So how do you get it to add? Specifically, what representation of arbitrary numbers are we using with our finite automaton? Infinite read-only tape plus infinit

So how do you get it to add? Specifically, what representation of arbitrary numbers are we using with our finite automaton? Infinite read-only tape plus infinite write-only tape for output, in base 10? If so, it should be simple to do multiplication by representing the numbers in factorized form and applying our adder.