We usually use Arabic numbers, which are base 10, or decimal. Computers use binary, which is base 2. This page deals with numbers in other bases. Enter a number to convert it to a different base, or count in a base.

In Arabic numbers (decimal, or base 10), there are 10 digits: 0,1,2,3,4,5,6,7,8,9. You need one digit each to count up to 9, but two digits for ten, and three digits for a hundred, which is ten times ten. In Binary, base 2, you need two digits for two, as you only have two digits, 0 and 1. Base 5 has five digits, and the number five becomes 10. For base 16, you will need sixteen digits, and there are only ten numerals. So we use the letters A,B,C,D,E,F. These represent the decimal numbers 10, 11, 12, 13, 14 and 15. Look at the table below and find the pattern for these bases.

Base 10 | Base 2 | Base 3 | Base 4 | Base 5 | Base 8 | Base 16 |
---|---|---|---|---|---|---|

1 | 1 | 1 | 1 | 1 | 1 | 1 |

2 | 10 | 2 | 2 | 2 | 2 | 2 |

3 | 11 | 10 | 3 | 3 | 3 | 3 |

4 | 100 | 11 | 10 | 4 | 4 | 4 |

5 | 101 | 12 | 11 | 10 | 5 | 5 |

6 | 110 | 20 | 12 | 11 | 6 | 6 |

7 | 111 | 21 | 13 | 12 | 7 | 7 |

8 | 1000 | 22 | 20 | 13 | 10 | 8 |

9 | 1001 | 100 | 21 | 14 | 11 | 9 |

10 | 1010 | 101 | 22 | 20 | 12 | A |

11 | 1011 | 102 | 23 | 21 | 13 | B |

12 | 1100 | 110 | 30 | 22 | 14 | C |

13 | 1101 | 111 | 31 | 23 | 15 | D |

14 | 1110 | 112 | 32 | 24 | 16 | E |

15 | 1111 | 120 | 33 | 30 | 17 | F |

16 | 10000 | 121 | 100 | 31 | 20 | 10 |

17 | 10001 | 122 | 101 | 32 | 21 | 11 |

18 | 10010 | 200 | 102 | 33 | 22 | 12 |

19 | 10011 | 201 | 103 | 34 | 23 | 13 |

20 | 10100 | 202 | 110 | 40 | 24 | 14 |

All these bases are positional, like Arabic numbers (base 10).

The common number bases are decimal numbers (Arabic numbers) or base 10, and binary or base 2.

Hexadecimal (base 16) and octal (base 8) are sometimes used in programming, as a short-hand for binary.

All these different bases are positional systems, like Arabic numbers. They all have a zero, unlike older number systems.

© Jo Edkins 2006 - Return to Numbers index