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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.

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8  
Traditionally, A, B, C, D, E, F, etc are used; this is standard for base-16, for instance, which is very common in computer science. But in principle, you can use any symbol you wish; we could agree that # represents 10, & represents, etc. –  Arturo Magidin Nov 20 '11 at 23:07

3 Answers 3

up vote 4 down vote accepted

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.

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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.

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The additional symbols are pronounced "dek" and "el". See this for instance. –  J. M. Nov 21 '11 at 0:55
    
+1 for "School House Rock" episode –  Hartley Brody Nov 21 '11 at 2:51
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See this as well. –  J. M. Nov 21 '11 at 14:28

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".

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