Calculator Addition

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

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
ADD?

Thanks,
Anthony

Date: 7/8/96 at 13:33:2
From: Doctor Ceeks
Subject: Re: Calculator Addition

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/