Then it occurred to me … I bet I can build a binary half-adder using TIM.
You can see my TIM binary half-adder here. I demonstrate adding 0+0, 0+1, 1+0, and finally 1+1.
The trick to doing the 1+1 addition is the XOR gate consisting of two bellows and a balloon between them. The way it works is that if either bellows is pushed, the balloon moves and the light is triggered. If both are pushed, the balloon stays in the centre and the light stays dark. Obviously, if neither bellows are pushed the balloon also stays in the centre.