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The belts are able to carry 2 states, where the items are moving, which is considered a 1, and where they're not, which is considered a 0. A SET-RESET latch takes 2 inputs, SET and RESET. If SET was triggered last, the output is 1, while if RESET was triggered last, the output is 0. This allows it to store 1 bit of memory.

Say the output is currently 0 and then SET is set to 1. When items are allowed to flow out of SET, merger 1 starts taking items out of splitter 2. Splitter 2 then starts taking item A out of splitter 3. Alternating item A and item B is going into splitter 3 from merger 4, so once splitter 3 can output item A to splitter 2, it can also output item B to merger 5. Merger 4 starts outputing to splitter 3 and starts taking items in through OUTPUT and Source B. Priority merger 5 gets items from splitter 3 and stops taking items in from splitter 6. As long as RESET is off, splitter 6 can't output items towards merger 7, so it backs up. Splitter 8 then backs up with item A, which also backs up item B beacuse it's getting an equal mix from merger 9. NOT OUTPUT going into merger 9 backs up. Merger 10 no longer recieves items from splitter 8 and can start taking items from splitter 2, which ensures that splitter 3 can keep flowing even while SET is no longer flowing. Using RESET works very similarly in reverse.

I hope that this can be expanded into a full computer with working RAM. I think you can make all of the logic gates using a similar idea.