This week's book giveaway is in the OO, Patterns, UML and Refactoring forum. We're giving away four copies of Refactoring for Software Design Smells: Managing Technical Debt and have Girish Suryanarayana, Ganesh Samarthyam & Tushar Sharma on-line! See this thread for details.
Normally one would just use BigInteger objects if one wanted to add together two integers with 1000 digits.
However I expect you are asking about some homework problem, in which case BigInteger wouldn't be acceptable. If that's the case, please read these links: DoYourOwnHomework and ShowSomeEffort, and then if you still have a question, don't hesitate to ask that question here.