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If we counted in hex, how would it vary? It appears to me to be "not much" because it says most things scale to express as instances of the first non-zero value in the number system plus an arbitrary number of powers of the base. So.. it's Fermi arithmetic 0, 1, 10, 100 ...

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In base b, the probability of the leading significant digit to be d (where 0 < d < b) is log_b(1 + 1 / d).

That's why for base 10, the probability of the leading significant digit to be 1 is log_10(1 + 1/1) = 0.301. In base 2, the probability of the leading significant digit to be 1 is, quite trivially, log_2(1 + 1/1) = 1.0. Of course, all numbers in binary must begin with the digit 1.

Benford's law works in any base.

Except base 1.

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