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Date: 6/30/96 at 15:44:2
From: Anonymous

How does a calculator add?  I know this seems like a fairly stupid
question at first, but I can't seem to figure it out.  I've written
a program for my TI that'll multiply using addition, but how does it

Thanks,
Anthony
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```
Date: 7/8/96 at 13:33:2
From: Doctor Ceeks

Hi Anthony,

This is a terrific question!

A complete answer would take quite a long time to write.  I suggest
that you go to the public library and look for books on digital
electronics.  You will need to learn about binary numbers too.

Here's a summary of how it works:

Calculators store numbers by converting the numbers to binary
(sequences of zeroes and ones) and store these ones and zeroes by
literally representing ones and zeroes by the presence or absence of
electric charge.  In the last fifty years, advances in electrical
engineering have made it possible to use very very small amounts of
charge...so small that you can literally represent millions of zeroes
and ones on a wafer the size of a thumbnail.  (This is semiconductor
technology).

Now, addition can be thought of as a process whereby two numbers are
given and a third number is returned.

In the calculator, the two numbers are given as presence or absence of
charge, which can manifest itself in the form of an electric current.

So, to make the calculator add, what is needed is some device which
has wires coming in and wires going out so that the current in the
wires going out represent the binary digits of the number which is the
sum of the numbers which are represented in binary by presence or
absence of current in the wires going in.

This problem was solved by first reducing to the case where the
numbers had only one binary digit.  In other words, people figured out
how to add just the numbers 0+0, 0+1, 1+0, and 1+1.  From this, using
more intricate circuits, the entire addition problem was solved.

The electrical circuit designed to do this nowadays requires special
materials in addition to wires and batteries.  Lots of specially
treated silicon is needed.  The silicon is treated in various ways and
put together to form "transistors".

I wish I could take the time to describe how transistors work in
detail to you, but I don't have so much time.  Plus, there are many
books that will explain this.

What's amazing is that today people are capable of putting hundreds of
thousands of transistors on a small silicon wafer less than a square
inch in size...along with all the wiring!

The story that unfolds if you look into your question further is one
of the stories which will characterize the twentieth century, and
especially the generation of adults that live today.

-Doctor Ceeks,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
High School Calculators, Computers
High School History/Biography
High School Number Theory

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