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Multiplication

Tool to make multiplication with large numbers. Multiplication is a basic arithmetic operation defined as the repetition of an addition. 3 times 2 = 2+2+2. Standard calculators are limited with big numbers.

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Multiplication -

Tag(s) : Arithmetics

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# Multiplication

## Multiply many numbers

Tool to make multiplication with large numbers. Multiplication is a basic arithmetic operation defined as the repetition of an addition. 3 times 2 = 2+2+2. Standard calculators are limited with big numbers.

### How to calculate a multiplication with big numbers?

The dCode multiplication tool with big integers uses arbitrary precision calculation algorithms. That is to say that it can multiply exact values without rounding nor need of a scientific notation. It is called large/huge number multiplication.

### What are multiplication tables?

Traditionally multiplication tables refers to this table:

1 2 3 4 5 6 7 8 9 10 \ 1 2 3 4 5 6 7 8 9 10 2 4 6 8 10 12 14 16 18 20 3 6 9 12 15 18 21 24 27 30 4 8 12 16 20 24 28 32 36 40 5 10 15 20 25 30 35 40 45 50 6 12 18 24 30 36 42 48 54 60 7 14 21 28 35 42 49 56 63 70 8 16 24 32 40 48 56 64 72 80 9 18 27 36 45 54 63 72 81 90 10 20 30 40 50 60 70 80 90 100

### What is the Karatsuba algorithm?

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

Example: 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).

## Source code

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