The Half Adder
The half adder is a fundamental building block of computing. The device is made from an XOR gate and an AND gate. There are two inputs, which are fed into both the XOR and the AND gate. There are also two outputs, one from the XOR gate and one from the AND gate. The XOR output is called the sum, S and the AND output is called the carry, C.
The device adds binary numbers, as the name suggests! That is, in the case of adding two bits together, the sum of 0+0 = 0, carry 0; 0+1 = 1, carry 0; 1+0 = 1, carry 0 and 1+1 = 0, carry 1. Unfortunately it can only add two bits, which obviously limits its usefulness. However, by combining two half adders, one can get a full adder, which in turn can be cascaded to produce a binary adder of any size.
The pictures below show the LEGO half adder in its four different states. There is also a video available to be downloaded (680 KB).