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For an n-bit adder, just chain together a few full adders by linking the carry output (Cout) into the carry in of the next adder like this
To make the adder subtract, use the two's complement method by inverting inputs A and B and holding the initial carry-in input high :)
For more advanced "computers", I prompt you to buy The Elements of Modern Computer Systems - Its a fantastic book that will take you through everything from basic combinational and sequential logic (like adders) all the way to a full blown computer, complete with compiler, operating system and programming language virtual machine knowns as the "Hack platform".
You can even read some of it online here!
Good luck!