Before we start measuring information, let's introduce a definition and figure out what we are dealing with.
Definition
Information is information, messages, data in all its manifestations, forms, regardless of their content. Even complete rubbish written on a piece of paper can be considered information. However, this definition is from Russian federal law.
The following values can be distinguished from international standards:
- knowledge of objects, facts, ideas, meanings, opinions that people exchange in a specific context;
- knowledge of facts, events, meanings, things, concepts, which in a specific context have a certain meaning.
Data is a materialized form of presentation of information, although in some texts these two concepts can be used as synonyms.
Measurement methods
The concept of information is defined in different ways. It is also measured in different ways. The following main approaches to measuring information can be distinguished:
- Alphabetical approach.
- Probabilistic approach.
- A meaningful approach to measuring information.
They all correspond to different definitions and have different authors, whose opinions regarding the data differed. The probabilistic approach was created by A.N. Kolmogorov did not take into account the subject of information transfer, that is, he measures its amount regardless of how important it is for the transmitting and receiving subject. The substantial approach to measuring information, created by C. Shannon, takes into account more variables and is a kind of assessment of the importance of this data for the host. But let's look at everything in order.
Probabilistic approach
As already mentioned, approaches to measuring the amount of information are very different. This approach was developed by Shannon in 1948. It lies in the fact that the amount of information depends on the number of events and their probability. The amount of information obtained in this approach can be calculated using the following formula, in which I is the required number, N is the number of events, and p i is the probability of each specific event.
Alphabet
Absolutely self-sufficient method of calculating the amount of information. It does not take into account what exactly is written in the message, and does not associate the amount written with the content. To calculate the amount of information we need to know the power of the alphabet and the volume of the text. In fact, the power of the alphabet is not limited. However, computers use a sufficient alphabet with a capacity of 256 characters. Thus, we can calculate how much information carries one character of printed text on a computer. Since 256 = 2 8 , one character is 8 data bits.
1 bit is the minimum, indivisible amount of information. According to Shannon, this is such a quantity of data that halves the uncertainty of knowledge.
8bit = 1 byte.
1024 bytes = 1 kilobyte.
1024 kilobytes = 1 megabyte.
Think
As you can see, approaches to measuring information are very different. There is another way to measure its quantity. It allows you to evaluate not only quantity but also quality. A meaningful approach to measuring information allows us to take into account the usefulness of data. Also, this approach means that the amount of information contained in the message is determined by the amount of new knowledge that a person will receive.
If expressed in mathematical formulas, the amount of information equal to 1 bit should reduce the uncertainty of human knowledge by 2 times. Thus, we use the following formula to determine the amount of information:
X = log 2 H, where X is the amount of data received, and H is the number of equally probable outcomes. For example, solve the problem.
Let us have a trihedral pyramid with four sides. When tossing it up there is a chance that it will fall on one of four sides. Thus, H = 4 (the number of equally probable outcomes). As you understand, the chance that our object will fall on one of the faces and remain so standing is less than if you toss a coin and expect it to become an edge.
Decision. X = log 2 H = log 2 4 = 2.
As you can see, the result is 2. But what is this figure? As already mentioned, the smallest indivisible unit is a bit. As a result, after the fall, we received 2 bits of information.
Approaches to measuring information use logarithms for calculations. To simplify these actions, you can use a calculator or a special table of logarithms.
Practice
Where can the knowledge gained in this article come in handy for you, especially the data about a meaningful approach to measuring information? Without a doubt, on the exam in computer science. This issue allows you to better navigate in computer technology, in particular, in the size of internal and external memory. In fact, this knowledge has no practical value, except in science. No employer will force you to calculate the amount of information in a printed document or written program. Unless in programming, where you will need to set the size of the memory allocated for the variable.