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of Contents for this
issue..... 1.
Authors
Comments 2.
Q
& A, Suggestions
and Comments 3.
Understanding
Numbering
Systems 4.
Understanding
HTML Color
Codes Author's
Comments We
are hosting our friends from We
are showing her and her traveling companion all about Q & A, Suggestions and
Comments No
input for this section this issue. If
you have anything for this section or you have a suggestion for a topic
for an article, please go to http://www.boomerezine.com/Suggestion_Form1.htm
and give us your input. With
your input, we can improve the Boomer Video eZine. Understanding Number Systems The
number system we are taught and with which we deal daily in our lives
is
decimal. The base
of this
number system is 10. We
are
taught early that the positional values for this number system are
ones,
tens, hundreds, thousands, etc. We
are taught this by rote, but we are not taught the rule on how to
calculate them. But
that is
easy. Number
systems always
start with the ones position. The
positional value to the left of one will be one times the base of the
number system or ten (1 X 10 = 10).
The next positional value to the left will be that
positional
value times the base of the system or 100 (10 X 10 = 100).
This is how the ones, ten, hundreds, thousands are
calculated. Each
number system has one character multiplier values in it that range from
zero to one less than the base of the number system.
In decimal, the multipliers are 0 – 9. When
we look at the number 123, we just accept it as the decimal value, but
in number system theory, it is the sum of all multipliers times the
positional value for the multiplier.
Follow this example: 3 X 1 = 3 2
X 10 = 20 1
X 100 = 100 Add
up the numbers to the right of the equal signs (3 + 20 + 100) and you
get 123. You
have heard that computers use binary.
This is because in electrical circuits there is an
on or on off
value (two possible values). The
base for binary is two (2). Follow
the rule for multipliers that they will be from 0 to one less than the
base of the system so the multipliers for binary are zero and one. Follow
the rule for determining the positional values for the system.
Start at one and multiply it by the base (two) so
the position to
the left of the one position is two (1 X 2).
The next position to the left is the two position
times the base
(2) or 4 (2 X 2). The
next
position to the left is the four position times two (4 X 2) or 8.
Here are the first few positional values in binary: 256
 128  64  32  16  8  4  2  1 Notice
that each position is doubled the value to its right.
This makes sense since the base is two and we are
multiplying
each positional value by two to get the value of the next position to
the left. Let’s
look at this binary number. 10011 To
convert this to decimal, we multiply the positional value by the
multiplier. 1
X 1 = 1 1
X 2 = 2 0
X 4 = 0 0
X 8 = 0 1
X 16 = 16 Now
add up the values to the right of the equal sign and we get 19 decimal
for the binary number 10011. What
is the decimal value of 111 binary?
If you got 7 decimal then you understand how binary
works. 1
X 1 = 1 1
X 2 = 2 1
X 4 = 4 1
+ 2 + 4 = 7 Convert
one more binary number – 1000000.
If you got 64 decimal, you are right. A
weakness of binary is that it takes so many positions to express a
large
value. To get
around this,
the hexadecimal base system was devised.
This is the base 16.
We
abbreviate hexadecimal as “hex”. Since we said earlier that the multipliers for the system were zero to one less than the base of the system (16), how can we get one position multipliers when we only have 0 – 9 as numeric numbers? Well, we use the first six letters of the alphabet for the multipliers above nine. Here are the multipliers in hex. 0 1 2 3 4 5 6 7 8 9 A=10 B=11 C=12 D=13 E=14 F=15 OK,
now stick with me and remember the rules for number systems.
The positional values start with one and are
determined by
multiplying the base by the number to get each succeeding positional
value from right to left. The
first positional value is one. The
next one to the left is 16 (1 X 16).
The next one to the left is 256 (16 X 16).
The next one to the left of 256 is 4,096 (256 X 16).
The next one to the left of 4,096 is 65,536 (4,096 X
16). The
first few positional values of hex are: 1,048,576
– 65,536 – 4,096 – 256 – 16 – 1 You
can see that we can express a very large number in hex with fewer
positions than we can in our standard decimal numbering system. Let’s
convert a few hex numbers to decimal.
Convert hex 1F to decimal.
Just
follow the rule and multiply the positional value by the multiplier. F
(=15) X 1 = 15 1
X 16 = 16 Add
15 and 16 and the number 1F in hex is 31 in decimal. Convert
2AB hex to decimal. Just
follow the rule. Remember,
multiply each positional value by its multiplier. B
(=11) X 1 = 11 A
(=10) X 16 = 160 2
X 256 = 512 Add
up the values to the right of the equal signs and you find that 2AB in
hex is 683 in decimal. Why
learn hex? In some
instances
when you are writing HTML for web pages, hex numbers are used.
A two position hex number will express a number from
0 (hex 00)
to 255 (hex FF). Since
zero
is a number, this will give 256 total values. Another
reason that hex is used is that each four positions of a binary number
can be expressed in one hex position so it is much easier to write a
large number in hex than in binary. Let’s
look at the binary value 1111. If
you use the rules, this will be 1+2+4+8 = 15.
This can be written as “F” in hex. (the multiplier
“F” in
hex is equal to decimal 15. Let’s
convert another number in binary to hex.
Start at the ones position and break the binary
number into four
position groups. Express
each four position group as its hex value Binary
1011
1100
1001
0111 Hex
B
C
9
7 To
double check that the two are equal follow the rules and convert both
number systems to decimal. If
you came up with 48,279 you are right. Thank
goodness, we do not have to keep our check books in hex or binary, but
remember that the computer is using binary as its native language.
Binary easily translates into hex.
Be glad it does this and converts the answers to
decimal for us. There
are times when we do have to use hex in working with computers.
I went through this lesson to prepare you for the
next article
which talks about hex color codes used in HTML. Understanding HTML Color Codes Authors note:
This article was sent to me by
Fred Black who sells a course for making money online.
I have not seen the course, so I will not make a
recommendation
about it. I thank
Fred for
sending this informative article for publication. Guest
article starts here. I
help people with web pages a lot and I usually encourage them to edit
the HTML directly and not rely on GUI layout programs like Microsoft
FrontPage or Adobe GoLive to layout their pages. A lot of people have
trouble understanding what HTML Color Codes mean and how they work. HTML
Color Codes are 6 characters wide and look like this "#80FF12"
and are really made up of 3 2digit hex numbers that represent Red,
Green, and Blue. Ok... I just lost a good portion of the crowd didn't
I?
Let's back up and explain a few things. How
do you describe a color with numbers? One of the ways that's used with
computers is to specify the values of Red, Green, and Blue that are
mixed together to achieve the desired color. As you vary the amounts of
Red, Green, and Blue you can create most any color. How
does this relate to computers? Computer displays, TVs, and other
"projected light" display devices use pixels to display what
you see on the screen and the color value for those pixels is specified
in a RGB (Red, Green, Blue) value. For example if your monitor is set
at
1024 x 768 resolution, then there are 768 lines (from top to bottom)on
your screen, and each line has 1024 pixels or little dots in it. Each
of
those pixels or little dots is actually made of three smaller dots or
light sources: a red one, a green one, and a blue one. Ink
is different. Printers that you use with your computer generally
specify
color as a four (or more) color "reflective" ink value made up
of Yellow, Magenta, Cyan, and Black which is abbreviated as YMCK. Your
computer uses formulas to convert the RGB values to CMYK values so that
you can print what you see on your screen accurately. How
does the computer represent a RGB color value? RGB
values are stored as 3 separate values (one for Red, one for Green, and
one for Blue) between 0 and 255. If you count the 0 as a value, then
that's a total of 256 possible values.
When you combine the Red, Green, and Blue values
together to
represent a color you get a possibility of 16.7 million colors (256 x
256 x 256). That's a lot of colors and most people consider this to be
"true" color because it can represent most photographs and
images accurately and naturally. OK
then, what is a Hex value? I'm glad you asked! Your computer stores
information as single ones and zeros. Each of these tiny single values
is called a "bit". We then combine 8 of these "bits"
to make a "byte". So a byte is 8 bits. If you recall from high
school math, you can count in various "bases". We normally use
base 10 or "decimal", which uses 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
to represent a number. Likewise, if we use the ones and zeros I just
mentioned, we're talking about just two possible values for each digit,
0 or 1, and this is called base 2 or "binary".
However, in computers, we also use base 16, or
hexadecimal (hex
for short) because it packs more values into a single space. Hex uses
the following digits to represent a number: 0, 1, 2, 3, 4, 5, 6, 7, 8,
9, A, B, C, D, E, F. To represent the number 128 in decimal or base 10
takes 3 digits (128), in binary it takes 8 digits (10000000), and in
hex
or base 16 it takes just 2 digits (80). So by using hex values we save
storage space and gain efficiency. How
does this relate to HTML color codes? HTML colors codes are made up of
3
sets of hex numbers, one for Red, one for Green, and one for Blue. For
example: 000000
is black (0's for all three colors) FFFFFF
is white (255's for all three colors) FF0000
is all RED (255 for Red, 0 green, 0 blue) 00FF00
is all GREEN (0 Red, 255 green, 0 blue) 0000FF
is all Blue (0 red, 0 green, 255 blue) FFFF00
is Yellow (255 red, 255 green, and 0 blue) 808080
is a gray (128 red, 128 green, and 125 blue) Generally
in HTML, you also put a "#" in front of the color code, but
this is not necessary if you specify all 6 digits, it's used as an
abbreviation. If you ever make a profile for MySpace.com, leave off the
"#" too because they filter them and won't display the color
correctly if you use the "#". You
can use the calculator that comes with Microsoft Windows to convert
between Decimal and Hex values. You need to select View and then
Scientific from the calculator's menu. Once you do this, you'll see
more
buttons and controls on the calculator than before. To convert from Hex
to Dec, click on "Hex", key in the number, and then click
"Dec". Sometimes you'll get a color specification in Decimal,
for example (128, 30, 80) and you can use this method to convert it to
hex (80, 1E, 50) which would look like this for your HTML color #801E50. I
hope you understand more about HTML Color Codes and how colors are
stored and specified in computers. You
can visit Fred Black's web site http://www.internetmakemoneyonline.com,
Discover how to Make Money Online with internet marketing techniques
and
skills that are easy to master  100% Guaranteed. That wraps up our
issue for this week. Until
next week, stay tuned. John and Linda
Howe (http:/stores.ebay.com/BOOMERRETIREMENTSTORE) http://www.boomerezine.com/Amazon_Page.htm
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