Posted by Sonali Agarwal on June 21, 2010
Computer does not understands our human languages. It understands only binary language. All the input we feed in the computer is converted into binary language.
The programming languages e.g. Basic, C, C++ are either compiler based or interpreter based.
Interpreter:
An Interpreter is a program which converts the higher level language in lower level language or assembly language or binary language i.e. the language of 0’s and 1’s. It reads one line of code at a time, converts it into binary language and then runs the code on the machine. So the initial start up time to run the program is almost negligible. If there is any error on the middle of the program then the program is interrupted in between. After removing the error the programs needs to run again from the beginning. Languages like BASIC is interpreter based languages. So in this interpreter converts one line of code at a time, and then runs it.
Compiler:
A compiler is also a program which convert the higher level language in lower level language. In case of compiler, it reads a whole block of code at a time, converts it into executable code, and runs the code. The initial start up time to run program is more as compared to Interpreter. Once the code is compiled, then the initial start up time to run the program is negligible. Languages like C, C++ are compiler based languages.
Posted by Rajneesh Tripathi on
Concept of Last Two Digits
Hello All,
First of all let me appreciate the opportunity of being a part of this team. This is my first article to this project.
Before I start the concept of last two digits lets have a quick look at the concept behind unit’s digit. I know most of you might be aware of this concept called cyclicity. All you need to do, is just catch the last digit of the base and apply the rule of cyclicity. You can follow the cyclicity table give below for your convenience.
| Base |
Index-1 |
Index-2 |
Index-3 |
Index-4 |
| Type |
4K+1 |
4K+2 |
4K+3 |
4K |
|
1
|
1
|
1
|
1
|
1
|
|
2
|
2
|
4
|
8
|
6
|
|
3
|
3
|
9
|
7
|
1
|
|
4
|
4
|
6
|
4
|
6
|
|
5
|
5
|
5
|
5
|
5
|
|
6
|
6
|
6
|
6
|
6
|
|
7
|
7
|
9
|
3
|
1
|
|
8
|
8
|
4
|
2
|
6
|
|
9
|
9
|
1
|
9
|
1
|
|
0
|
0
|
0
|
0
|
0
|
e.g Last digit or unit digit of 127 to the power 127 .
Just pick up last digit of the base i.e 7 and divide the given power by 4 & check out the remainder.
The remainder when 127 is divided by 4 is 3. Hence the power of the given expansion is of the type 4K+3. Therefore the unit’s digit will be 3.
How simple is that.
Now lets move on to the concept of last two digits. The fundamental behind the last two gits is just like unit’s digit concept.
Here you just need to catch the last two digits.
e.g Find the last two digits of the product of 1023 X 2027 X 5096 X 5979.
Just pick up the last two digits of all the numbers.
i.e 23, 27, 96 & 79
Multiply any pair using crisscross method of multiplication and note down the last two digits only.
i.e 23 X 27 gives you 21 as last two digits similarly 96 x 79 gives you 84 as last two digits.
Now again multiply the obtained results to get the answer.
i.e 21 x 84 which gives you 64 as last two digits.
Hope you find it doable comfortably.
Now lets move on to the cyclicity concept of last two digits.
- If you have 1 as your unit’s digit in any base then whatever be the ten’s place, you just need to write 1 as your unit’s place as simple as that & just multiply the unit digit of index/power to the ten’s place of the base and note down the unit digit of multiplication as your ten’s digit of expansion.
e.g Last two digits of 21 to the power 144.
You have 1 as unit’s place and 2 as ten’s place in your base in the given example.
You know that unit digit of this expansion has to be 1 always.
Now for ten’s digit of this expansion you pick up the unit digit of the power 144, which is 4 & multiply it to the ten’s digit of the base which is 2.
i.e 4 X 2 which will be 8 & this will be the ten’s place of the expansion.
Hence last two digits come out to be 81.
Similarly 3, 7 & 9 can be converted to such an extent so that you can get unit digit 1 and after that you can easily do the process of 1 as unit’s place.
One more very interesting and very important result is the cyclicity of 24 as last two digits of the base.
Please follow if , it will always end by 76 as last two digits
& if , it will always end by 24 as last two digits.
Also 2, 4 & 6 can be broken into factors to get the last two digits.
e.g Last two digits of 196 to the power 224.
The base 196 can be converted to small factors like 196 = 4 X 49
Now the problem becomes simple
Or ( which gives you 76, 56 & 01 as last two digits respectively.
Multiply step by step as the process discussed earlier and get the last two digits.
The answer will be 56 for this example.
Concept of compliment of the base
e.g Last two digits of 39 to the power 44.
Compliment of the base will be 61, hence lets take out last two digits of which results to -41 as last two digits. But this has to be positive and to make it positive just add the complimentary base i.e 100 to the last result -41. Hence the answer comes out to be 59.
And lastly when 5 is your unit’s place in the base. It can be of two forms.
Either ten’s place is odd or ten’s place is even.
i.e either of the type 15, 35, 55, 75, 95, (Lets say Case-1)
or of the type 25, 45, 65, 85. (Lets say Case-2)
Case-1 last two digits will be 75 for any odd power .
And for any even power last two digits will be 25.
Case-2 Last two digits will be 25 for any power .
Now you can have any example of the types discussed in this article and easily take out the last two digits of the same.
Thats all for now. I believe that you all will be able to understand the concept of last two digits from this article. I will be waiting for your responses and valuable suggestions.
All the best
Rajneesh Tripathi
Posted by Vijayashree Padmanabhan on June 4, 2010
Communication skills play an important role everywhere. Our ability to communicate effectively determines whether people around us will listen or just pose to listen. Listening, which seems to be an easy activity, is taken for granted by most. It’s not that we do in intentionally. We ‘think’ we are listening. Only when we fail to respond appropriately or miss something important we realize that we had not been listening. We should listen to others as much as we would like to be listened. Wherever we are and with whomsoever we communicate listening needs to be taken more seriously and sincerely. ‘Listen’ is to ‘give one’s attention to a sound’. In the language context, it means paying attention to speech sounds – that is ‘speaking’. We gain a lot by being good listeners. We not only learn and earn but also convey that we care and share.
Let’s check whether we have been good listeners today. Please ask yourself the following questions and answer them honestly!
Did I listen to my family members today?
Did they find fault with me for not having responded as they expected? (because of poor listening skill)
Did I make matters worse because of not listening?
How did my family members listen to me? Are they better listeners?
How was my listening skill among my friends?
Did I bore them by compelling them to listen too much to me?
How attentive was I when I listened to my colleagues/superiors etc.?
Did I put myself in trouble by not listening?
The questions can go on. Your answers to these will help you to assess your listening skill. Then you could go ahead to improve your listening skill as required and enjoy the benefits!
Posted by jayanthy on June 1, 2010
It so happens that in most times, a student is never satisfied with what he gets. This is so because his expectations move in a direction, where if unmet will lead to dissatisfaction and even frustration. What as a student we fail to realise is that, it’s the mind which actually affects our performance. To control that mind from losing its focus, it’s very much important to manage the expectations and their effect on the mind.
While it is true that it is not possible to be without expectations, it is also very important to know what to expect and what not to. Expectations have to be arrived at after a proper assessment of the current state of affairs and capabilities, a realistic setting of goals and also being prepared for the worst case scenario.
When you prepare for your examinations, it is important to focus on the subject and the perfection of your performance over the possible outcomes and results. This is because the result is an uncontrollable variable and hence a result which is unexpected provides a fair degree of disappointment. So keep your expectations on the results low and be open for every possible result.
How do I manage to perform though my expectations are low?
To make sure your performance is high while your expectations are low, you have to focus on how well you can do a particular test. It is important to prepare but it is equally essential to understand that no matter how one prepares it is those 3 hours or so of the examination time that actually matters. Hence while preparing, always be prepared and expect the unexpected and keep telling yourselves that you will manage whatever comes in your way!
This allows you to keep your mind focussed and free and unaffected by the uncertainty of the results.
What is in your hands is what is in your control. The moment you realise this golden truth you will starting focussing more on the means than the end and this by itself will lead to your success.
To conclude, expect the unexpected. Stick to performance. Be realistic. You are meant to see success!!
All the best!
Jay
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