| Many have cursed their computer for taking | | | | much simpler. Starting off at zero we have |
| things too literally! It's easy to blame the | | | | 0,1 - and that's it. We follow the same rule |
| computer when something goes wrong.You get to | | | | and add in a 1, making "one,zero". Next come |
| the checkout at the market, and the item you | | | | "one, one"; then "one, zero, zero"; -"one, |
| bought 'on special' comes up at the full | | | | zero, one"; etc. These are equivalent to |
| price. The manager has to be called to fix | | | | Decimal 0,1,2,3,4,5. How does this relate to |
| it up, and what does he say? | | | | computers? That's next.BINARY - 0 1 10 11 |
| | | | 100 101 |
| "We've been having problems with the | | | | |
| computer, it gets the wrong price on some | | | | DECIMAL- 0, 1, 2, 3, 4, 5In our computer we |
| things."You put in a list of addressess to | | | | have transistor switches, as described above. |
| your Word processor, and print off party | | | | For the math example we just looked at, we |
| invitations for next week. Then you find | | | | need 3 switches. These each represent a |
| that today's date has been inserted in the | | | | Binary Digit, or Bit. To represent a Decimal |
| signature block - by the computer!Maybe you | | | | 1, these switches would be OFF,OFF,ON or 001. |
| have heard the expression 'Garbage in Garbage | | | | For a Decimal 5 we would have ON,OFF,ON, or |
| out"? Someone, at some point instructed the | | | | 101. By extension you can see that with 4 |
| computer to do what it did, It didn't decide | | | | switches we could go to 1111 or 15 |
| to screw you up deliberately. Computers can | | | | Decimal.TRANSISTORS [OFF OFF ON] [ON OFF ON] |
| only do what they are told, they are more | | | | [ON ON ON ON] |
| logical than Spock and they take everything | | | | |
| literally.We are going to look at why they | | | | BINARY...... 001 101 1111 |
| are so pedantic!The world around us has many | | | | |
| aspects which work in the same way as a | | | | DECIMAL..... 1, 5, 15Another point to note |
| computer. There are many examples of | | | | is that each binary digit, or bit, has a |
| opposites, for instance Up and Down, Left and | | | | value. Just as in Decimal we have units, |
| Right, Forwards and Backwards. A light may | | | | tens, hundreds, etc. in Binary the values are |
| be On or Off, maybe it's Night or Day. Yes or | | | | 1,2,4,8,16,32,64,128 etc. etc. The binary |
| No? You can think of many others. This | | | | code 1111 mentioned above is thus 1+2+4+8=15. |
| system of two possible states is called a | | | | what would BINARY 1010 be in decimal?BIT |
| Binary System. If it's not one, it must be | | | | VALUE 8 4 2 1 |
| the other.A computer uses the Binary System | | | | |
| to perform all its functions, the basic unit, | | | | BINARY.... 1 0 1 0 |
| originally a vacuum tube, then a transistor, | | | | |
| then a chip, is used thousands of times over | | | | DECIMAL... 8+2=10If you wanted to work out |
| to make the total unit. The light being On | | | | what binary 100101100 was in decimal, you |
| or Off which we mentioned above is controlled | | | | could add up the individual values. In fact |
| by a switch. In the computer this switch is | | | | people who work on the basic machines need to |
| a transistor, which is either On or Off.Now | | | | know "machine code"! To them 1010 would be A |
| we get to the Math! Don't worry, it's very | | | | in Hexadecimal or 12 in octal.One of the |
| simple Math! In fact it's so simple we only | | | | reasons for using the octal or hexadecimal |
| count up to 1. That's right, we can only | | | | code is to enable humans to interpret machine |
| have two states so we count from 0 to 1. | | | | codes. Some mainframe computers use 'words' |
| (That's another thing computers are pedantic | | | | composed of 24, 32, 36 or 72 bits. These are |
| about, they insist on starting at zero).The | | | | displayed or printed in groups of three for |
| Binary system is a Number System. You are | | | | octal, or four for hexadecimal. For example |
| familiar with the Decimal system which has 10 | | | | the 24 bit binary word in a computer may be |
| numerals 0 to 9 (think like a computer 0 | | | | interpreted as shown here.BINARY 100 111 000 |
| comes first). You can make up all sorts of | | | | 011 010 000 011 100 |
| number systems for whatever purpose you want. | | | | |
| You probably know about a dozen (12) and | | | | OCTAL.. 4 7 0 3 2 0 3 4BINARY 1001 1100 0011 |
| have also heard of a half dozen. If you've | | | | 0100 0001 1100 |
| used your computer much you may have come | | | | |
| across the Hexadecimal system. This one has | | | | HEX.... 9 D 3 4 1 DThis probably seems a |
| 16 'numerals' 0-9and A-F. Another number | | | | very long-winded way to work out numbers, |
| system used by computer people is the Octal | | | | until you remember that these 'switches' can |
| system which has 8 numerals, 0-7.Ok so how do | | | | operate at nanosecond speed, in the order of |
| we count with only 0 and 1. Simple, in | | | | 1,000,000,000 times per second, large |
| exactly the same way you count in decimal. | | | | calculations become possible.Thats probably |
| The first ten numbers are OK, 0-9, but what | | | | enough to digest in one go. Next we will |
| next? We start again but add in a 1 making | | | | look at how a computer adds and |
| 10 or "one, zero". This gets us to "one, | | | | multiplies.Tony is an experienced computer |
| nine" and we go to "two, zero", and so on up | | | | engineer. He is currently webmaster and |
| to "nine, nine" then we again add a 1 to make | | | | contributer to looking at things you can |
| 100 - "one, zero, zero."DECIMAL 0-9, 10-19, | | | | do At Home. A set of diagrams accompanying |
| 20-.....-99, 100.If you've followed me so far | | | | these articles may be seen on that website. |
| you are ready for the Binary sequence, it's | | | | Go to to start. |