Tuesday, 30 June 2009

Application of Boolean AND operation

Boolean, though, of 2 states, can still be useful.

The concepts of multiplication in this AND operation can be used to perform cancellation of unknowns.

Anything times zero gives zero.
This is a common knowledge.

Here we are talking about basic fundamental maths. Nothing difficult.

Cancellation of unknowns in the AND operation means that we are able to mask out the unwanted or redefine the unknowns to a definite state.
Here the unknown become a zero, a known state or condition.

A more specific application is in the masking of unconnected inputs to a processing system. If the inputs are scanned and compared for status updates, the inputs have to be accurate or of a known status. Otherwise, comparison results become meaningless.

Here the Boolean multiplication (AND) forces the unconnected input to a zero. This is then an accurate input status for comparison.

Here, maths is applied to technical application, and its usefulness become apparent.
This is the power of understanding maths , and is exactly what makes maths interesting.


Thursday, 25 June 2009

Boolean AND operation | A Special Multiplication

There is a special field of algebra called the Boolean Algebra.

Here the algebra operates in the base 2 number system.

One special operation it performs is the AND operation.

What AND?

A simple analogy is " Mary AND John went to the park".
The meaning is that BOTH Mary and John moved together as a whole.
If either one is absent, they did not go to the park!

This is a form of multiplication.
0 x 0 = 0
1 x 0 = 0
0 x 1 = 0
1 x 1 = 1

Only when Both are present , the outcome becomes present.

Here you will notice that maths is applied to real life situation, forming into the English word "AND". But in maths, we call this "AND" as multiplication.

Boolean is utilised when the outcome is of 2 states (on or off, present or absent).

Do you see the interesting part of maths here?

Maths is mingled into daily events and is always around us if you keep an eye for it.

... :D

Tuesday, 23 June 2009

Percentage Humor

Father: How many marks did you get for your math test?

Son: I obtained 100 marks!

Father: Great! You have done me proud. You deserve an ice-cream.

Son: Thanks Dad!

Son to brother: Actually my math test is over a total of 200 marks. I almost failed the test! Luckily dad did not master percentage, otherwise I would not get my free ice-cream.

(To understand percentage, click this link).


Tuesday, 16 June 2009

What is Percentage?

Many people do understand what percentage is about.

If you see a sales offer with 50% discount, you will know that it is cheaper by half.
If the offer is with 40% less, you will also realise that is a good deal since it is almost half the original price.

But what is this percentage in detail?

A mark of 4 / 5 is reflected as a fraction.

A learned maths person will understand that it is (4 /5) x 100 = 80%

If you tell a student that he achieved 50 marks. Is that enough?

The information will not be enough as the total score is not known (unless using the default told before hand).

Thus a mark of 50 upon 50, and a mark of 50 upon 100 means different story altogether.

I believe you will agree totally!

A percentage will always reflect better information since 80% means 80 / 100.
The base of 100 is taken as the default.

The actual base number is immaterial in this matter.

An information of 50 marks compared to 50% showed the power of using percentage.

For absolute marks, you need to tell the total marks to form a complete message.
Using percentage, the fraction part of the calculation can be ignored.

Percentage and fraction are related. But percentage used a common base number (100) to commonise the value.

For comparison sake, percentage, thus stand a more proper way to tell the result.


Is it easy to tell the closeness between 49 / 56 and 46 / 56,
or is it easier to tell between 78% and 81% ?

The answer is obvious, I hope.

Maths is interesting, and mastering simple concept makes maths learning even more interesting.
Happy learning.

Cheers! :D

Monday, 8 June 2009

Meaning of Minus

To the ignorant, a "-" or minus is a strange symbol.

Is this more so when it is expressed as "-6", "-5 km", "-$3", etc.

What is then the true meaning of this "minus" sign?

Answer: It indicates a reversal of action of intention.

Maths is a useful tool to help explain this concept.


When a car moves forward by 5 km, it moves +5 km. ( By default, no sign means positive)
When it reverses by 5 km, it moves -5 km. The direction of movement reverses!

When a person gain $3, he has +$3 in his pocket.
When he loses $3, he has -$3.

From the 2 examples above, you can see that the "minus" sign is a reversal to the default.

If you "reverse" and then "reverse" again, you find yourself in the positive direction.
(-1) x (-1) = + 1

If you reverse 5 times, 5 x (-1) = -5 . You are facing the reverse to the default starting direction.

Now take note of this coming information.
If you reverse the car by 5m and another 5m, you reversed in total (-5) + (-5) = -10m.

If you reverse the car by 5m, followed by changing the direction and moving by another 5m, you moved (-5) + (+5) = 0m.
(Reverse direction followed by forward direction).

Does all these "reversing" cause a daze in you?

Do not despair.
Message is "When there is a reversal, put a minus in front of the number". Simply that!

I owe you $5 ==> -$5.
I gained $5 but lost $3 ==> + $5 + (- $3) = $2 (Action followed by another using "+").


Hope this post on minus sign reduces your anxiety about this little maths symbol.

Cheers :-)