Hexadecimal numbering system is one of the numeral systems that are commonly used in computers and other digital systems. It is base 16 and it has 16 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and A, B, C, D, E, F.

On the other hand, decimal system is probably the most familiar numeral system in the world. It is the standard system for denoting integer and non-integer numbers. It is base 10 and it has 10 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

**Table #1: Hexadecimal to Decimal conversion table**

Hexadecimal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |

Decimal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |

We can say that a decimal number is a sum of listed decimal digits multiplied by the power of 10. We can say the same thing for a hexadecimal number, but we need to count each decimal representation of a digit as a power of 16. In order to make it easier to understand, here is a list of steps that you can use:

- Start with any hexadecimal number,
- Take the last digit (use decimal counterpart), multiply it with 1 (because 16
^{0}= 1), - Take second digit from the end (use decimal counterpart), multiply it with 16 (because 16
^{1}= 16), - Take third digit from the end (use decimal counterpart), multiply it with 256 (because 16
^{2}= 256), - Continue with the sequence by increasing the power of 16 by 1 on each iteration until you've used up all the digits,
- Sum up the numbers from the sequence.

Hexadecimal to decimal calculation formula |
---|

DECIMAL = d_{n-1} x 16^{n-1} + ... + d_{3} x 16^{3} + d_{2} x 16^{2} + d_{1} x 16^{1} + d_{0} x 16^{0} |

We can see that the last power of 16 depends on the number of digits in the starting hexadecimal number. Let's take a look at few examples.

**Example #1: Convert hexadecimal 9E into decimal**

Step description | Multiplication | Result |
---|---|---|

Multiply decimal representation of E with 16^{0} |
14 x 1 | 14 |

Multiply decimal representation of 9 with 16^{1} |
9 x 16 | 144 |

Resulting decimal number |
158 |

**Example #2: Convert hexadecimal 7E3 into decimal**

Step description | Multiplication | Result |
---|---|---|

Multiply decimal representation of 3 with 16^{0} |
3 x 1 | 3 |

Multiply decimal representation of E with 16^{1} |
14 x 16 | 224 |

Multiply decimal representation of 7 with 16^{2} |
7 x 256 | 1792 |

Resulting decimal number |
2019 |

Convert hexadecimal to decimal numbers.

Convert decimal to hexadecimal numbers.

Learn how to manually convert numbers between decimal and hexadecimal numbering systems.