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ENCYCLOPEDIA OF RADIO ELECTRONICS AND ELECTRICAL ENGINEERING How to present information in digital devices? Encyclopedia of radio electronics and electrical engineering
Encyclopedia of radio electronics and electrical engineering / Beginner radio amateur Information in a broad sense is commonly understood as various information about events in public life, natural phenomena, and processes in technical devices. It is contained in our speech, in the texts of books and newspapers, in the readings of measuring instruments and reflects the diversity inherent in objects and phenomena of the real world. Information embodied and fixed in some material form is called a message and is transmitted using signals. The nature of most physical quantities is such that they can take on any values within a certain range (temperature, pressure, speed, etc.). The signal that displays this information and occurs at the output of the corresponding sensor can have an infinite number of values at any time interval. Since in this case a continuous signal changes similarly to the original information, it is usually called analog, and devices in which such signals operate are called analog. There are also discrete messages whose parameters contain a fixed set of individual values. And since this set is finite, the amount of information in such messages is finite. In practice, continuous messages can be represented in discrete form. The continuity of messages in magnitude cannot be realized due to the error of sources and receivers of information and the presence of interference in the channel transmitted information. Therefore, both level and time quantization can be applied to continuous signals displaying messages. In level quantization, the set of possible voltage or current values is replaced by a finite set of discrete values from that of that interval. Time quantization provides for the replacement of a continuous signal by a sequence of pulses following at certain intervals (Fig. 1), called clock pulses. If the clock intervals are chosen appropriately, then there is no loss of information. With the simultaneous introduction of time and level quantization, the amplitude of each sample will take the nearest allowed value from the selected finite set of values. The totality of all samples forms a discrete or digital signal. Each value of a discrete signal can be represented by a number. In digital technology, such a process is called coding (sampling), and the totality of the obtained numbers is called the signal code.
Instead of converting or transmitting specific signals, these operations in digital technology devices can be performed on their codes. At the same time, it is possible to operate with analog signals, which are converted into digital ones using the ADC. Thus, a discrete message consists of a set of numbers and symbols (eg "+" and "-" signs). Each number is made up of digits. The way numbers are written in digital characters is called the number system. In digital technology, the so-called positional number systems are used [20, 32]. The meaning of each digit included in the number depends on its position in the notation of the number. The number of different digits used in a positional system is called the base of the system. Depending on the base, positional number systems can be decimal - with base 10, binary - with base 2, etc. The formation of numbers in any number system is carried out as follows: positions are fixed, called digits; each digit is assigned its own weight hi (where i is the digit number); hi=pi(p is the base of the system); the digits a are placed in the digitsi Then any number A can be represented as A=((n-1)∑(i=-1))a1h1 Here n is the number of decimal places; m - number of decimal places. Sequence of numbers. an-1,an-2, ...., a1,0,-1,-2, ..., The-m can be considered as a number code in a given number system. In digital technology, the most widely used binary number system, containing only the numbers 0 and 1, and its base is the number 2. For example, the number 25,5 in decimal and binary systems can be represented as
Octal and hexadecimal systems are used much less often. They, in particular, are used in the preparation of programs for more convenient. and short notation of binary command codes, since these systems do not require special operations for translation into a binary system. So, to convert an octal or hexadecimal number to binary, each digit of the translated numbers is replaced by three- and four-digit binary numbers, respectively. For example, the octal number 726,4 in binary has. view (726,4)8== (111010110,1)2. For convenience in depicting hexadecimal digits greater than 9, the six highest digits are usually depicted as A, B, C, D, E, F. In digital devices, the so-called binary-decimal code is also widely used. In this code, each digit of a decimal number is represented in binary code. Table 1 shows the codes of numbers in various number systems. Table 1
The numbers of the decimal number system are easy to convert to the numbers of the binary system. In this case, the order of translation of integers differs from the translation of fractions. To convert an integer X with base 10 to a system with base 2, you must sequentially divide the given number and the resulting quotients by 2 until the last quotient is less than 2. The translation result is written as a sequence of numbers from left to right, starting with the last quotient and ending with the first remainder (the number of the least significant digit is the first remainder). All actions in the process of dividing a number are performed in the decimal number system. Author: -=GiG=-, gig@sibmail; Publication: cxem.net
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