Push-pull Half-adder

"No, no, you're not thinking; you're just being logical." - Niels Bohr

This page has details about the Half-adder. The half adder is a composite of an XOR gate and an AND gate. Without the half adder you wouldn't be viewing this page!

The XOR gate

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, where A and B are the inputs, S is the sum and C is the carry bit. There is also a video available of it being operated.
Here is the video of the half adder gate being operated.