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Volume 1 - Issue 35 12-8-06

 

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Table 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 England right now.  Diana (Di) is the lady who has let us housesit her house for three long visits to the UK over the last several years.  She lives in a 400 year old mill house in a small village about 45 miles north of London .  We have used “Mill Farm” as our home base for travels all over England , Scotland , and Wales .

 

We are showing her and her traveling companion all about South Texas and the Mexican border.  We took them shopping to Mexico (two hour drive for us) on Thursday and had a great time.  We are off to San Antonio for a few days to see the sights there.  They will fly home from San Antonio on 12/11.

 

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.boomer-ezine.com/Suggestion_Form1.htm and give us your input.  With your input, we can improve the Boomer Video eZine.  

Understanding Number Systems

This is a somewhat technical subject, but it is one that will come in handy when you are working with computers, so stick with me through this article and you will understand number systems.  I taught this subject to Army officers when I was on active duty many years ago, and I still remember it well.  I was able to get it across to my students, and I can do the same for you if you will concentrate on it with me.  I recommend that you work the problems to fully understand the subject.  

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 2-digit 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

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