This topic is kinda old but still I think I'd like to add something to it.
I'm more of a teorethical person, I prefer f.e. proving that you can make something in a certain way or you can't, not making the contraptions themselves.
From the easy-to-prove Chinese Reminder Theorem you can deduct that to make a 192 outputs randomizer you will need:
-6 times 2 output randomizers
-one 3 output randomizer
In general - you only need to make prime number randomizers (like 2 output, 3 output, 5 output...) and then you can somehow combine them (I have several ideas of how to do it) to make other output randomizers (like 6, 100, 192)
Also, you can make rational, non-whole numbers randomizers (like you have f.e. 3/5 probability that the gate will be lit up), which is also deducted from the CRT.
One more thing. You can't make irrational probability randomizers ONLY with logic gates. Prooving is very easy, but kinda long. In short: we will look at the probability of each logic lamp litting up after clicking a button. Now its the long part, we will see that every gate corresponds to an arythmetic thing (except the faulty ones). F.e. the AND one is multiplication. If you have two lamps, one has 50% probability and the other lamp has 20% probability of being lit, then the resulting lamp has a 10%=20%*50% probability of being lit. Now - faulty gates provide us only with rational numbers probability, like 4/5. But the other gates do only do things like multiply, add, substract... And when we do this we rational numbers, we get rational numbers. So that's why making an irrational probability randomizers can only be made with non-gate things. But still - maybe you can make it with things other than logica gates, but I don't have any ideas for a randomizer like that. But if somebody had an idea, or a proof that you actually can't do it- then please tell me.
One more, even harder problem. If it turns out that you can make irrational probability randomizers, then is it possible to do a transcendensal probability randomizer? (like 1/pi)