Daddy Bob

DADDY BOB'S COMPUTER Q & A

 

BINARY NOTATION

 

To gain just a little knowledge into the inner workings of the computer, it is necessary to know something about the way it handles numbers. After all, EVERYTHING a computer does, it does with numbers. Numbers are all it knows, and to make matters worse, it only knows two of them. Strange as it may seem, everything your computer does, it does by manipulating just the two numbers: 0 and 1. This is referred as working to the "Base two", and should explain why it is called binary notation.

Two terms used frequently when talking about computers and programs are BIT and BYTE. BIT is short for "BInary digiT", and just where the term Byte came from is anyone's guess. Possibly the one who coined it was just hungry at the time, and couldn't spell too well. (Half a byte is called a nibble, so who knows). The Binary Digits referred to are the same 0 and 1 mentioned above. When eight (8) of these BITs are in the correct combina­tion with each others, they make up a Byte. When set correctly, a byte can hold any number from 0 to 255. Bytes usually contain 8 Bits, and for the purpose of this explanation, we will work on that basis.

This graphic representation can be used to visualize how the bits must be set to represent any of the numbers, 0-255. 

BIT No.

 7

 6

 5

 4

 3

 2

 1

 0

BIT Value

128

64

32

16

 8

 4

 2

 1

 ------

----

----

 ----

 ----

----

----

---- 

----

0

 0

 0

 0

 0

 0

 0

 0

 0

255

 1

 1

 1

 1

 1

 1

 1

 1

 34

 0

 0

 1

 0

 0

 0

 1

 0

200

 1

 1

 0

 0

 1

 0

 0

 0

139

 1

 0

 0

 0

 1

 0

 1

 1

127

 0

 1

1

219

 1

0 

1 

 The values from the chart are written as follows:

            0 = 00000000      255 = 11111111

           34 = 00100010      200 = 11001000

          139 = 10001011

 Now, the computer is perfectly happy using the designation of 00000000 for the decimal number zero, and 00001­001 for the decimal number nine. However, we humans have difficulty relating to this type notation, since we are accustomed to using decimal notation. The decimal or even the metric systems are base 10, and not a power of two as required by the computer, so something else had to be devised to suit both.

The first attempt was the "Octal" system which is base 8. Since 8 is a power of two, it would work and, for a while, was used. Data Point computers, like the ones used by CE before the PCs, used Octal numeration. Using it, the numbering sequence would go like this. 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, etc., where the 10 actually equals 8, and the 11 equals 9, and the 20 equals 16. Perfectly acceptable to the computer, but, alas, still too confusing to man.

The solution finally was the Hexadecimal system, simply referred to as Hex. Hex uses base 16, which again is a power of two so acceptable to the computer. Although it eliminates the 10 equals 8 syndrome it added the 10 equals 16 and also posed another problem to us. Since there are only 10 digits, 0 through 9, what could be used as a single digit for the numbers 10 through 15 needed by the Hex system? Well, it was decided to use the letters A through F for these numbers. Therefore, counting in hex goes like this. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, 1B, 1C, 1D, 1E, 1F, 20, etc.

Still look confusing? Well it is until you really start to work with hex numbers, and then they become more convenient to use than decimal. As an example, it is easier to use the number FFFF than 65535 when programming. It is immediately possible to see that FFFF is the largest number that will fit into two bytes. This is not so easy to see with 65535. If you are not a programmer, or don't plan to become one, and then just take my word for this. Now and then, a hex number is displayed on your screen during an error condition or while using some disk utili­ties. Even if you still don't understand Hex numeration, at least now when you see a number like 14E6h, on your screen, you'll know what it is.

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