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If you really want to be pedantic, you say that every base is base 10 :) (in its own representation)

> Other bases would have different words for their numbers - bit in binary, for example

Do we have another example? I don't think there are special terms for "octal digits" or "hexadecimal digits".

> Being further pedantic - aren't all digits base ten? I thought that was part of the definition of digit.

We call computer circuits "digital" even though they work in base 2.

Regardless of the word's origin, digits are simply the symbols in a positional number system: https://en.wikipedia.org/wiki/Numerical_digit