Vectors and 3D Models
Local Search - Computers
Weather Information
Get the App for Smartphones and Tablets

Go Back

WhmSoft Free Articles Directory
Free Articles for Reprint
Free Articles to Publish
Free Articles for Newsletters
Videos to Watch

Page Generation Date and Time:
08/08/2022 00:40:13

Free the Animation VR / AR
Play to reveal 3D images and 3D models!
Demonstration A-Frame / Multiplayer
Android app on Google Play
vlrPhone / vlrFilter / vlrMemos
Project of very low consumption, radiation and bitrate softphones / Multifunction Audio Filter with Remote Control / App to measure the quality of the voice!

Alexa Data

Go To Articles Directory Home Page

To get the current article, - See Below (at the bottom of the page) -.
For top news titles, see below.
Web sites and videos listed in this page are frequently updated.
If you find that this page is useful (quality of web sites, images and videos, ...), you can add it to your favorites.
Bookmark Page !

Tell a Friend:

With your mobile phone (WAP / I-Mode / iPhone / PDA), for free:
The Top News -
The Daily Files -
All the Directory Files -

Web version of feeds:
Podcast Music -
Daily Files -

You can play the Guitar Drum Revolution game (flash game) by following the link below:
Play Guitar Drum Revolution Game

You can play free online games (flash games) by following the link below:
Free Online Games

Play the samples below:
Mimi CuisineEgypt PuzzleBaffleballBoom Boom VolleyballDui

You can view the people (celebrities) news and the front page news (with videos, images and constant updates) by following the link below:
View Recent News
or by visiting the WhmSoft Service blog:
News Photos Slideshows

Article Keyword Videos to Watch
Click on the image to start the video.

Related Topics
Images - Links - Articles


Related Images

Article Category Videos to Watch
Go to the Videos Pages

Understanding the Octal Numbering System

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.

Letís look at this binary number.


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.

Now, with this background in number system rules and examples, letís move on to the octal numbering system. As the name implies, the base for the octal numbering system is eight (8). Since the rule for the multiplier values says that the multipliers will be zero through one less than the base, the multipliers will be 0 - 7.

The positional values start with one. The next position to the left is one time the base (8). 1 X 8 = 8. The next position is the 8 position times 8 or 64. The first few positional values for octal are:

2,097,152 - 262,144 - 32,768 - 4,096 - 512 - 64 - 8 - 1

Convert this octal number to decimal:


Multiply each multiplier by its positional value.

2 X 1 = 2
3 X 8 = 24
5 X 64 = 320
7 X 512 = 3,584

Add up the values to the right of the equal signs and you get 3,930 decimal.

Another reason that octal is used is that each three positions of a binary number can be expressed in one octal position so it is much easier to write a large number in octal than in binary.

Letís look at the binary value 111. If you use the rules, this will be 1+2+4 = 7. Seven is the highest multiplier value in octal.

Letís convert a binary number to octal. Start at the ones position moving from right to left, and break the binary number into three position groups. Express each three position group as its octal value

Binary 1 011 110 010 010 111

Octal 1 3 6 2 2 7

So 1011110010010111 in binary equals 13622 in octal.

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.

Octal was used in computers until the hexadecimal numbering system was developed and "hex" has largely replaced it, but you may still run into situations where the octal numbering system is still used. Just remember the rules from this article and you will have no problem understanding the octal numbering system.

Copyright 2006 John Howe, Inc.

About the Author: John V. W. Howe is an entrepreneur, author, inventor, patent holder, husband, father, and grandfather. He has been involved in entrepreneurial activities for over 40 years. He founded and to help Boomers (baby boomers) become entrepreneurs when they retire.

Recommended Web Site(s):

Easy Articles Home Page - Articles Directory

Recommended WhmSoft Web Sites, Feeds and WAP Address:

WhmSoft Software Home Page - Software
WhmSoft Services Login Page - Music and Images
WhmSoft Moblog Home Page - Blog - Photo Gallery
WhmSoft Free Online Games Home Page - Flash Games
WhmSoft Services RSS Feed - Daily Music, Image and 3D Flash Animation
Classical Music with Drum RSS Feed - MIDI and MP3 Files
Classical Music with Drum Podcast Feed - MP3 and MP3 Files
WAP / I-Mode / PDAs - Daily Music, Image and Flash Animation

Home Pages:

WhmSoft Free Articles for Reprint Home Page
WhmSoft Services Home Page - Music and Images
Copyright (C) 2006-2022 WhmSoft - All Rights Reserved.