I designed and built this binary adding machine entirely out of Legos at the suggestion of one of my professors at the University of Illinois. It was a fun little diversion from my classes. It took a few hours of designing and a few more of construction. An eight-bit binary adder built in circuitry could appear about 10,000 times on a single microchip; whereas this Lego adder requires about 5 feet by 3 inches of counter space.
The Lego adder has two parts -- the stationary part and the "train". One number is represented by the positions of the "flags", which are in the stationary part. The other is represented by rods that are attached to the train and are free to rotate up and down. The train's number is added to the number represented by the flags. To add two 8-bit binary numbers (for example 00000101 + 00000110 = 00001011, or 5 + 6 = 11) you would flip the flags to represent 6, and you would position the rods of the train to represent 5. Then you would push the train and the rods would cause the flags to toggle in such a way that they would be set to the binary representation of 11.