In any case, I suppose I could have stated in the original statement that my assumption that all numbering systems are base 10 was the digits are counted by having the rightmost digit count from 0 to the maximum value, then reset to 0 and simultaneously incrementing the digit to the left of it, with 0's implied whenever there is blank space. But that wouldn't be any fun to state everything so explicitly.
I think what you mean to say is that all the numbering systems with a base (like binary, hexidecimal, etc.) are
decimal systems (meaning that moving one column to the left increases the value by one base, and a decimal point indicates where the value is base*0).
First of all, a binary system (for example) is by definition base 2. It can't possibly be base 10 and base 2 at the same time.
Second, not all numbering systems are decimal. The Roman system (I, II, III, IV, etc), for example, is not. And it doesn't have a base, really - though one could argue that it has several: I, V, X, L, C, M, etc.