# Converting Hexadecimal(16) to Decimal(10)

The Hexadecimal system work in base 16 which means that we have 15 (fifteen) numbers as shown bellow.

HEX | Value |
---|---|

0 | 0 |

1 | 1 |

2 | 2 |

3 | 3 |

4 | 4 |

0 | 0 |

0 | 0 |

5 | 5 |

6 | 6 |

7 | 7 |

8 | 8 |

9 | 9 |

A | 10 |

B | 11 |

C | 12 |

D | 13 |

E | 14 |

F | 15 |

# PHP and Hex

In the table above we have 16 numbers and its corresponding values, the highest is 15 and the lowest is 0. Knowing this rule what will the code bellow will output ?

The right answer is **255** !

When I first saw this expression I thought, it will output 1515. No doubts! If in the content table above the F represents 15 it is easy, with two F it will concatenate.

But be careful with that ! It is wrong thinking, the conversion is made as the same way as octal conversion (you can see the octal post conversion here).

First of all we need to convert the letters F into numbers which are 15, if it was the letter A would be 10 and so on, just look to the hexadecimal table. (tip: I like to think that from A to F its just 10 to 15)

Now that we have the value of F we can use this in the equation :

15×16¹ + 15×16° = 255_{10}

15×16¹ = 240

15×16° = 15

240 + 15 =** 255 !**

Remember the sample that we use is { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F }