Multiplication

Multiplication is a fundamental mathematical operation defined as the repetition of addition.

Calculation tools such as calculators or computers are limited by their ability to display or manage a large number of numbers in the result.

Standard calculators generally have a limited capacity in terms of displayed digits, which can make it difficult to manipulate multiplication results with many digits.

Processors and computers are generally limited in handling overflows, as integers cannot exceed a certain allocated memory size, which can lead to errors or the loss of significant information.

Enter numbers (up to several thousand digits) and click the button to calculate.

The dCode multiplication tool with big integers uses arbitrary precision calculation algorithms. That is to say that it is not limited to a few billion (like most other software) 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:

The Karatsuba algorithm is a fast multiplication technique for large numbers. 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).