Tool to make multiplication with large numbers (with lots of digits/figures). Standard calculators are limited with big numbers.

Multiplication - dCode

Tag(s) : Arithmetics

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**Multiplication** is a basic arithmetic operation defined as the repetition of an addition.

__Example:__ 3 times 2 $ = 3 \times 2 = 2+2+2 $

The dCode **multiplication** tool with big integers uses arbitrary precision calculation algorithms. That is to say that it is not limited to 4 billion and it can **multiply** exact values without rounding nor need of a scientific notation. It is called large/huge number **multiplication**.

Traditionally * multiplication tables* refers to this table:

\ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 |

3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 |

4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 |

5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |

6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 |

7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 |

8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 |

9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 |

10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |

In order to improve calculation time the **multiplication** is accelerated by decomposing it:

ab * cd = (a * 10^k + b) * (c * 10^k + d) = ac * 10^2k + (ad + bc) * 10^k + bd

This **multiplication** needs 4 values ac, ad, bc and bd. More:

(a * 10^k + b) * (c * 10^k + d) = ac * 10^2k + (ac + bd - (a - b)(c - d)) * 10^k + bd

The same **multiplication** needs 3 values: ac, bd and (a - b)(c - d).

dCode retains ownership of the online 'Multiplication' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any 'Multiplication' algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any 'Multiplication' function (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and no data download, script, copy-paste, or API access for 'Multiplication' will be for free, same for offline use on PC, tablet, iPhone or Android ! dCode is free and online.

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Source : https://www.dcode.fr/big-numbers-multiplication

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