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Q&A #2601


Base 2 numbers

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From: Suzanne A. (for Teacher2Teacher Service)
Date: Nov 20, 1999 at 12:19:02
Subject: Re: Base 2 numbers

Dear Gail,

I guess what we can do is try to explain what base 2 means to you and then
you will be able to help your child? Sometimes it's fun to learn something
new with your child because not only can you help them understand, but they
can help you understand, too!

Just to give you a little introduction - Normally we work in a base 10
system. That just means that we have the numerals 0, 1, 2, 3, 4, 5, 6, 7, 8,
9 and to represent the next number we combine the 1 and the 0. Another way to
think about it is, if we take any number, say 364 we can think of it like
this:

	3 x 100  +  6 x 10  +  4

Base 2 is another story, however. In base two we only have two numerals to
represent our number. The numerals are 0 and 1. Base 2 is also often called
the binary system. Computers use this system to operate and I have often had
it explained to me in terms of a light switch - it is either in the "on" or
the "off" position. It ends up that binary numbers are quite long since you
use up the possibilities quite quickly and you continue to have to go to the
next place to represent the number!

There is a great Ask Dr. Math FAQ that has links to a variety of information
pages on bases. I suggest you browse through them to read about bases,
converting between one base to another, and doing a variety of operations in
other bases. It is here:

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

Other pages that have information to help you include:

Different Ways to Represent Numbers
http://www.cs.indiana.edu/classes/h212-lake/number_representations/index.html

Concepts of Adding in Base 2
http://mathforum.org/dr.math/problems/ross8.18.98.html

Addition and Multiplication Tables in Various Bases
http://cut-the-knot.com/blue/SysTable.html

I hope that helps.

 -Suzanne A., for the Teacher2Teacher service

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