Introduction

Perhaps right after the addition at school we’ve learned how to multiply two numbers. This algorithm isn’t as easy as addition, but besides that we’re so familiar with it and that we even don’t recognize it as an “algorithm”. We just know it by heart.

However, as I already said, multiplication is a bit more difficult than addition. This algorithm is interesting because for several reasons. First of all, let’s compare multiplication in binary and decimal.

So, let’s see how to multiply two numbers.

Overview

Multiplying and adding is practically the same thing, so where’s the difference?

It’s clear that a product of two numbers (each with N digits) can be represented as N sums, as we can see on the next picture.

Now, for larger integers each time we shift left the next intermediate sum.