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[Miscellaneous] Introduction to Basic Numbering Systems


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Posted by Author knoledgesponge On 2007-04-29 10:02:28




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Introduction to Basic Numbering Systems

Category
Miscellaneous
Summary
Body
Introduction to Basic Numbering Systems:


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Introduction:

Numbering systems, however basic are something everyone who wishes to work in *ANY* kind of computer field must master. Whether you wish to work with graphics, hardware design/repair, programming, or web design you must have a basic understanding of how they work.



Table of Contents:
Goals

The Decimal System

The Binary System

The Hexadecimal system




Basic Goals for This Tutorial:

Have a firm grasp of how the decimal, binary, and hexadecimal systems work.


Advanced Goals For This Tutorial:

Be able to convert between decimal, binary, and hexadecimal.


The Decimal System:

First things first: LOOSEN UP! Do not make things more complex than they are. Almost everyone in the western hemisphere with an understanding of basic arithmetic knows about the decimal system. The prefix being 'deci' means 10, which makes the decimal system base 10.


We have 1, 2, 3, 4, 5, 6, 7, 8, 9…and then 10. The one carries over to the next placeholder and we start over. The decimal system does not need any more explanation, but be sure to remember the basic concepts behind the decimal system when thinking about the binary and hexadecimal systems.


The Binary System:

Just as ‘deci' means 10, ‘bi' simply means 2. Binary is a base 2 system. Think about how the decimal system works with 1, 2, 3, 4, 5, 6, 7, 8, 9 and then 10 Binary being much more simpler has 0, 1…then 10. This is not as confusing as it may seem when you first look at it! To understand how this works think of how you would convert a number from the decimal system to binary. If 01 is one and 10 is two, then 11 (2+1) would be three, 100 would be four 101(4+1) would be 5, 110(4+2) six, and 111 would be 7; etc.
  1. - 0001
  2. - 0010
  3. - 0011
  4. - 0100
  5. - 0101
  6. - 0110
  7. - 0111
  8. - 1000
  9. - 1001
  10. – 1010

How Binary Relates To Computers:

All computers use binary. Everything you see on your screen and every program when read by the computer starts out as binary. Programmers who write these programs use a language called “Assembly”, but even other programs made in other computer languages such as “C” or “C++” are translated back into Assembly code to be understood by the computer, this translating is what makes these programs run slower but it is much easier to program something in a higher level language such as “C” or “C++”.

The Hexadecimal System:
Hexadecimal is by far the most confusing, but if you can understand binary then you will understand hexadecimal. Warning: If you did not understand the above section on binary, then do not proceed to hexadecimal until you understand …you will only be confused even more!

‘Hex' means 6, therefore hexadecimal is base 16 (6+10). We only have 9 standard numbers, so with hexadecimal we are required to borrow letters to substitute. A quick number line would be 1, 2, 3, 4, 5, 6, 7, 8, 9, A(10), B(11), C(12), D(13), E(14), F(15) and then 16 would be 10.


How Hexadecimal Relates To Computers:

Hexadecimal, commonly known as “Hex” is commonly used when you reverse engineer a program(when trying to crack various protections you must do this, and the code is viewed in hex) and even more commonly colors are expressed through hex i.e. white is #FFFFFF and black is #000000. Notice that hex numbers when used are usually preceded with a #.


Closing:
I hope someone finds this tutorial useful, everyone has to learn the basics somehow and when I was first trying to learn numbering system basics it took me two weeks until it finally ‘clicked' so do not be discouraged if at first you don't get it! Remember Google has a million other websites that will tell you exactly what I told you in a million different ways and in all likelihood one of those ways will make it click for you. If you continue having problems try using SNEAK (found at http://snarkles.net), a conversion tool to convert all sorts of things :)


Sources:

Decimal system table taken from: http://cstl.syr.edu/fipse/Decunit/intrdec/intrdec.htm
Binary system table taken from: http://www.subterrane.com/bintab.shtml


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Written by Knoledgesponge (17th Jan 2006)

Knoledgesponge is the X/O of CAU Testing Center

Edited by Rae



This article was imported from the CyberArmy University site. (original author: knoledgesponge)


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