Tool to write / convert a number from factorial base/number system to base 10 and vice versa from decimal base to factorial base automatically.

Factorial Base - dCode

Tag(s) : Arithmetics

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!

A suggestion ? a feedback ? a bug ? an idea ? *Write to dCode*!

Tool to write / convert a number from factorial base/number system to base 10 and vice versa from decimal base to factorial base automatically.

The **factorial base** is a writing of the numbers whose position of the figures is defined by the factorial of the position. The nth digit (from the right) of a number is written in base i, and its value in base 10 will be multiplied by $ (i - 1)! $

__Example:__ $ 3210_{(!)} = 3,2,1,0_{(!)} = 3_{(3)} 2_{(2)} 1_{(1)} 0_{(0)} = 23_{(10)} $

All the numbers in **factorial base** end with 0, thus, it is current to omit it on condition of specifying it clearly.

To write a number $ n $ in **factorial base**, noted $ n_{(!)} $ Or $ n_! $, perform the successive divisions of $ n $ by $ i $ ranging from 1 to infinity, as long as the result of the Euclidean division is not zero. The factorial notation consists of the remainders obtained in reverse order.

__Example:__ $ 1234_{(10)} = 1,4,1,1,2,0,0_{(!)}= 1411200_{(!)} $

n | i | calculation | remainder |
---|---|---|---|

1234 | 1 | 1234 ÷ 1 = 1234 | 0 |

1234 | 2 | 1234 ÷ 2 = 617 | 0 |

617 | 3 | 617 ÷ 3 = 205 | 2 |

205 | 4 | 205 ÷ 4 = 51 | 1 |

51 | 5 | 51 ÷ 5 = 10 | 1 |

10 | 6 | 10 ÷ 6 = 1 | 4 |

1 | 7 | 1 ÷ 7 = 0 | 1 |

Number conversion from $ n _ {(!)} $ (In factorial basis) to base/radix 10, carry out the successive multiplications of its digits (starting from the right) by $ i! $ ranging from 1 to infinity.

__Example:__ $ 1411200_{(!)} = 1 \times 6! + 4 \times 5! + 1 \times 4! + 1 \times 3! + 2 \times 2! + 0 \times 1! + 0 \times 0! = 1234 $

dCode retains ownership of the source code of the script Factorial Base online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Factorial Base script for offline use on PC, iPhone or Android, ask for price quote on contact page !

factorial,base,convert,radix,number,factoradic

Source : https://www.dcode.fr/factorial-base

© 2020 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.

Feedback

▲