Question

find the product of two number x1=732912 and x2=1026732 by using karatsuba's method

Answer 1

x × y = (1026 × 0732)  
10²×³ + 732 × 912+ [(1026 + 732) × (732 + 912)- (1026 × 0732) ─ (732 × 912)]10³
= (1026 × 0732) 10⁶ + 732 × 912 +[(1758 × 1644) ─ (1026 × 0732) ─ (732 × 912)]10³
 now after finding this you will have to compute the products as:-
U = 1026 × 732V = 732 × 912P = 1758 × 1644

first only considering 1026 × 732 and taking others which are computed similarly as A we can get,

U = 1026 × 732 = 
 (10 × 10² + 26) (07 × 10² + 32)=
(10 × 7) 104 + 26 × 32 + [(10 + 7) (26 + 32) -10 × 7 ─ 26 × 32)] 10²
= 17 × 10⁴ + 26 × 32 + (17 × 58 ─ 70 ─ 26 × 32) 10²