Encoding:
https://cdn.discordapp.com/attachments/1207753334518456381/1345841003256610947/image.png?ex=67c6039b&is=67c4b21b&hm=a0339d12e8dd85bef10b347d7ab7fd1e06c8df54c00bc3bdc5c95458352ae001&

This processes the input atom by atom, starting from the most significant bit.
When it processes salt, the two index wheels get yoinked. When it processes fire, they don't and they spin in place. The numbers of spins when fire compared to salt are the following:

1st pulled atom: left wheel +4, right wheel +3
2nd atom: +4, +1
3rd atom: +2, +1
4th atom: +1, +1
5th atom: +0, +1

Note that the wheels spin in opposite directions, so the right wheel promotes metals and the left wheel demotes them. To find these spin amounts, I used a Python script.