# Number System Definition Types Examples

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

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.