of all other gates. So they are also called universal gates as with these gates you can implement any logic gate.

So I hope that after reading this article you will be comfortable for logic gates.