What are the additional symbols used in numeral systems with more than 10 base digits? What would the last digit be in a base 11 system? Base 12?
I'm mostly wondering because I was thinking of a base 36 system with digits 0-9 immediately followed by the letters A-Z but I wasn't sure if that would be considered a proper numeral system, or if there was something else in place.
 A: In addition to the standard A-F, etc. for hexadecimal and other systems, this old Schoolhouse Rock video (which implicitly talks about duodecimal) uses symbols that look an awful lot like the Greek chi ($\chi$) and epsilon ($\epsilon$) for ten and eleven, respectively.
A: The extra digits can be anything you want (the symbols 0-9 themselves are arbitrary, and could be switched around or replaced by other things, though that'd be adding unnecessary confusion). As Arturo mentions above, hexadecimal notation is common in computing, and there it is conventional to use $A=10$ through $F=15$. 
If you want to stick to using the 10 Hindu-Arabic numerals and 26 English letters, and want to go past base 36, the Wikipedia article on positional notation describes how one might solve this by using groups of these symbols in each position. 
A: IIRC, on the SWAC at UCLA in the 50's and 60's, the 6 hex digits beyond 9 were U V W X Y Z.
Also, for some reason, this pops into my mind for the hex digits: G B N J F L. These stood for "Great Big Numbers Just For Laughs".
