first time posting. This has probably been found before, but I found it myself, exciting for me. Sorry if my math language is bad. My question is about number systems with fractions/benath one.
I found that if you make a number tree, there's a pattern in amount of numbers. I mean a number tree like 00, 01, 10 and 11. This would be in the 2-digit system and you would have 2 "sets of branches". I found that the equation (x+highest digit in system)^branches would find the amount of zeros in one line (sub-branch). In a 2-digit system with 2 branches, as listed above would be 00, 01, 10 and 11, or $(x+1)^2 = x^2 + 2x + 1$. The one with a square would be amount where there are no zeros, therefore one. The seconds part (2x) would tell us amount of subbranches with one zero, which is 2 (01, 10). I found this works for any number system. Are there anyone else that know where I can find more about this, and if it works with number systems below 1? Thanks for reading! :)