What is the result when you add
10000000000000000 + 1? If you answered
Once you have the numbers stored as arrays, you can add them together in the same way they teach primary school kids. Add each digit together and carry the leftover to the next.
Note, this demo only works with positive numbers. Following the same concepts, it'd be trivial to write other operators and dealing with negative numbers. It is beyond the scope of this post.