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The base-2 numbering system is called binary.

The base-8 numbering system is called octal.

The base-10 numbering system is called decimal.

The base-16 numbering system is called hexadecimal.

How should the base-64 numbering system be called?

(A word of Latin origin like the above would be nice.)

Mike Nakis
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It should be "Tetrasexagesimal". Here is a great number of the bases named: Wikipedia.

"Tetra" stands for the final "4" according to this system; "sexagesimal" stands for "60".

LPH
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    So much more convenient than saying "base-64" :) – user888379 Aug 12 '21 at 17:14
  • @user888379 For the sake of completeness it is still justifiable, but, of course, even with respect to that criterion, the naming—which has to stop somewhere— might have stopped at "hexadecimal", which is nevertheless very commonly used, surprisingly maybe, enormously more than "base 64". https://books.google.com/ngrams/graph?content=hexadecimal%2Cbase+64&year_start=1800&year_end=2019&corpus=26&smoothing=3&direct_url=t1%3B%2Chexadecimal%3B%2Cc0%3B.t1%3B%2Cbase%2064%3B%2Cc0 – LPH Aug 12 '21 at 18:29
  • @user888379 it may not be as convenient, but it is certainly far more erudite. – Mike Nakis Aug 12 '21 at 18:57
  • @MikeNakis I understand your concern for the systematization of concept labelling, but I still think that somehow (perhaps unknowingly) you indulge in a divergence from what true erudition is, and that is, I believe, essentially, pure knowledge of a relatively important proportion of the concepts pertaining to a given field, and not a matter of what system you use to identify those concepts. – LPH Aug 12 '21 at 20:06
  • @LPH In practice, "hexadecimal" decays pretty quickly to "hex". There's never been any ambiguity in my experience. – user888379 Aug 12 '21 at 21:46
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    @user888379 The result in the ngram mentioned above amounts to approximately the same thing if it were the correct but it is wrong; this is the correct one: https://books.google.com/ngrams/graph?content=hexadecimal%2Cbase+16&year_start=1800&year_end=2019&corpus=26&smoothing=3&direct_url=t1%3B%2Chexadecimal%3B%2Cc0%3B.t1%3B%2Cbase%2016%3B%2Cc0#t1%3B%2Chexadecimal%3B%2Cc0%3B.t1%3B%2Cbase%2016%3B%2Cc0 – LPH Aug 13 '21 at 01:11
  • @LPH The pedantry that I'm prone to is saying "radix" rather than "base". – user888379 Aug 13 '21 at 13:35
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    @user888379 Personally, I wouldn't call it pedantry, and I tend to agree with this trend: there is at least one other concept in mathematics that uses the word "base" (the base set in the theory of mathematical structures); as long as adopting a new form makes for the diversity of the forms used, it seems to me that the practice is commendable; if, on top of that the new form has a particular semantically catchy quirk which is missing in the former term—as is the case for radix (radix, root, inverse of raising to a power)—it's all for the better, in my opinion. – LPH Aug 13 '21 at 13:51