Every computer store numbers, letters, and other special characters in a coded form. So it is essential to have a basic understanding of the number system.

There are two types numbering system: non positional and positional.

## Non-Positional

Number Systems In this system, we have symbols such as I for 1, II for 2, III for 3, IIII for 4 etc.. Since it is very difficult to perform arithmetic with such number system, positional number systems were developed.

## Positional Number Systems

Positional number systems consist of a limited set of digits that represent varying values depending on their position within the number. The value of each digit is determined by three factors.

- The digit itself.
- Digit’s position in the number, and
- The base of the number system (where base is determined as the total number of digits available in the number system)

There are 4 positional number systems:

- Decimal Number System
- Binary Number system
- Hexadecimal Number System
- Octal Number System

## Decimal number system

The number system that we use in our daily activity is called the Decimal number system. Decimal number system is a base 10 system which means there are 10 digits starting from 0 to 9 to represent any quantity. In Decimal number system Value of the digits depends on the position they hold.

Look at the following example:

1234= one thousand two hundred and thirty four.

In this example we have four digits 1,2,3,4. The value of each digit in this example is based on their position.

1 in this example means 1×10^{3}

2 in this example means 2×10^{2}

3 in this example means 3×10^{1}

4 in this example means 4×10^{0}

So the total value is 4×10^{0 }+ 3×10^{1 }+ 2×10^{2 }+1×10^{3 }=1234

## Binary Number System

The Binary Number system is a base 2 system with only two digits 0 and 1. Each position in a binary number represents a power of the base (2).

Look at the following example:

If the given binary number is 1100.

1 | 1 | 0 | 0 |

1×2^{3} | 1×2^{2} | 0x2^{1} | 0x2^{0} |

In 1×2^{3}

- 1 is binary number
- 2 is the base
- 3 is the power of base.

## Octal Number System

Octal Number System is a base 8 system. in octal number system there are only eight digits: 0,1,2,3,4,5,6,7. The position in octal number represents a power of the base 8. Since there are only 8 digits in the octal number system, 3 bits are sufficient to represent any octal number in binary.

Look at the following example:

If the given octal number is 1457.

1 | 4 | 5 | 7 |

1×8^{3} | 4×8^{2} | 5×8^{1} | 7×8^{0} |

In 1×8^{3}

- 1 is octal number
- 8 is the base
- 3 is the power of base.

## Hexadecimal Number System

Hexadecimal number system is a base 16 system with 16 digits namely 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F; Where A represents 10 in decimal, B represents 11 in decimal , C represents 12 in decimal , D represents 13 in decimal, E represents 14 in decimal and F represents 15 in decimal.

Look at the following example:

If the given Hexadecimal number is 1457.

1 | 4 | 5 | 7 |

1×16^{3} | 4×16^{2} | 5×16^{1} | 7×16^{0} |

In 1×16^{3}

- 1 is hexadecimal number
- 16 is the base
- 3 is the power of base.

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