# DEC, BIN, HEX (Base 2-36) converter / Tool

## How to use this tool

- Enter a number in any radix and it will be automatically converted to everything from binary to 36th decimal.
- Decimals are not supported.

## Base Number Conversion Method

Since radix conversion only changes the notation of the number, the value will not change. However, this is only the case when dealing with integers, and is difficult when dealing with decimals. This tool and article do not support decimals.

### Base-N (non-decimal) to decimal

Multiply each n-digit number by $N^0, N^1, ... N^n$ to compute the sum.

e.g. To convert 1101100 in binary to decimal.

e.g. To convert 6C in hexadecimal to decimal (C = 12).

### Decimal to base-N (non-decimal)

- Divide the decimal number until the quotient is less than N.
- Arrange the remainders in order from the last, with the last quotient at the top.

e.g. To convert 108 in decimal to binary.

108 / 2 = 54, remainder of 0

54 / 2 = 27, remainder of 0

27 / 2 = 13, remainder of 1

13 / 2 = 6, remainder of 1

6 / 2 = 3, remainder of 0

3 / 2 = 1, remainder of 1

-> 1101100

In other words, an algorithm that decomposes into the following forms.

e.g. To convert 108 in decimal to hexadecimal.

108 / 16 = 6, remainder of 12 (C)

-> 6C

## Cheat sheet

Dec (10) | Bin (2) | Qua (4) | Oct (8) | Hex (16) |
---|---|---|---|---|

1 | 1 | 1 | 1 | 1 |

2 | 10 | 2 | 2 | 2 |

3 | 11 | 3 | 3 | 3 |

4 | 100 | 10 | 4 | 4 |

5 | 101 | 11 | 5 | 5 |

6 | 110 | 12 | 6 | 6 |

7 | 111 | 13 | 7 | 7 |

8 | 1000 | 20 | 10 | 8 |

9 | 1001 | 21 | 11 | 9 |

10 | 1010 | 22 | 12 | A |

11 | 1011 | 23 | 13 | B |

12 | 1100 | 30 | 14 | C |

13 | 1101 | 31 | 15 | D |

14 | 1110 | 32 | 16 | E |

15 | 1111 | 33 | 17 | F |

16 | 10000 | 100 | 20 | 10 |