# Measures and units of quantity and volume of information - Information technology in economics and management

## Measures and units of quantity and volume of information

In the theory of information, the following approaches to its measurement are used: volumetric, probabilistic, algorithmic, semantic and axiological:

1. Quantitative (in terms of information volume) approach . In the binary system, the signs 0 and 1 are called bits ( from English Binary digiTs - binary digits). They prefer the binary system because it is the easiest to use in a computer and is implemented using two opposite physical states: magnetized/unmagnetized, on/off, charged/uncharged, etc. The amount of information recorded by binary digits in computer memory or on an external storage medium is counted simply by the number of binary symbols required for such recording. In this case, it is impossible to integrate a number of bits. For convenience, larger numbers of information than bit are introduced. Thus, a binary word of eight characters contains one byte of information (200 = 1 byte), 210 = 1024 bytes form 1 kilobyte (KB), 220 = 1024 kilobytes - 1 megabyte (MB), 230 = 1024 megabytes - 1 gigabyte (GB) , and 2 40 = 1024 gigabytes - 1 terabyte (TB). Thus, for the decimal number system, we have a series of 1000, 1001, 1002, 1003, 1004, and for the binary - 200, 210, 220, 230, 230.

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2. Entropy (probabilistic) approach . This approach is generally accepted in the theory of information and coding. This method of measurement is based on the following model: the recipient of the message has a definite idea of ​​the possible occurrence of certain events. These representations are generally unreliable and are expressed by the probabilities with which it expects an event. The general measure of uncertainty is called entropy. Entropy is characterized by some mathematical dependence on the totality of the probability of occurrence of these events. The amount of information in a message is determined by how much this measure decreased after receiving the message: the greater the entropy of the system, the greater the degree of its uncertainty. The incoming message completely or partially removes this uncertainty, therefore, the amount of information can be measured by how much the entropy of the system has decreased after receiving the message. For the measure of the amount of information, the same entropy is accepted, but with the opposite sign - negentropy.

3. Algorithmic approach . Any message can be assigned a quantitative characteristic, reflecting the complexity (size) of the program, which allows it to be produced (AN Kolmogorov). Because there are many different computers and programming languages, i.e. different ways of specifying an algorithm, then for definiteness a certain specific machine is specified, for example, a Turing machine. Then, as a quantitative characteristic of the message, you can take the minimum number of internal machine states required to reproduce this message.

4. Semantic approach . To measure the semantic content of information, i.e. its quantity on a semantic level, the thesaurus measure received the greatest recognition, which connects the semantic properties of information with the ability of the user to receive the incoming message. This is done using the concept of the user's thesaurus & quot ;. Thesaurus is the aggregate of information that a user or system has. Depending on the relationship between the meaning of the information S and the thesaurus of the user Sp , the amount of semantic information Iс, perceived by the user and included by him later in his thesaurus.

For example, with Sp ≈ 0 the user does not perceive, does not understand incoming information; and with Sp → ∞, the user knows everything, and incoming information is not needed. The consumer acquires the maximum amount of semantic information Ic by agreeing on its semantic content S with its thesaurus Sp, when the incoming information is understandable to the user and carries him previously unknown (missing in his thesaurus) information.

Therefore, the amount of semantic information in the message, the amount of new knowledge received by the user, is relative. The same message can have a semantic content for the competent user and be meaningless (semantic noise) for an uninformed user. When evaluating the semantic (content) aspect of the information, it is necessary to strive to match the values ​​ S and Sp.

5. The axiological approach is based on the value, the practical significance of the information, i.e. qualitative characteristics, significant in the social system.

Note that the last two approaches do not exclude quantitative analysis, but it is significantly more complicated, because it should be based on modern methods of mathematical statistics.

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