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mikroElektronika | Free Online Book | PIC Microcontrollers | Introduction: World of Microcontrollers
Did you know that all people can be classified into one of 10 groups- those who are familiar with binary number system and those who are not
familiar with it. You don’t understand? That means that you still belong to the later group. If you want to change your status read the following
text describing briefly some of the basic concepts used further in this book (just to be sure we are on the same page).
World of Numbers
Mathematics is such a good science! Everything is so logical and simple as that. The whole universe can be described with ten digits only. But,
does it really have to be like that? Do we need exactly ten digits? Of course not, it is only a matter of habit. Remember the lessons from the
school. For example, what does the number 764 mean: four units, six tens and seven hundreds. Simple! Could it be described in a bit more
complicated way? Of course it could: 4 + 60 + 700. Even more complicated? Naturally: 4*1 + 6*10 + 7*100. Could this number look a bit more
scientific? The answer is yes: 4*10^0 + 6*10^1 + 7*10^2. What does it actually mean? Why do we use exactly these numbers: 100, 101 and 102 ?
Why is it always about the number 10? That is because we use ten different digits (0, 1, 2, ... 8, 9). In other words, because we use base-10
number system, i.e. decimal number system.
Fig. 0-2 The number 764 represented in three different ways
Binary Number System
What would happen if only two digits would be used- 0 and 1? Or if we would not know to determine whether something is 3 or 5 times greater
than something else? Or if we would be restricted when comparing two sizes, i.e. if we could only state that something exists (1) or does not
exist (0)? Nothing special would happen, we would keep on using numbers in the same way, but they would look a bit different. For example:
11011010. How many pages of a book does the number 11011010 include? In order to learn that, follow the same logic like in the previous
http://www.mikroe.com/en/books/picmcubook/ch0/ (4 of 30)5/3/2009 11:28:39 AM