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/
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