Applications of Different Bases

Date: 03/27/2002 at 05:57:06
From: L. McCrory
Subject: Base numbers

Dear Dr. Math,

I am trying to find three bases other than base 2, and find a use for 
them. Any help would be greatly appreciated.

Thank you.
L. McCrory

Date: 03/27/2002 at 23:43:11
From: Doctor Twe
Subject: Re: Base numbers

Hi - thanks for writing to Dr. Math.

First, check out our "Number Bases" FAQ at:

   http://mathforum.org/dr.math/faq/faq.bases.html   

Some number bases (other than 2 and 10) that come immediately to mind 
for their practical use are:

Octal (base 8) and hexadecimal (base 16): These are used in computer 
sciences as a "shorthand notation" of binary values. Their use extends 
to diagnostics, programming, and html, among other computer-based 
applications.

Sexagesimal (base 60): Used in hour:minute:second representation of 
time, as well as degree*minute'second" representation of angular 
measure. (We don't represent the minutes and seconds with a single 
symbol, but the minutes and seconds can be thought of as a single 
"digit" represented by a two-symbol combination.) The Babylonians also 
used a sexagesimal-based number system.

Vigesimal (base 20): The Mayans used a vigesimal-based number system. 
The names of numbers in French are also loosely based on 20's.

Senary (base 6): Sometimes used in dice-based games. Multiple dice are 
read by color as a multi-digit senary value. The result is usually 
then looked up on a chart of some sort.

There are also some specialized "weird" uses of number bases. See, for 
example, the following from our Ask Dr. Math archives:

   Paint Formulas in Base 48
   http://mathforum.org/dr.math/problems/behymer8.20.98.html   

   Duotrigesimal (Base 32) Numbers
   http://mathforum.org/dr.math/problems/deboer6.11.99.html   

In the latter entry, you'll also find references to uses of base 64, 
base 85, and base 36 in specific computer applications.

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
  http://mathforum.org/dr.math/