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

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

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 all data and information like audio, video, graphics, and 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 Computers?

Humans have used numbers for ages.

Gradually humans evolved themselves, and with the help of their exceptional intelligence, they discovered numbers to make their life easier and more 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 first convert that data and instructions into binary form, which is easily understood by computers.

All the letters, words, symbols, and 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 in 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, the Decimal consists of 10 digits, the Octal has 8, and finally, the hexadecimal number system consists of 16 digits in their number system.

## Useful Video On: Importance of Number System

## Types of Number Systems 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

### 1. 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 “**Binary Number Systems**”.

Let us understand with some examples.

1100011000

In the above number system, we can only see two numbers that are 0s and 1s. Such a system with only two numbers 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.

### 2. 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****”.**

### 3. 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 of 8.

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

**EXAMPLE:-**

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

**Next Example.**

In 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 the “**Octal Number System**”.

### 4. 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, and 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.**

## Importance of Number System in Our Daily Life

The importance of the number system can be witnessed in day-to-day life. The number system is essential for our existence.

They are for thousands of years now; their uses and applications are endless. We can not imagine our life without the use of Numbers.

Take out the number system from our society, and we will return to the **“Stone Age”.**

The critical aspect of the number system is that it helps us to understand and learn the world around us more knowledgeably and intelligently for more productivity.

The number system is used and utilized in Mathematics as without using numbers, math becomes useless. lets us understand the whole system and world more comparably.

The number allows us to compare things like which is greater or smaller.

In math, students should learn counting of a number using fingers or objects. This helps students understand that each number represents its value that cannot be changed or edited.

The number helps students to solve problems and assignments related to school and college.

## The Main Uses of Number System

The number system is one of the essential aspects of our daily life. It helps us to count, compare and measure things around us.

The number system also helps us express ourselves through telephone numbers, house addresses, or even social security numbers.

- The number system is widely and extensively used in daily life. It helps us compare things, count objects, and measure.
- The number systems are used in Telephone Numbers and Our Addresses.
- To compare and register the height and weight of anything using numbers.
- Comparing prices at Malls and Shopping Plazas.
- It is used in calculations like Addition, Subtraction, multiplication, and Division.
- It helps in making our monthly budgets.
- Paying Bills and Debts.

## 5 Examples of Numbers in Daily Life

- Numbers can be written as fractions, decimals, and whole numbers.
- You can count temperature and distance using a number system.
- Measuring distance (Miles/ KM).
- Counting and comparing objects.
- Keeping track of daily budgets.

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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

## What are Four Important Number Systems?

- Decimal Number System.
- Binary Number System.
- Octal Number System.
- Hexadecimal Number System.

## Frequently Asked Questions [FAQs]

### What number systems are used in everyday life?

Decimal Number System.

### What are the properties of number system?

There are four number properties:

commutative property, associative property, distributive property, and identity property.

### What is the number system used by humans?

Positional Decimal System

### Who invented the number system?

Aryabhata is considered **“Father of Number System”.**

### What is the largest number in the world?

A number followed by 100 zero is the largest number. The number is called **“googolplex”.**

### Which number is the smallest?

Zero

### What is the oldest number system?

The Babylonian number system is the oldest in the world.

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