Question

Demonstrate Karatsuba’s algorithm for multiplying integers using just three half-size multiplications as detailed below.

Assume that you can use a calculator to do all operations (half-size (2 or 3 digit) multiplication, and adding, subtracting, and shifting of any size), but write down everything you do. (you are also encouraged to use a calculator to check your process by doing the 4-digit multiplication directly).

Suppose we want to multiply 3275 · 2876.
Write here the three half-size products that you are using:

Show how you can combine (adding or subtracting) some of these products to obtain whatever else you need:

Show how you can do shifting and adding to obtain the final answer:

Answer 1

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