Specifications
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example, but in reverse order. Bear in mind that all this is about mathematics with only two digits- 0 and 1, i.e. base-2 number system (binary
number system).
Fig. 0-3 The number 218 represented in binary and decimal 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 that there are 10 groups of people? Welcome to the world of binary arithmetic! Do you have any idea where it is used?
Excepting strictly controlled laboratory conditions, the most complicated electronic circuits cannot accurately determine the difference between
two sizes (two voltage values, for example) if they are too small (lower than several volts). The reasons are electrical noises and something
called the “real 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? A far simpler solution is the use of binary logic where 0 indicates that there is no
voltage and 1 indicates that there is voltage. It is easier to write 0 or 1 instead of “there is no voltage” or “there is voltage”. It is called logic
zero (0) and logic one (1) which electronics perfectly conforms with and easily performs all those endlessly complex mathematical operations. It
is 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.
Hexadecimal Number System
At the very beginning of computer development it was realized that people had many difficulties in handling binary numbers. Because of this, a
new numbering system had to be established. This time, a number system using 16 different digits. The first ten digits are the same as digits we
are used to (0, 1, 2, 3,... 9) but there are six digits more. In order to keep from making up new symbols, the six letters of alphabet A, B, C, D, E
and F are used. A hexadecimal number system consisting of digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F has been established. What is the
purpose of this seemingly bizarre combination? Just look how perfectly everything fits the story about binary numbers.
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