M. Amer Iqbal Qureshi
tải về 3.06 Mb. Chế độ xem pdf
|
- Điều hướng trang này:
- Binary number system
| World of numbers
Mathematics is such a good science! Everything is so logical and is as 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. It is easier to work with decimal numbers, however computers can not do so, they use only two digits, 0 and 1. these are represented within a computer by presence or absence of volts on a specific line. 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 Fig. 4 Different methods of representing a decimal number Teach Yourself PIC Microcontrollers | www.electronicspk.com | 12 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 example, but in inverse order. Have in mind that all this is about mathematics with only two digits- 0 and 1, i.e. base-2 number system (binary number system). Clearly, it is the same number represented in two different ways. The only difference is in the number of digits necessary for writing some number. One digit (2) is used to write the number 2 in decimal system, whereas two digits (1 and 0) are used to write that number in binary system. Do you now agree with the first sentence in this text? Welcome to the world of binary arithmetic! Do you have any idea where it is used? E x c e p t i n g s t r i c t l y c o n t r o l l e d laboratory conditions, the most complicated electronic circuits cannot with accuracy determine difference between two sizes (two voltage values, for example) if they are too small (lower than several volts). The reasons for that are electrical noises and something quite uncertainly called “realistic working environment” (unpredictable changes of power supply voltage, temperature changes, tolerance to values of built in components etc.). Imagine a computer which would operate upon decimal numbers by recognizing 10 digits in the following way: 0=0V, 1=5V, 2=10V, 3=15V, 4=20V... 9=45V !? Did anybody say batteries? Far simpler solution is the use of binary logic where 0 indicates that there is no voltage and 1 indicates that there is voltage. Simply, it is easier to write 0 or 1 instead of “there is no voltage” or “there is voltage”. It is so called logic zero (0) and logic one (1) which electronics perfectly cope with and easily performs all those endlessly complex mathematical operations. It is apparently electronics which in reality applies mathematics in which all numbers are represented by two digits only and in which it is only important to know whether there is voltage or not. Of course, we are talking about digital electronics. tải về 3.06 Mb. Chia sẻ với bạn bè của bạn:
|