An anonymous commenter suggested that I look at logisim, a circuit simulator written in Java. It has many nice features. For instance, you can specify a combinatorial circuit either as a truth table or as equations, and it will convert to the other representation (in minimized forms) and will also build a circuit to implement those equations. You can tell it to use only 2 input gates, or even to use only NAND gates, and it will layout a little circuit to implement it.
For instance, I entered the truth table for a full adder, and told it just to use 2 input NAND gates. The resulting (29 gates? I didn't count carefully) 1 bit full adder emerged as a circuit:
Pretty neat. I am not sure that logisim is quite good enough to design an actual, physical CPU (it doesn't model propagation delays, as far as I can tell) but it's a very good tool to exercise your nascent digital design skills. Check it out.