**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].
- It is also called as
**radix**of a number system.

**Examples-**

Consider the following examples-

**Base 10 Number System-**

Consider base 10 number system popularly called as decimal number system-

- Total number of digits used in this number system are 10 since it has base 10.
- These digits are 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9.
- These digits clearly lie in the range [0 , base-1] = [0 , 9].

**Base 2 Number System-**

Consider base 2 number system popularly called as binary number system-

- Total number of digits used in this number system are 2 since it has base 2.
- These digits are 0 and 1.
- These digits clearly lie in the range [0 , base-1] = [0 , 1].

**Important Note-**

It is important to note that-

- All the digits of any number system with base ‘b’ are always less than ‘b’.
- This is clear from the range [0 , base-1] in which the digits of any number system lie.

**Types of Number System-**

Four most commonly used number systems are-

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

The following table shows the base and digits used in these number systems-

Number System | Base | Digits Used |

Decimal Number System | 10 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 (Total 10 digits) |

Binary Number System | 2 | 0, 1 (Total 2 digits) |

Octal Number System | 8 | 0, 1, 2, 3, 4, 5, 6, 7 (Total 8 digits) |

Hexadecimal Number System | 16 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F (Total 16 digits) |

To gain better understanding about Basics of Number System,

**Next Article-** **Converting Any Base to Base 10**

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Summary

Article Name

Base of Number System | Types of Number Systems

Description

Base of a Number System is the total number of digits used in that number system. Types of Number Systems- Decimal Number System, Binary Number System, Octal Number System, Hexadecimal Number System.

Author

Akshay Singhal

Publisher Name

Gate Vidyalay

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