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Logical Electronic

Hexadecimal Numbers System

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

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.

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

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.


Keywords : Hexadecimal, Binary, Decimal, Numbers, Logic, Systems, Numbers, Digital, Digit
Writer : delon  |
17 Mar 2006 Fri   
|  5.749 Views
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