Answer:
We can use Karatsuba algorithm to achieve the required goal as follows:
let the two numbers be X = 36 and Y = 52,
let X = X0X1 and Y = Y0Y1 ( for given example)
so, X0 = 3, X1 = 6 and Y0 = 5, Y1 = 2
Now, product of two numbers be:-
X * Y = X0X1 * Y0Y1
= 100 ( X0*Y0) + 10 (X0 * Y1 + X1 * Y0) + X1 * Y1
36 * 52 = 100 ( 3 * 5) + 10 (3 * 2 + 6 * 5) + (6 * 2)
= 1500 + 360 + 12
= 1872
by doing this we only need 3 atomic multiplications to multiply two 2-digit numbers.
