Generating Formulas with criteria (13 = 3)

Hi forum, this is my first post here so a big hello to everyone.

I'm an engineer and have to log into a custom database everyday. The password for the database is generated by adding two numbers together.

So lets say 1234 + 5678

Now, if a value goes over 9, only he last unit is used, e.g. 6+7 = 13 therefore 3 is the right number

So the answer to the above value would be 6802:
1 + 5 = 6
2 + 6 = 8
3 + 7 = 10 therefore 0 is used
4 + 8 = 12 therefore 2 is used

I'd like to write a spreadsheet that will work this out automatically using the given rules. I've been trying for days and not getting anywhere, can anyone help?

Thanks in advance