Algodoo

It's just an adder, but "calculator" sounds so much better.
~Completely mechanical~

Press S to add the 2 numbers and display the result in binary.
Press R to reset
I provided some numbers (which I *think* I did correctly) but you can make your own if you're feeling ADVENTUROUS.

Works from 100-300Hz. Can't be bothered tweaking at this point, I'll make an improved one later probably.

I tried to make this one both fast and small. At 100Hz it produces an output in about 3.5 seconds, and it takes up less than a metre square.

Uses rod-logic to make logic gates, which in turn makes 8 full adders in series. (I could have replaced the first with a half adder, but by the time I realised that I couldn't be bothered). The rods are pushed in the correct sequence using a central cam in each full adder. One half of a turn pushes all the rods, and the other half resets them in the correct order.



I stole the binary-reading explanation off Rastamoose c:

Related reading: Conundrumer made a bunch of counters using rod logic. http://www.algodoo.com/algobox/details.php?id=62815

This shows some basic gates using rod logic
http://www.halfbakedmaker.org/blog/58

A lot longer, but is interesting reading even if the maths goes right over your head (like it does mine).
http://www.zyvex.com/nanotech/mechano.html

EDIT: slightly tweaked