## Monday, 11 August 2008

### Binary Maths Operation And Applications

Binary maths operations are similar to that of the Decimal number system that we are all familiar with. Decimal is of base 10, whereas Binary is base 2. Base 2 means there is only 2 states. It is either OFF or ON, or another way to put it 0 or 1.

This binary number system can still go through the common maths operations of addition and subtraction. It also means that multiplication and division is possible, though I will not venture into that in this post (the concept is similar to the decimal operations).

0 + 1 = 1
1 + 0 = 1
1 + 1 = 10
10 + 1 = 11
10 + 10 = 100
10 + 10 + 10 = 110

Binary Subtraction examples:
1 - 0 = 1
1 - 1 = 0
10 - 1 = 1
10 - 0 = 10
11 - 1 = 10
100 - 10 = 10
100 - 10 - 10 = 0

From the examples above, we can see that the digits are only "1" and "0". This is so because base 2 is represented by these "1"and "0" only (2 numbers). Our mindset has to change when dealing with binary number system. The number 2, 3 , 4, etc never exist in this binary number system.

The count up starts from 0, 1, 10, 11, 100, 101, 110, 111, ..... Interesting?

What is the usefulness of this binary operation?

The invention of this binary number system by the German-born mathematician, Gottfried Wilhelm Leibniz, opens up a whole range of mathematical applications that has the whole world captivated. Without this invention, our current Internet cannot exist, and data or digital transmission is not possible.

This binary know-how is applied in the area of digital electronics where computers form a major category. Data in this area are stored as either OFF or ON, and a sequence of these OFF and ON states can convey information or message. With the help of digital circuits, maths operations can be performed on these stored data. An example is our companion, the handy Pocket Calculator and Pocket PC or PDA.

Computer programmers also uses this binary notation to write software programmes that serves many applications. Electronics hardware engineers use this binary concept to design products like the counters, light displays, precision motor controls and many others.

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