7. (15 points) Large integer multiplication a. Design the mathematical formulas and steps for the divide-and-conquer algorithm to e the multiplication of two large integers a b where a and b are n-bit integers that can be written as a ado a1, ao,bi, bo are 2bit integers. 0 Derive a recurrence relation for the number of single-digit multiplications needed by this algorithm. Solve the recurrence relation and analyze why this algorithm needs fewer single-digit multiplications than the conventional method. b