Calculator AdditionDate: 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/ |
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