I like to split both numbers into digits and then have different programs/threads/processes add them and provide the carry etc.. and get the final answer.
So you mean you want to write a computer program to add 5 digit numbers, the way we did it manually before calculators and computers?
Why? The whole purpose of computers is to avoid having to do that! :-)
P.S. If you are serious, learn to split numbers into digits, then learn to add them via modulus. See grep integer and fractional part from a division (modulus ?)