Its A Binary World How Computers Count

It's a​ Binary World - How Computers Count.
Many have cursed their computer for taking things too literally! It's easy to​ blame the​ computer when something goes wrong.
You get to​ the​ checkout at​ the​ market,​ and the​ item you bought 'on special' comes up at​ the​ full price .​
The manager has to​ be called to​ fix it​ up,​ and what does he say?
We've been having problems with the​ computer,​ it​ gets the​ wrong price on​ some things.
You put in​ a​ list of​ addressess to​ your Word processor,​ and print off party invitations for next week .​
Then you find that today's date has been inserted in​ the​ signature block - by the​ computer!
Maybe you have heard the​ expression 'Garbage in​ Garbage out? Someone,​ at​ some point instructed the​ computer to​ do what it​ did,​ It didn't decide to​ screw you up deliberately .​
Computers can only do what they are told,​ they are more logical than Spock and they take everything literally.
We are going to​ look at​ why they are so pedantic!
The world around us has many aspects which work in​ the​ same way as​ a​ computer .​
There are many examples of​ opposites,​ for instance Up and Down,​ Left and Right,​ Forwards and Backwards .​
a​ light may be On or​ Off,​ maybe it's Night or​ Day .​
Yes or​ No? You can think of​ many others .​
This system of​ two possible states is​ called a​ Binary System,​ if​ it's not one,​ it​ must be the​ other.
A computer uses the​ Binary System to​ perform all its functions,​ the​ basic unit,​ originally a​ vacuum tube,​ then a​ transistor,​ then a​ chip,​ is​ used thousands of​ times over to​ make the​ total unit .​
The light being On or​ Off which we​ mentioned above is​ controlled by a​ switch .​
In the​ computer this switch is​ a​ transistor,​ which is​ either On or​ Off.
Now we​ get to​ the​ Math! Don't worry,​ it's very simple Math! In fact it's so simple we​ only count up to​ 1 .​
That's right,​ we​ can only have two states so we​ count from 0 to​ 1 .​
(That's another thing computers are pedantic about,​ they insist on​ starting at​ zero).
The Binary system is​ a​ Number System .​
You are familiar with the​ Decimal system which has 10 numerals 0 to​ 9 (think like a​ computer 0 comes first) .​
You can make up all sorts of​ number systems for whatever purpose you want .​
You probably know about a​ dozen (12) and have also heard of​ a​ half dozen .​
If you've used your computer much you may have come across the​ Hexadecimal system .​
This one has 16 'numerals' 0-9and A-F .​
Another number system used by computer people is​ the​ Octal system which has 8 numerals,​ 0-7.
Ok so how do we​ count with only 0 and 1 .​
Simple,​ in​ exactly the​ same way you count in​ decimal .​
The first ten numbers are OK,​ 0-9,​ but what next? we​ start again but add in​ a​ 1 making 10 or​ one,​ zero .​
This gets us to​ one,​ nine and we​ go to​ two,​ zero,​ and so on​ up to​ nine,​ nine then we​ again add a​ 1 to​ make 100 - one,​ zero,​ zero.
If you've followed me so far you are ready for the​ Binary sequence,​ it's much simpler .​
Starting off at​ zero we​ have 0,​1 - and that's it .​
We follow the​ same rule and add in​ a​ 1,​ making one,​zero .​
Next come one,​ one; then one,​ zero,​ zero; -one,​ zero,​ one; etc .​
These are equivalent to​ Decimal 0,​1,​2,​3,​4,​5 .​
How does this relate to​ computers? That's next.
In our computer we​ have transistor switches,​ as​ described above .​
For the​ math example we​ just looked at,​ we​ need 3 switches .​
These each represent a​ Binary Digit,​ or​ Bit .​
To represent a​ Decimal 1,​ these switches would be OFF,​OFF,​ON or​ 001 .​
For a​ Decimal 5 we​ would have ON,​OFF,​ON,​ or​ 101 .​
By extension you can see that with 4 switches we​ could go to​ 1111 or​ 15 Decimal.
Another point to​ note is​ that each binary digit,​ or​ bit,​ has a​ value .​
Just as​ in​ Decimal we​ have units,​ tens,​ hundreds,​ etc .​
in​ Binary the​ values are 1,​2,​4,​8,​16,​32,​64,​128 etc .​
etc .​
The binary code 1111 mentioned above is​ thus 1+2+4+8=15 .​
If you wanted to​ work out what binary 100101100 was in​ decimal,​ you could add up the​ individual values .​
In fact people who work on​ the​ basic machines need to​ know machine code! To them 1111 would be F in​ Hexadecimal or​ 17 in​ octal.
This probably seems a​ very long-winded way to​ work out numbers,​ until you remember that these 'switches' can operate at​ nanosecond speed or​ 1,​000,​000,​000 times per second,​ large calculations become possible.
Thats probably enough to​ digest in​ one go .​
Next time we​ will look at​ how a​ computer adds and multiplies.

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