**Number System**

- Number system is mathematical way to represent numbers using literals such as digits, characters or symbols.
- It is also known as Positional Number System because value of each literal (digit, character or symbol) in a number depends upon its position within number.
- There are different number system and all have their own set of unique literals.
- The count of literals of number system is called Base or Radix.
- The value of each literal in a number is calculated using-
- The literal itself

- Position of the literal

- Base of the number system

- There are four number systems used in the context computer-
- Decimal Number System

- Binary Number System

- Octal Number System

- Hexadecimal Number System

**Decimal Number System**

- It is used by humans
- It uses 10 different digits from 0 to 9 to represent numbers.
- Decimal number system has base 10
- Each place to the left is ten times greater than the place to its right which means each place represent a specific power of the base (10).

Following figure represents the Integer and fractional part of decimal number 1253.76 alongwith calculation of the decimal number using positional values-

**Binary Number System**

- It is used by Computer and other Digital devices.
- It uses two different digits 0 and 1 called as bit to represent any information
- Binary number system has base 2
- Each place in a binary code represents a specific power of the base (2).
- Binary Number System is also referred as Machine Language.

**Application of Binary Number System**

- Used as Machine Language for Computer Hardware and other Electronic Devices.
- Used in ASCII Code and Unicode
- Used in Internet Protocols.
- Used in Image processing, High-end audio recordings, HD Videos recordings and data processing and storage.
- Used in Boolean algebra that is a branch of Mathematics.

**Octal Number System**

- It is used to represent large and complex binary codes into concise manner.
- It uses 8 different digits from 0 to 7 to represent information.
- Octal Number System has base 8.
- Each place in Octal code represents a specific power of the base (8).

**Applications of Octal Number System**

- It is used in register and flip flop of Computer Motherboards.
- It is used in Mainframe such as UNIVAC, PDP etc.

**Hexadecimal Number System**

- It is used to represent large and complex binary codes into concise manner.
- It uses 16 different literals which are 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F to represent information.
- Hexadecimal Number System has base 16.
- Each place in a Hexadecimal code represents a specific power of the base (16).

**Applications of Hexadecimal Number System**

- It is used to represent Memory Address for storage devices used in computers.
- It is used to describe colors in the Web Pages.
- It is used to represent Media Access Control (MAC) addresses.
- It is used to display error messages.