Let's be 'logical' - 1
Here is a problem for those of you who
either like mathematics
or
wish to know how interesting maths
really can be:
Have you ever been wondering why we use
only ones and zeros in the language that computers use?
What if we didn't?
Let us discuss this by using a simple example: You
wish to make some calculations from zero up to 15. That's 16 numbers. As
we work with electronic data processing, you wish to represent all these
numbers by electrical values.
That is simple enough: You take 16 resistors of different values, say from 1 k up to 16 kOhms. You connect 16 switches, one to each resistor. In combination with a few additional components and a given voltage you can easily send any number up to 15 to a friend far away or perhaps record it on disk or magnetic tape.
You could even combine some of the switch functions. For example, if you switch the 4 k and the 5 k on together, the resultant value would be 2 k. Well that's not quite correct but may be close enough. - However - firstly, what happens if your battery goes a little flat or the power supply varies. Instead of a 12 you might get an 11 or even a 10. Or even 14. Secondly, look at the circuitry that is necessary to convey our message.
Fig. 1
Is there a better way?
Yes, there is. We are using a different number system: Boolean Logic. (How this is done in practice is explained in Fact Sheets 23 to 28) Look at the diagram Fig. 2. All we now need is four switches and with those we can express any number from zero to 15 (that's 16 numbers) just by the different combinations of the switch settings.
Fig. 2
If we add four more, bringing it up to eight switches, we can take the numbers right up to 255. Again this includes zero so the total is 256 numbers. Imagine this with the resistor and switch combination above and compare it to the arrangement in Fig. 3 below.
Fig. 3
But there's more: If the mains voltage drops (or goes high) or our battery is not fresh anymore, there won't be any mistakes (unless the battery is really at the end of its life) because the on/ off state system leaves no doubt even if there is a difference in the supply voltage. The sytem is virtually mistake-proof.
Computers use microscopically tiny switches and many millions of them. They are extremely fast and so computers can create the wonderful functions we take for granted in our modern world.
In the following Fact Sheet we will explain how this Boolean Logic system works.
Did you find this hard going? If you have any questions you may send them to me, Peter, at my email address.
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Copyright © 1997-2010 Peter Schmedding, Child Development Projects, Canberra, Australia.