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Almost every book on computer applications at the school level skip the beauty of the mathematics behind it
In fact basic counting principles are very easy to understand & should be part of every curricula
Excluding it leaves the interesting & easy but important basic part
The concept of 2
Most of the computational data is stored & evaluated as binary numbers
Each digit of a binary number(base 2) is either 0 or 1(one less than the base of the system)
Why just 2 ?
A computer or any other electronics device generally uses logically 0 & 1 to represent either if any 2 states-one for 0; the other for 1
It is not necessary that 0 always represents low/off/false. That depends on the predefined logic
Most common situations are such that there are only two possible answers/outcomes/values for it
For example, a CFL can either glow(ON) or not(OFF) depending on the switch position
A coin generally when tossed either gives a head or a tail; in many movies we have seen a funny situation arising when the coin lands on its rim(neither head nor tail)
If we also consider this outcome, how many possibilities are there? Simply 3
Taking the base of the number system to be equal to the number of possibilities we reduce the chances of redundant data & wastage of memory
WASTAGE OF MEMORY. HOW?
Here I will go into very basic counting problems to explain the memory allocation. It is part of the +2 mathematics syllabus as well
#1. A coin on being tossed either results in a head or a tail. How many outcomes are possible?
#2. Two coins are tossed. A coin on being tossed either results in a head or a tail. How many outcomes are possible?
Representing head by H & tail by T, I point out the possibilities
Now you must be thinking that this is such a lengthy process ! In face there is a theorem in mathematics that states that no matter how many independent processes are carried one after the other the outcome is their product.
Now the process of tossing a coin doesn’t affect the results we obtain on tossing the other coin; hence they are independent processes.
#3. A two digit binary storage unit can store how many numbers?
4; this is a situation analogous to #2
the possibilities are-
#4. A 100 digit binary storage unit can store how many numbers?
2^100, its a huge number
quite boring. I too feel the same. Answer the next question & you will not feel the same.
#5. How many mobile numbers are possible in India at present? Assume that the first digit is always 9, the rest can be anything(0 to 9).
Recently it was reported in the news papers that TRAI is considering adding an extra 9 to the beginning
of all mobile numbers. Any idea why??
In our case it was a ten digit mobile number beginning with 9, now its a eleven digit mobile number beginning with 9. So how many mobile numbers are possible now? 10^10; 10 times the previous
NOTE : you may ask why not simply let the first digit start with any number(0-9). Then there can be 10^10 number of possible 10-digit mobile numbers. True
I don’t know the reason & will update this part of the text after finding it out
#6. Now this final question will illustrate the memory wastage on using say, a base-7 number system, to store values that have 2 possible outcomes.
How many possible values can a 10-digit base 7 number have? This is exactly its storage capacity.
In how many possible ways, can a combination of a serial-array of ten bulbs be lighted? This is exactly the storage that will be used.
Ten bulbs A, B, C ,D, E, F, G, H, I, J are arranged in a line ABCDEFGHIJ. The various ways they can be lighted equals 2*2*2…=2^10, each bulb can either be on or off.
So if the base-7 system is used to store values then the wasted memory=?
7^10 – 2^10, a huge number.
#7. then why are hexadecimal & octal numbers used by computers?
This is the basic concept, that once understood , will not ever create confusion.
The last question, asked for a storage of a 10-digit binary linear array into a 7-digit octal linear array.
However, a binary number can be converted to any base. Not just binary numbers, any number in a given base-n can be converted to its corresponding equal number in another base-m.
What is the binary equivalent of the decimal number 10? 1010
how? It can be found in any standard textbook
10=1*(2^3) + 0*(2^2)+ 1*(2^1)+0*(2^0)
noticed any pattern? Each digit of the decimal number is multiplied by 2 raised to its positional-index(numbered from 0 & not 1).
noticed anything else?
The same number required 4-digits in the binary system but required only 2 in the decimal system.
In the hexadecimal system, the number of digits would be even less-one for the decimal number 10, represented by the hexadecimal number A.
So what exactly is our benefit if the number of digits s less or more?
Less number of digits implies less number of electronics signals have to be transmitted
next-cylinders, storage units(mb,gb,etc), meta data, why does a 250 GB hard disk have less available space, etc..
I have the same problem. i got a pop-up suggestion in Firefox itself(enclosing screenshot). I am also providing the link to the Mozilla help page I was led to-http://support.mozilla.com/en-US/kb/The+bookmarks+and+history+system+will+not+be+functional?style_mode=inproduct
I have still not used it due to lack of time but will do it soon & also update the post then.
What should I do if Fedora 11 shows “Hard Disc Failing”?
Is it anything serious?
I am attaching the screen-shots here on my blog-http:// aveek.wordpress.com/ & also uploading to the NIT Durgapur GLUG-named aveek1.png & aveek2.png.
If you go through the links provided by Indranil Das Gupta on the NIT Durgapur LUG mailing list(link above), we would see its NOTHING to worry about in most cases.
I got my BSNL EVDO card today itself. I used it for some time on my friend’s laptop with Windows XP. I had to install a driver. The attached disc with the EVDO(manufacturer-ZTE), had a file on Linux that stated that I had to modify the Kernel source code & all. However, all I did on my Fedora 11 was to edit network connections & add a “Mobile broadband”–>CDMA. I don’t know why the vendor’s default option didn’t work(i got 3 options-vendor’s, GSM & CDMA). I saved my username & password & I was instantly connected.
I used Google’s translation utility to translate everything- options, et. al for the translated Google group of NIT Agartala GNU/Linux Users group in Hindi.
Here are a few screenshots:
Before using Google translator, I was unable to translate the options atop the menu buttons.
Freenode no longer supports Mibbit. Discoverd it today, while helping a friend in a cyber cafe via gtalk.
Just use this & solve your problems- http://webchat.freenode.net/
If you do not have a registered “nick”(user id), then try out any you wish & if already registered try another choice. do register your “nick” later if you are regular on the IRC. Nick setup help.
Making your own radio-station?
Try GNU Radio-http://gnuradio.org/
I am doing the same for my college radio at NIT Agartala, India.
Being Open Source, it is cheap & much more reliable. It has been extensively tested for bugs by various users. It has a vibrant community & they are willing to help you for any problems that you face for free.
The USRP2 costs around $1,500(USD) outside of the USA for organizations but is extremely robust.
For details visit-http://www.ettus.com/sales
I found the youtube downloader too slow. So, I found another way out.
I opened youtube, let the full video be streamed. Then I went to the temp(temporary) directory & copied the video file after the full video got streamed.
Upto 50% quicker!! Works same ways with Windows. All files are copied to the directory, even the pictures you view on a webpage. They are erased as soon as you close the webpage.
In Linux, the directory is /temp. Find out the flash video file(.flv) or try to find the file whose size is increasing & is of size suitable t be the video file. Try playing it by VLC player.
For Windows XP, the directory is C:\Documents and Settings\User\Local Settings\Application Data\Mozilla\Firefox\Profiles\8axcg82l.default\Cache for Firefox. …./User/….may also have your own username. Just find the file of increasing size. Rename as <filename>.flv if you don’t wish to select the program used to open it repeatedly.
Sadly, the cache of Google Chrome is cached & you cannot copy easily from there.
I used my printer on both my laptop & desktop so easily. It is a HP psc 1210, an all-in-one printer & scanner.
I added it without need to use any CD/DVD as is required in Windows to install drivers. All the drivers are pre-loaded. I just clicked on add printer. Just a one minute job.