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But your counts are all using base 10! If we were to count the number of digits in binary using binary, we would get 10 digits. If we were to count the number of digits in hexadecimal in hexadecimal, we would still get 10 digits. This is true for all bases.


Changing the representation doesn't change the number. Ten, two, sixteen...


Try this:

Base 10 is count(0, 1, 2, 3… 9) = ||||||||||

Base 16 is count(0, 1, 2,… a, b, …f) = ||||||||||||||||




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