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Welcome to **decimal to hex**, our website which explains the decimal to hexadecimal conversion to you.

The decimal numeral system is also referred to as dec, base 10 and denary, whereas the hexadecimal writing system for numbers is also called hex or base 16.

If you have been wondering about how to convert decimal to hexadecimal, or if you have been looking for how to convert dec to hex, then you’re perfectly right here. 🙂

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Next, you can find more information about the numeral system under consideration; how to convert decimal to hexadecimal is explained further below.

## Dec to Hex

In the mathematical operation called exponentiation b^{n} *b* is the base and *n* is the exponent.

The *decimal system* is a positional numeral system with a base b of 10, and the exponents are 0, 1, 2, … n, according to the (n-1)_{th} position of the digit, starting the count with one.

10^{0} = 1, 10^{1} = 10, 10^{2} = 100, etc.

The decimal notation uses the symbols zero to nine.

If it is clear which base is meant, such as in daily use of counting, the base is omitted.

When a base is explicitly stated, then it is usually put in subscript as can be seen in the case below.

For example, 4329_{10} denotes 4 x 1000 + 3 x 100 + 2 x 10 + 9 x 1

The *hexadecimal system* a positional numeral system with the base 16 and the exponents are 0, 1, 2, … n, according to the (n-1)_{th} position of the digit, assuming one is the first number.

16^{0} = 1, 16^{1} = 16, 16^{2} = 256, 16^{3} = 4096 and so forth.

The hex system of numeration uses the symbols 0–9 and a–f.

The letters a–f or A-F denote the numbers ten to fifteen.

**1 – 9(hex) = 1 – 9(dec), 10(hex) = a, 11(hex) = b, 12(hex) = c, 13(hex) = d, 14(hex) = e, 15(hex) = f**

For example, 10e9_{16} denotes 1 x 4096 + 0 x 256 + 14 x 16 + 9 x 1, that is 4329_{10}.

The table below translates between the two notations:

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

0 | 0 |

1 | 1 |

2 | 2 |

3 | 3 |

4 | 4 |

5 | 5 |

6 | 6 |

7 | 7 |

8 | 8 |

9 | 9 |

10 | a |

11 | b |

12 | c |

13 | d |

14 | e |

15 | f |

16 | 10 |

17 | 11 |

18 | 12 |

19 | 13 |

20 | 14 |

50 | 32 |

100 | 64 |

1000 | 3e8 |

## How to Convert Decimal to Hexadecimal?

Here we are going to show you how to conduct the operation using the remainder method, which can be broken down to this four steps:

- Divide the decimal by 16, record the integer part of the result as new quotient
- Write down the remainder of the result in hexadecimal notation using our table above
- Proceed the two steps above with the quotient until the result is 0
- Build the result as a sequence of the hex remainders from right to left, from top to bottom.

Below is the example for 4329_{10}:

Decimal | Divisor | Quotient | Remainder_{10} | Remainder_{16} |
---|---|---|---|---|

4329 | 16 | 270 | 9 (4329 – 16 x 270) | 9 |

270 | 16 | 16 | 14 (270 – 16 x 16) | e |

16 | 16 | 1 | 0 (16 – 1 x 16) | 0 |

1 | 16 | 0 | 1 (1 – 0 x 16) | 1 |

4329_{10} = 10e9_{16}

Proof: 1 x 16^{3} + 0 x 16^{2} + 14 x 16^{1} + 9 x 16^{0} = 4096 + 0 + 224 + 9 = 4329.

Below is another example, 7777_{10}:

Decimal | Divisor | Quotient | Remainder_{10} | Remainder_{16} |
---|---|---|---|---|

7777 | 16 | 486 | 1 (7777 – 16 x 486) | 1 |

486 | 16 | 30 | 6 (486 – 16 x 30) | 6 |

30 | 16 | 1 | 14 (30 – 1 x 16) | e |

1 | 16 | 0 | 1 (1 – 0 x 16) | 1 |

7777_{10} = 1e61_{16}

Proof: 1 x 16^{3} + 14 x 16^{2} + 6 x 16^{1} + 1 x 16^{0} = 4096 + 3584 + 96 + 1 = 4329.

If you need more examples, then you may want to check out our frequent conversions located below our calculator.

Every posts contains the math in full detail.

As a side note: In programming it is common to write a base 16 number with the 0x prefix.

Therefore, for instance, 1e61_{16} = 0x1e61.

### How to Convert a Decimal Number with Fractional Part into Hexadecimal?

For this, we split the number into a whole number part and a decimal part, then combine the results. Thus, in this section we only discuss the fractional part.

- Multiply the decimal number by 16 and write down the integer part in hex notation
- Repeat the first step until the fractional part equals zero
- Build the result as a sequence of the hex remainders from right to left, from top to bottom, following the decimal separator

Observe that, depending on the input, the process might take an endless number of iterations, thus you may want to stop after n digits and use the result as an approximation.

Here’s an example of how to convert dec to hex with digits, the number is 0.00390625:

Decimal | Multiplicator | Product | Integer Part | Fractional Part |
---|---|---|---|---|

0.00390625 | 16 | 0.0625 | 0 | 0.0625 |

0.0625 | 16 | 1 | 1 | 0 |

0.00390625_{10} = 0.01_{16}

Proof: 0 x 1/16 + 1/(16×16) = 0 + 1/256 = 1 /256 = 0.00390625_{10}

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## Summary

You have reached the concluding section of our dec hex article.

This image sums denary to hexadecimal up:

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– Article written by Mark, last updated on January 10th, 2024