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### Base Number

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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.
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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.")

different bases:

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

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

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!
```

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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!
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