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### Binary Numbers

```
Date: 12/25/95 at 22:42:18
From: Bruce Zaktzer
Subject: Binary Number Systems

Dear Dr. Math:

My name is Courtney Zaktzer, I am in 9th grade and I am doing a
project on Binary Numbers and Systems.

numbers.

Thank You,

Courtney Zaktzer
```

```
Date: 3/18/96 at 2:9:9
From: Doctor Jodi
Subject: Re: Binary Number Systems

Hi there!

I think what you're talking about is base two.  Different bases
are REALLY cool.

One base we use every day is base 60 - can you think of where we
use it? This is a tradition that the Babylonians left us...

I believe that base 10 was popularized by the Arabs (who gave us
the numerals currently in use).

Base two is best known for its use in computing:  0 and 1 can
represent off and on, yes and no, etc.

yet?

Well, here's a brief intro, just in case...

Here's what Dr. Steve said:

We have ten symbols for counting (0,1,2,3,4,5,6,7,8,9). So what do
we do when we need to use numbers higher than 9? We make different
places in our numbers and know that each place has a different
meaning. The first place is the "ones" place. The second is the
"tens". The third is the "hundreds" and so on. Each place is ten
times greater than the one to its right.

So the number 159 means: 1 hundred + 5 tens + 9 ones
----end
notice:  10^2      10^1       10^0 (aka 1)

in base 2, the places are similar:

Instead of being 100, 10, 1, they are 4(2^2), 2 (2^1), 1 (2^0),
etc.

So, what does

1011
mean?

Anyway, write us back with more questions or if you want to know
more.

-Doctor Jodi,  The Math Forum
```

```
Date: 3/18/96 at 9:49:50
From: Bruce Zaktzer
Subject: Re: Binary Number Systems

All,

Thank you for the information. It arrived just in time to complete
the project!

CZ

```
Associated Topics:
High School Number Theory

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