Subject: How does one calculate large numbers on a computer?

E.g. cryptography needs large numbers (with some hundred digits) which are 
multiplied, moduli are used on them etc. How does that work on a computer 
which can only work with numbers up to 16 digits or so? => How do I get 
the correct result - down to the least significant digit - of e.g. 
[(10^20)-1]? The computer will return 1e20 where the correct result would 
rather be 9'999'999'999'999'999'999... 

Thanks for answering and a big HI! from Switzerland

Re: How does one calculate large numbers on a computer?