## → Number system:-

The classification of number on the basis of their uses is known as **number system.**

**Note:-** The number system has radix or base to represent the types of number system.

## ∴ Base represents the following information:-

- Identify the type of number system
- Total number contained by number system
- Range of number contained by the number system

• **Formula to find the range of any number system:-**

**Range**= 0 – (**base** – 1)

eg. 0 – (10-1)

=0 – 9

## → Types of number system:-

## ⁘ Decimal Numbers:

The number system which consist digits from **0 to 9** and whose base is **10 **is called** decimal number system**. In the decimal system, there are ten possible digits:** 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.**

## ⁘ Binary Numbers System:

The number system whose base is 2 and has only two possible digits: 0 and 1 is called as **binary number system.**

• Here, **1 **represents high-voltage and **0 **represents low- voltage.

• Each digit (i.e. **0 or 1**) in a binary number is called a “**bit**” (short for binary digit).

• **Note**: Binary number is less complicated than the decimal system because the binary system has only two digits.

∴ **Here’s an example of a binary number,**

**Binary Number**: (10100)2, (11011)2, (11001)2, (000101)2, (011010)2.

## ⁘ Hexa-decimal Number System:

The number system whose base is **16 **and the number contained is** 0-9** and **A-F** is called** hexa-decimal number system**. eg:-0 1 2 3 4 5 6 7 8 9 A B C D E F

## ⁘ Octal Number System:

The number system which consist digits from **0 **to **7 **and whose base is **8 **is called **octal number system**.

**Here’s an example of an octal number:Octal Number**: 345