A hexadecimal number is a number that uses the `base-16`

numbering system. This means that each digit in a hexadecimal number represents a power of 16. Hexadecimal numbers are often used in computing because they can represent large numbers in a compact form.

In the hexadecimal numbering system, the digits 0-9 represent the values 0-9, and the letters A-F represent the values 10-15. For example, the hexadecimal number 1A can be represented as:

$1 \times 16^1 + A \times 16^0$

In this representation, the first digit (1) represents 16 ($1 \times 16^1$), and the second digit (A) represents 10 (1$0 \times 16^0$). When you add these values together, you get the decimal number 26.

$1 \times 16^1 + A \times 16^0 = 16 + 10 = 26$

In addition to hexadecimal numbers, there are other numbering systems, such as binary and decimal, that are used in computing. However, hexadecimal numbers are particularly useful because they can represent large numbers in a compact form and are easy to convert to binary.

## Examples

The following table shows the decimal, binary & hexadecimal representations of the numbers 0 through 15:

Decimal | Binary | Hexadecimal |
---|---|---|

0 | 0000 | 0 |

1 | 0001 | 1 |

2 | 0010 | 2 |

3 | 0011 | 3 |

4 | 0100 | 4 |

5 | 0101 | 5 |

6 | 0110 | 6 |

7 | 0111 | 7 |

8 | 1000 | 8 |

9 | 1001 | 9 |

10 | 1010 | A |

11 | 1011 | B |

12 | 1100 | C |

13 | 1101 | D |

14 | 1110 | E |

15 | 1111 | F |