The nice people over at Waiting for Friday has written a nice story on how to build a simple 4-Bit_Computer. Calling it a computer might be a bit over the top, it is actually a small adder circuit.
The nice thing about the design is that it is built from transistors. All the steps involved are explained, from binary addition, logic gates, all the way down to how to build each electrical sub-component.
For those of you who do not want to read the text, there is a video summarizing the contents as well. Well worth watching!