Denary 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.

On the other hand, hexadecimal system is probably more familiar as a numeral system that is 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.

**Table #1: Denary to hexadecimal conversion table**

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

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

**Instructions:**

- Start with any denary number,
- Divide it by 16 and treat the division as an integer division,
- Find out the remainder in a hexadecimal system,
- Divide the result by 16 again,
- Continue with remainder division until result is 0,
- Resulting hexadecimal number is the digit sequence from the last to the first.

**Example #1: Convert denary 158 into hexadecimal**

Step description | Division | Result | Remainder |
---|---|---|---|

Divide 158 with 16 | 158 / 16 | 9 | 14 = E |

Divide 9 with 16 | 9 / 16 | 0 | 9 = 9 |

Resulting hexadecimal number |
9E |

**Example #2: Convert denary 2019 into hexadecimal**

Step description | Division | Result | Remainder |
---|---|---|---|

Divide 2019 with 16 | 2019 / 16 | 126 | 3 = 3 |

Divide 126 with 16 | 126 / 16 | 7 | 14 = E |

Divide 7 with 16 | 7 / 16 | 0 | 7 = 7 |

Resulting hexadecimal number |
7E3 |

Convert denary to hexadecimal numbers.

Convert hexadecimal to denary numbers.

Explore the manual conversion process between hexadecimal and denary numbering systems.