You're getting it wrong.
Everything the computer does, be it showing letters on the screen or doing some computation, can be viewed at different (many) levels of abstraction, from the electrical current to the manipulation of abstract concepts like money on a bank account.
That said, building the circuit for a simple microprocessor is not that hard, an ALU, some registers and some control logic. Altera has this as advanced tutorials for the Cyclone II starter board, but I can't find it on the web.
