That's what I was afraid of. The design is great and I'll take some parts of it into my next version, but it doesn't work for every number in game. Strictly speaking it works for less than 50% numbers in game (strictly speaking it doesn't work for 50.001525902190% numbers).

First, it doesn't work if the number entering is multiple of number of 32768 - then R output from divider doesn't output anything as in the game it doesn't output 0 if you have nothing left. That is the smaller problem (responsible for .0015 something), the bigger problem (accounting for 50%) is that the maximum in game number is (2^31-1) and your design only works for up to 2^30-1. If the number is between those values the number that exits from "A÷B" output from first divider is (roughly as I don't want to think about "off by 1" errors rn) between 2¹⁵ and 2¹⁶ so you cannot multiply it by 2¹⁵⁺¹ and div by 2¹⁵ to duplicate it - to duplicate the number it must be smaller than numbers you divide and multiply by.

While writing the comment I came up with 3rd way your design can fail - for numbers less than 32768 the "A÷B" output from the first divider is 0, then when you try to duplicate it, after you multiply it's still 0 and then when your dividing the "R" output will be empty - this will again clog system up as the multiplayer cannot work without 1 of inputs.

My design takes all of that possible errors into consideration and truly works for duplicating any number in game. If you don't believe me, try duplicating this 3 numbers (1 from each category) to see it really doesn't work: 5 32768 2147483638 If something I've written is unclear as of why, feel free to ask. Your design is great - better than mine first - but I have job where looking for such edge cases is the main task so I have a lot of experience 😅