## Converting HEX to Decimal

**Hex** |
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 |

## Convert HEX 1ADEF to decimal

HEX F = 15 |
15 * 16^{0} = 15 |

HEX E = 14 |
14 * 16^{1} = 224 |

HEX D = 13 |
13 * 16^{2} = 3328 |

HEX A = 10 |
10 * 16^{3} = 40960 |

HEX 1 = 1 |
1 * 16^{4} = 65536 |

Therefore, HEX 1ADEF = (15 + 224 + 3328 + 40960 + 65536) = 110063

## Converting Decimal to HEX

When converting decimal to hex, we simply take the remainder and match it to a HEX character.

**Convert 10253 to HEX**

Calculation |
Remainder |
HEX |

10253/16 |
13 |
D |

640/16 |
0 |
0 |

40/16 |
8 |
8 |

2/16 |
2 |
2 |

Therefore, decimal 10253 = HEX 280D

**To get the remainder of a number without a modulo function, e.g. 374 / 8, do the following:**

374 / 8 = 46.75 0.75 * 8 = 6 Remainder is 6.

## Convert Decimal to Binary

Convert 278 to binary

Explanation: Assign a 0 to whole numbers, else assign 1. Continue dividing the whole number by 2.

278 / 2 = 139 |
0 |

139 / 2 = 69.5 |
1 |

69 / 2 = 34.5 |
1 |

34 / 2 = 17 |
0 |

17 / 2 = 8.5 |
1 |

8 / 2 = 4 |
0 |

4 / 2 = 2 |
0 |

2 / 2 = 1 |
0 |

1 / 2 = 0.5 |
1 |

Therefore, 278 = Binary 100010110

## Convert Binary to Decimal

Convert 10111 to decimal

Index |
Calculation |
Binary |

4 |
(2^4) * 1 = 16 |
1 |

3 |
(2^3) * 0 = 0 |
0 |

2 |
(2^2) * 1 = 4 |
1 |

1 |
(2^1) * 1 = 2 |
1 |

0 |
(2^0) * 1 = 1 |
1 |

Therefore, 10111 = (16 + 4 + 2 + 1) = 23