Binary puzzle?

Question

How many operations does it take to multiply 2 numbers X,Y together,assuming X has N binary digits in its binary representation and Y and M binary digits in its binary representation

Answer 1

Assuming you mean a single bit add to be a binary operation, it's 2*M*N operations for the 'shift and add' algorithm.


Doug

Answer 2

To convert a binary number(N digits) to usual number we have
N multiplication and N-1 addition.

So, for two numbers we have to perform 2N multiplications and 2(N-1) additions.

To add the usual numbers we perform one more addition.

So, the total number of steps are
2N + 2(N-1) + 1 = 2N + 2N - 2 +1 = 4N + 1.

So ,the total number of mathematical operations needed is 4N+1.