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This is a bad puzzle, because the solution does not make full use of the evidence.
It looks as if any ring has three states: Top, bottom, and full.
Naturally, someone would try to create a complex system from these three-state rings that generates the numbers shown.
However, the puzzle tricks the player by having the "three state rings" actually be a pair of two-state semicircles.
This kind of trick is just bad puzzlemaking because it means the actual solution is much more simple than the apparent solution, but the only people who will figure out the actual solution are those who make an unreasonable (yet correct) assumption about the nature of the puzzle.
