To help you understand the algorithm, the video shows a simple two-digit by two-digit multiplication. You can see that the first and last digits are essentially the result of one multiplication.

The multiplication algorithm in question takes advantage of a discovery that was the first advance in multiplication made in thousands of years. The traditional grade-school method for multiplication ...

Even for computers, the long multiplication algorithm, defined as n to the power of, could reportedly take months if each number had a billion digits.

Karatsuba’s divide-and-conquer multiplication algorithm takes advantage of this saving. Consider a multiplication algorithm that parallels the way multiplication of complex numbers works.