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### Number Bases beyond 36

```Date: 06/22/2003 at 11:00:05
From: Scott
Subject: Number bases

There is plenty of information around about the common number bases,
e.g. binary, hexadecimal, etc.

Going up to base 36 is relatively easy, as the characters used to
represent to digits are in the ranges [0-9] and [A-Z].

My question is, what characters are used to represent numbers in a
base greater than 37... i.e. beyond Z?
```

```
Date: 06/22/2003 at 12:00:08
From: Doctor Mike
Subject: Re: Number bases

Scott,

Beyond base 16 doesn't seem to have much practical use, but we can
still be interested in it. One suggestion I have seen to extend the
base beyond 36 is to use both upper and lower case letters. That adds
another 26. A possible problem with that is that the digit 0 and the
letter o and the letter O tend to look similar when written.  So, 1Oo
could be mistaken for 100.

Other extensions would involve other of the ASCII characters, like
&^#@, etc. You might think of using ! too, but then it could be
confusing if 5Aa&! were mistaken for 5Aa& factorial.

The short answer is that no system is widely used for what you
describe. But go ahead and think about the possibilities.

- Doctor Mike, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Number Theory

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