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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:


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 

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

   Duotrigesimal (Base 32) Numbers

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
Associated Topics:
High School Number Theory

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