Table of Contents

*Introduction*

In today’s post, we will learn and discuss what are the importance of number system in computers with meaning, definition, types, uses with illustrative examples and images.

The number system is used in the computer system for better communication and representation.

The computers can only understand numbers; therefore, it converts every letter and word into numbers for better understanding and processing.

The Digital computer converts or translates every data and information like audio, video, graphics, text into binary form, i.e., 0s and 1s, which is easily read and understood by computers for better functionality and proper outputs.

The output generated by computers is in human-readable form.

*Let us dig into the topic.*

## What is the Number System and Importance of Number System in Computer?

Humans have used the numbers for ages. Gradually humans evolved themselves, and with the help of their exceptional intelligence, they discovered numbers to make their life more easy and convenient.

Before, numbers were used for counting, numbering, and calculations, but they were used for multiple purposes as the days passed.

We already know that computer systems cannot recognize or understand the data or instructions given to them.

They firstly convert that data and instructions into binary form, which is easily understood by computers.

All the letters, words, symbols, special symbols are converted into binary form, and this is done with a standard code commonly known as *ASCII {American Standard Code for Information and Interchange}*.

In other words, any number which is symbolically represented to the system and the method is called a “*number system.*”

These numbers can efficiently perform mathematical operations like addition, subtraction, multiplication, and division.

Every number can be uniquely represented using this technique.

The Number System is defined by the numbers or digits in the number system.

The binary number consists of 2 digits, Decimal consists of 10 digits, Octal has 8, and finally, the hexadecimal number system consists of 16 digits in their number system.

## Types of Number System in Computer

The 4 different types of number systems are categorized below. Please have a look.

*Binary Number System**Decimal Number System**Octal Number System**Hexadecimal Number System*

Binary Number System

Binary Number Systems are also used in machine language, and hence it is commonly known as “*Machine Language.*”

The digital computer converts all the data and instructions in a binary system, i.e., 0s and 1s. The base or radix value of the number system is 2.

The binary number systems use only 2 digits and are therefore called as “*Binary Number System*.”

Let us understand with some examples.

*1100011000*

In the above number system, we can only see two numbers that are 0s and 1s.In such a system with only two numbers, it is called the “*Binary Number System.*”

Next Example

*11000111.001101*

In the above example, the digits are separated by a decimal point dividing the numbers into two parts. The decimal point is called a *binary point*.

*(101010)*_{2}*(1100)*_{2}*(10001)*_{2}

*More Examples:-*

*Now here in the above examples, 11002 can be written as 1100.*

Decimal Number System

The Decimal Number System is used in almost our daily routine. This number system includes all 10 digits i.e. 0,1,2,3,4,5,6,7,8,9.

The Base or radix value of this number system is 10, and this number system uses decimal numbers; therefore, they are called “*Decimal Number System*.”

*EXAMPLE:-*

*(5456)*_{10}*(1382)*_{10}*(1532)*_{10}*(5124)*_{10}

*Next Example*

*(9865)*_{10}*(5987)*_{10}

In the above example, we can see that the number system contains digits from (0 to 9); therefore, this type of number system is called the “*Decimal Number System*.”

Octal Number System

The Octal Number System is built and consists of 8 numbers that are “0, 1, 2, 3, 4, 5, 6, 7”. They have a base or radix value 8.

Therefore they are called an octal number system because 8 denotes as Octal.

*EXAMPLE:-*

*(4526)*_{8}*(1232)*_{8}*(3321)*_{8}

*Next Example.*

*I**n the above examples, the number of digits is in the range of (0 to 7) and has a base value of 8; therefore, they are called “ Octal Number System.”*

Hexadecimal Number System

The Hexadecimal number system consists of 10 digits and 6 letters. They are “0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F”.

In this system, the letter A is denoted by 10, B equals 11, C equals 12, D denotes 13, and F denotes 14.

In the hexadecimal number system, the base or radix value is 16 because it has 16 alphanumeric values.

The Hexadecimal Number can be divided into two parts Hexa and Decimal, where hexa=6 and decimal=10.

*Examples:*

*(DE5)*_{16}*(AB31)*_{16}*(DEF12)*_{16}*(ABC123)*_{16}

This number system is used for memory addressing where numbers from 0 to 9 are used with letters A, B, C, D, E, F.

In the above examples, there are numbers and letters with a base value of 16, and this type of combination is called a* hexadecimal number system*.

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## Number System Conversions

*Binary to Decimal**Decimal to Binary**Octal to Decimal**Decimal to Octal**Octal to Binary**Binary to Octal**Hexadecimal to Binary**Binary to Hexadecimal**Hexadecimal to Decimal**Decimal to Hexadecimal**Octal to Hexadecimal**Hexadecimal to Octal*

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