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<FONT COLOR="#FF33CC">
SAY WHAT?
When you are working with computers, and especially the Internet
and the Web, you will eventually run into things like the above
- - - Hexadecimal (HEX) Numbers.
The following will not pretend to make you a Hex math genius,
but we will explain just what those funny letters mean.
When people evolved, they did so with ten fingers. (Yes we do
have a few folks down in Horsepasture with 11 fingers and 12 toes,
but that's social commentary, not math.)
Since we have ten fingers, and since early man probably used them
as the first counting device, we learned to count in TENs. DECI,
Latin for Ten, gave birth to the term DECImal.
Decimal numbers are based on POWERS of Ten.
1 x 10 = 10 10 x 10 = 100, 10 x 10 x 10 = 1,000
etc.
Since everything is based on Tens, we only need Ten Digits to
represent every possible number.
1, 2, 3, 4, 5, 6, 7, 8, 9, 0
Note: The Romans had no number for, or possibly even the concept
of Zero
So, let's start counting up from Zero in Decimal
. . .
0 - 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - OOPS -
We're Out of Digits!
Since we ran out of digits, we need to do a bit of trickery to
represent numbers higher than 9. What we do is start over with
Zero as the rightmost digit, and put a One (1) to it's left. ----
10 - 11 - 12 ... 18 - 19 - 20 - etc.
The "Decimal Place Holders" are all
Powers of Ten
The rightmost digit tells us how many ONES are in the number.
The next digit to the left tells us how many TENS, the next, how
many HUNDREDS, etc. Take the number 14, 728
How the Brain Decodes a Decimal
Number
| Powers of Ten |
10,000s |
1,000s |
100's |
10's |
Ones |
| |
1 |
4 |
7 |
2 |
8 |
|
To "Decode" this number, the brain subconsiously
goes . . .
There is one Ten Thousand, Four One Thousands,
Seven One Hundreds, Two Tens and Eight Ones
Add them all together and you get 14,728
| 10,000 |
x |
1 |
= |
10,000 |
| 1,000 |
x |
4 |
= |
4,000 |
| 100 |
x |
7 |
= |
700 |
| 10 |
x |
2 |
= |
20 |
| 8 |
x |
1 |
= |
8 |
|
+ |
|
| 14, 728 |
That's how modern number systems work!
Now a fact, a question and
a conclusion.
Fact: For reasons best left to people with Pocket Protectors
and no personal skills, computers like to "Think" in
'groups' of EIGHT digits instead of Ten.
Question: What if people had evolved with Eight fingers
per hand instead of Five?
Conclusion: We'd have developed a number system based
on powers of Sixteen rather than powers of Ten
THAT is exactly what the HEXadecimal number system is, a number
system based on 16's, not tens.
Let's start counting upwards from Zero in Hex . . .
1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - OOPS - Out of Digits again,
but we don't do the add a Zero and scoot stuff over until we
get to 16.
Where do you get the
additional digits?
You Dont -- You Use Letters!
| Dec |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
... |
24 |
25 |
26 |
27 |
| Hex |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
A |
B |
C |
D |
E |
F |
10 |
11 |
12 |
13 |
14 |
... |
18 |
19 |
1A |
1B |
Let's Decode the Hex Number F2A4C=
993,868
| Powers of 16 |
65,536's |
4096's |
256's |
16's |
Ones |
| |
F |
2 |
A |
4 |
C |
|
To "Decode" this number, the NERD
BRAIN
(Or Calculator More Likely) consciously thinks . . .
| 65,536 |
x |
F |
= |
983,040 |
| 4,096 |
x |
2 |
= |
8,192 |
| 256 |
x |
A |
= |
2,560 |
| 16 |
x |
4 |
= |
64 |
| 1 |
x |
C |
= |
12 |
|
+ |
|
| 993,868 |
IF YOU'RE LOST,
DON'T FRET OVER IT!
There's no real need for you to take pencil
in hand to figure this stuff out.
IF you ever need to, you'll find handy Hex/Decimal calculators
are supplied with both Windows and the Mac OS.
Also, at the moment, it's only important that
you have a passing familiarity with this (and the
Binary - Powers of Two) number system.
Let's Examine a Typical Browser Color Code.
<FONT
COLOR="#FF33CC">
In our discussion of Hexadecimal Color
Codes we explained that the above is called a TRIPLET, or
group of THREE Numbers. (FF, 33 and cc)
Colors are specified by how much RED (from Zero to 255), Green
(from Zero to 255) and Blue (from Zero to 255) are in the final
color.
We must, however, specify these
color values in Hex.
FF 33 CC Is Therefore . . .
FF (Hex) = 255 (Decimal) Points of Red
33 (Hex) = 51 (Decimal) Poinrs of Green
CC (Hex) = 204 (Decimal) Points of Blue
The Result Is This
Color
Again please let me state that in the beginning, a passing
familiarity with these number systems is all you need.
At least you should no longer be intimidated when some piece
of software asks you to enter something in Hex.
Interesting Fact: The fact that computers use alternate
number systems explains why 1K (1000) in Computerese is REALLY
1,024 and 4K (4000) is Really 4,096. We're NOT working with even
powers of Ten, but powers of Two.
Here
Is A Handy Hex to Decimal
and Binary Conversion Chart
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