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View the Lessons →## Hexadecimal Numbering System

Hexadecimal is a base 16 numbering system which is made up of 16 digits: 0 – 9 and six more, which is A through F.

The table below shows how hexadecimal system works and its equivalent decimal number:

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

0 | 0 | 11 = (1 x 16) + 1 | 17 | |

1 | 1 | 12 = (1 x 16) + 2 | 18 | |

2 | 2 | 13 = (1 x 16) + 3 | 19 | |

3 | 3 | 14 = (1 x 16) + 4 | 20 | |

4 | 4 | 15 = (1 x 16) + 5 | 21 | |

5 | 5 | 16 = (1 x 16) + 6 | 22 | |

6 | 6 | 17 = (1 x 16) + 7 | 23 | |

7 | 7 | 18 = (1 x 16) + 8 | 24 | |

8 | 8 | 19 = (1 x 16) + 9 | 25 | |

9 | 9 | 1A = (1 x 16) + 10 | 26 | |

A | 10 | 1B = (1 x 16) + 11 | 27 | |

B | 11 | 1C = (1 x 16) + 12 | 28 | |

C | 12 | 1D = (1 x 16) + 13 | 29 | |

D | 13 | 1E = (1 x 16) + 14 | 30 | |

E | 14 | 1F = (1 x 16) + 15 | 31 | |

F | 15 | 20 = (2 x 16) + 0 | 32 | |

10 = (1 x 16) + 0 | 16 |

## Place Value

If decimal numbers have place values like ones, tens, hundreds, thousands and so on, hexadecimal numbers have place values as well. Decimals have powers of 10 while Hexadecimals have powers of 16.

The table below shows how the place value works for hexadecimal numbering system:

Exponent | 16^{3} |
16^{2} |
16^{1} |
16^{0} |
---|---|---|---|---|

Value | 4,096 | 256 | 16 | 1 |

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

10 | 16 |

100 | 256 |

1000 | 4,096 |

## Uses of Hexadecimal

Hexadecimal numbering system is often used by programmers to simplify the binary numbering system. Since 16 is equivalent to 2^{4}, there is a linear relationship between the numbers 2 and 16.

This means that one hexadecimal digit is equivalent to four binary digits. Computers use binary numbering system while humans use hexadecimal numbering system to shorten binary and make it easier to understand.

Hexadecimals are used in the following:

**To define locations in memory**. Hexadecimals can characterise every byte as two hexadecimal digits only compared to eight digits when using binary.**To define colours on web pages**. Each primary colour – red, green and blue is characterised by two hexadecimal digits. The format being used is #RRGGBB. RR stands for red, GG stands for green and BB stands for blue.**To represent Media Access Control (MAC) addresses.**MAC addresses consist of 12-digit hexadecimal numbers. The format being used is either MM:MM:MM:SS:SS:SS or MMMM-MMSS-SSSS. The first 6 digits of the MAC address represent the ID of the adapter manufacturer while the last 6 digits represent the serial number of the adapter.**To display error messages.**Hexadecimals are used to define the memory location of the error. This is useful for programmers in finding and fixing errors.

## Advantages of the Hexadecimal System

Here are some advantages of using the hexadecimal system:

- It is very concise and by using a base of 16 means that the number of digits used to signify a given number is usually less than in binary or decimal. It allows you to store more information using less space.
- It is fast and simple to convert between hexadecimal numbers and binary. Hexadecimal can be used to write large binary numbers in just a few digits.
- It makes life easier as it allows grouping of binary numbers which makes it easier to read, write and understand. It is more human-friendly, as humans are used to grouping together numbers and things for easier understanding. Also, writing in less digits lowers the possibility of error occurring.