Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

Base Number


Date: 10/07/98 at 18:11:41
From: steve
Subject: Base Number?

What does base number mean?  I know we have a base 10 system and I 
think it has to do with when the numbers switch to two digits, but I 
know I'm wrong. 

Thanks.


Date: 10/08/98 at 12:02:22
From: Doctor Peterson
Subject: Re: Base Number?

Hi, Steve. 

You have the general idea. A nice way to think of it is to look inside 
a counter, like the odometer in a car or the counter on some tape 
recorders, with a wheel for each digit. Each wheel has ten digits, 0 
through 9; when it turns past 9 back to 0, it turns the wheel to its 
left one place, meaning "we've just counted ten more; I've started 
over at zero, so please keep track of the number of tens for me." Then 
that "tens" wheel counts until it turns back to zero, and it tells the 
next wheel to count one more set of 100, or 10 tens.

Another way to think of it is that we count things by grouping them 
into stacks of ten, then stacks of ten into stacks of ten tens, and so 
on. When we write "123" it means we have one stack of 100, two stacks 
of 10, and three single items.

You can do the same with other bases besides ten. If we had only two 
fingers instead of ten, we might be counting in base two -- that's 
what computers do! (In fact, the word "digit" originally meant 
"finger.") 

Here is our FAQ with links to more answers in our archives about 
different bases:

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

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


Date: 10/08/98 at 15:51:29
From: Anonymous
Subject: Re: Base Number?

How do computers know what the numbers 1 and 0 mean? 

I understand how programmers do stuff now since I am one (kinda - I've 
programmed a calculator and one game), but how did they start? How could 
the computers just know 1 is an apple and 0 is no apples? It boggles the 
mind!


Date: 10/09/98 at 09:18:08
From: Doctor Peterson
Subject: Re: Base Number?

Hi, Steve. 

Good question - did my mention of computers stimulate this thinking, or 
have you wondered about this for a long time?

Computers don't exactly know what numbers (or words, or pictures) mean, 
they just "know" what to do with them. 

A transistor, which is the basic unit of a computer, is a switch that can 
be wired to respond to an input by either turning on or off. Wire them 
together the right way, and they can add numbers (with "on" representing 
1 and "off" representing 0); wire the adders together the right way, and 
they can do just about anything. It's the programmer who decides that a 1 
in a certain place should mean "apple" or "hit" or "beep"; and usually you 
have a programming language translated by a compiler or interpreter program 
to insulate you from the details. The computer just manipulates all those 
bits according to your plan, and what comes out means what you wanted it 
to mean - if you programmed it right!


Date: 10/09/98 at 22:14:00
From: Anonymous
Subject: Re: Base Number?

I have wondered about all those things but I kept thinking of more as 
I typed!
    
Associated Topics:
Elementary Number Sense/About Numbers
High School Number Theory
Middle School Number Sense/About Numbers

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/