The number system in computer science is the representation of numbers, typically in binary form, that is used by computers. The number system is a key component of nearly all aspects of computer science, including hardware, software, networking, and data storage.

In most cases, the number system is base 2, meaning there are only two digits (0 and 1). However, other number systems, such as base 10 (used by humans) and base 16 (used by some computer hardware), are also used in specific cases. The number system is a fundamental concept in computer science, and understanding it is essential to working with computers.

The most basic element of the number system is the bit. A bit is a single digit in the number system, and it can have a value of either 0 or 1. The value of a bit is determined by its position in the number system; the first bit (the rightmost bit) has a value of 1, the second bit has a value of 2, the third bit has a value of 4, and so on. This system is known as positional notation, and it allows for numbers to be represented in a compact form.

In this article, we list the four types of number systems used in computers alongwith example:

## Decimal Number System

The decimal number system is the most common number system in use today. It is a base 10 system, meaning it uses 10 digits (0-9). The decimal number system is used by humans because we have 10 fingers, making it easy for us to count and represent numbers using this system.

The decimal number system works by representing numbers in powers of 10. For example, the number 12 can be represented as 1×10^1 + 2×10^0, which can be simplified to 1 ten and 2 ones, or 12. The number 123 can be represented as 1×10^2 + 2×10^1 + 3×10^0, which can be simplified to 1 hundred, 2 tens, and 3 ones, or 123.

In the decimal number system, each digit has a value that is 10 times greater than the value of the previous digit. For example, in the number 12, the 1 has a value of 10 and the 2 has a value of 1. This system is used because it is easy for humans to understand and work with.

The decimal number system is used in many everyday applications, such as telling time, measuring weight or distance, and counting money. It is also the number system that is most commonly used by computers.

## Binary Number System

The binary number system is a base 2 system that uses only two digits, 0 and 1. The binary number system is the most common number system used by computers because it is easy for them to store and process information using this system.

In the binary number system, each digit has a value that is 2 times greater than the value of the previous digit. For example, in the number 10, the 1 has a value of 2 and the 0 has a value of 1. This system is used because it is easy for computers to understand and work with.

**Example**

Write (18)_{10} as a binary number.

Solution:

∴ (14)_{10} = (10010)_{2}

The binary number system is used in many everyday applications, such as networking and data storage. It is also the number system that is most commonly used by computers.

## Octal Number System

The octal number system is a base 8 system that uses only eight digits, 0-7. The octal number system is used in some computer applications because it is easy for computers to store and process information using this system.

In the octal number system, each digit has a value that is 8 times greater than the value of the previous digit. For example, in the number 10, the 1 has a value of 8 and the 0 has a value of 1. This system is used because it is easy for computers to understand and work with.

The octal number system is used in some computer applications, such as networking and data storage.

## Hexadecimal Number System

The hexadecimal number system is a base 16 system that uses 16 digits, 0-9 and A-F. The hexadecimal number system is used in some computer applications because it is easy for computers to store and process information using this system.

In the hexadecimal number system, each digit has a value that is 16 times greater than the value of the previous digit. For example, in the number 10, the 1 has a value of 16 and the 0 has a value of 1. This system is used because it is easy for computers to understand and work with.

## Number System Conversion

It is important to be able to convert between different number systems, as some applications may use one system while others use another. For example, a computer may store information in binary form but need to display it in decimal form. In this case, the computer would need to convert the binary number to a decimal number before displaying it.

You can refer to RapidTables number conversion tool to convert as well as learn more about it.

Conversion between number systems can be done manually or with the use of a calculator. To convert a number from one system to another, the number must first be broken down into its component parts.

**Why do we use Number system in Computer?**

The number system is used to represent everything from whole numbers to fractions, from text to images.

**How do Number system in Computer work?**

The most basic element of the number system is the bit. A bit is a single digit in the number system, and it can have a value of either 0 or 1.

**What are Four types of Number system?**

Decimal, Binary, Hexadecimal and Octal are the four types of number systems.

**What is the base of number system?**

Base of a number system is the total number of digits used in that number system. Number system with base ‘b’ has its digits in the range [0 , b-1]