storing more than 2 power 31 on a 32-bit system

Question

I have to write a program that can calculate the powers of 2 power 2010 and to find the sum of the digits. eg:

if `2 power 12 => gives 4096          


        

Answer 1

Knowing 2^32, how would you calculate 2^33 with pen and paper?

2^32 is 4294967296

4294967296
*        2
----------
8589934592

8589934592 is 2^33; sum of digits is 8+5+8+9+...+9+2 (62)

Just be aware that 2^2011 is a number with more than 600 digits: not that many to do by computer