## How to convert from hex to decimal

A regular decimal number is the sum of the digits multiplied with power of 10.

137 in base 10 is equal to each digit multiplied with its corresponding power of 10:

137_{10} = 1×10^{2}+3×10^{1}+7×10^{0} = 100+30+7

Hex numbers are read the same way, but each digit counts power of 16 instead of power of 10.

For hex number with n digits:

*d _{n-1} ... d_{3} d_{2} d_{1} d_{0}*

Multiply each digit of the hex number with its corresponding power of 16 and sum:

decimal = *d _{n-1}×16^{n-1} + ... + d_{3}×16^{3} + d_{2}×16^{2} + d_{1}×16^{1}+d_{0}×16^{0}*

#### Example #1

3B in base 16 is equal to each digit multiplied with its corresponding 16^{n}:

3B_{16} = 3×16^{1}+11×16^{0} = 48+11 = 59_{10}

#### Example #2

E7A9 in base 16 is equal to each digit multiplied with its corresponding 16^{n}:

E7A9_{16} = 14×16^{3}+7×16^{2}+10×16^{1}+9×16^{0} = 57344+1792+160+9 = 59305_{10}

#### Example #3

0.8 in base 16:

0.8_{16} = 0×16^{0}+8×16^{-1}
= 0+0.5 = 0.5_{10}

## Hex to decimal conversion table

Hex base 16 |
Decimal base 10 |
Calculation |
---|---|---|

0 | 0 | - |

1 | 1 | - |

2 | 2 | - |

3 | 3 | - |

4 | 4 | - |

5 | 5 | - |

6 | 6 | - |

7 | 7 | - |

8 | 8 | - |

9 | 9 | - |

A | 10 | - |

B | 11 | - |

C | 12 | - |

D | 13 | - |

E | 14 | - |

F | 15 | - |

10 | 16 | 1×16^{1}+0×16^{0} = 16 |

11 | 17 | 1×16^{1}+1×16^{0} = 17 |

12 | 18 | 1×16^{1}+2×16^{0} = 18 |

13 | 19 | 1×16^{1}+3×16^{0} = 19 |

14 | 20 | 1×16^{1}+4×16^{0} = 20 |

15 | 21 | 1×16^{1}+5×16^{0} = 21 |

16 | 22 | 1×16^{1}+6×16^{0} = 22 |

17 | 23 | 1×16^{1}+7×16^{0} = 23 |

18 | 24 | 1×16^{1}+8×16^{0} = 24 |

19 | 25 | 1×16^{1}+9×16^{0} = 25 |

1A | 26 | 1×16^{1}+10×16^{0} = 26 |

1B | 27 | 1×16^{1}+11×16^{0} = 27 |

1C | 28 | 1×16^{1}+12×16^{0} = 28 |

1D | 29 | 1×16^{1}+13×16^{0} = 29 |

1E | 30 | 1×16^{1}+14×16^{0} = 30 |

1F | 31 | 1×16^{1}+15×16^{0} = 31 |

20 | 32 | 2×16^{1}+0×16^{0} = 32 |

30 | 48 | 3×16^{1}+0×16^{0} = 48 |

40 | 64 | 4×16^{1}+0×16^{0} = 64 |

50 | 80 | 5×16^{1}+0×16^{0} = 80 |

60 | 96 | 6×16^{1}+0×16^{0} = 96 |

70 | 112 | 7×16^{1}+0×16^{0} = 112 |

80 | 128 | 8×16^{1}+0×16^{0} = 128 |

90 | 144 | 9×16^{1}+0×16^{0} = 144 |

A0 | 160 | 10×16^{1}+0×16^{0} = 160 |

B0 | 176 | 11×16^{1}+0×16^{0} = 176 |

C0 | 192 | 12×16^{1}+0×16^{0} = 192 |

D0 | 208 | 13×16^{1}+0×16^{0} = 208 |

E0 | 224 | 14×16^{1}+0×16^{0} = 224 |

F0 | 240 | 15×16^{1}+0×16^{0} = 240 |

100 | 256 | 1×16^{2}+0×16^{1}+0×16^{0} = 256 |

200 | 512 | 2×16^{2}+0×16^{1}+0×16^{0}
= 512 |

300 | 768 | 3×16^{2}+0×16^{1}+0×16^{0}
= 768 |

400 | 1024 | 4×16^{2}+0×16^{1}+0×16^{0}
= 1024 |

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