Solving tasks for measuring information

To solve problems, we need a formula that connects the informational weight of each character, expressed in bits (b), and the power of the alphabet (N):

N = 2 b

Objective 1:

The alphabet contains 32 letters. How much information does one letter carry?

1. 32 = 2 5, so the weight of one character b = 5 bits.

Answer: one letter carries 5 bits of information.

Objective 2:

A message written in letters from a 16-character alphabet contains 10 characters. How much information in bits does it carry?

1. 16 = 2 4 means the weight of one character b = 4 bits.

2. There are 10 characters in total, which means the amount of information is 10 * 4 = 40 bits.

Answer: the message carries 40 bits of information (8 bytes).

Objective 3:

An informational message of 300 bits contains 100 characters. What is the power of the alphabet?

1. Let's determine the weight of one character: 300/100 = 3 bits.

2. The power of the alphabet is determined by the formula: 2 3 = 8.

Answer: the cardinality of the alphabet is N = 8.

Try the following tasks yourself.

Task 4:

The size of a message containing 20 characters was 100 bits. What is the size of the alphabet used to write the message?

Task 5:

How many characters does a message written using an 8-character alphabet contain if it is 120 bits in size?

Task 6:

The book has 100 pages. Each page has 60 lines of 80 characters per line. Calculate the information volume of the book.

The purpose of the lesson: to acquaint with the concepts: “measurement of information”, “alphabet”, “power of the alphabet”, “alphabetical approach to the measurement of information”, to teach how to measure the information volume of messages, taking into account the information weight of symbols.

Lesson type: explanatory and demonstration with elements of a workshop.

Visible: presentation “Measurement of information” (Appendix 1).

Educational literature: textbook "Informatics". 8th grade (basic course) IG Semakin, “Informatics” problem book (1 part) IG Semakin.

Requirements for knowledge and skills:

Students should know:

• what is “alphabet”, “power of the alphabet”, “alphabetical approach to measuring information”;
• how to measure information volume;
• how is the unit of information bit determined;
• what is byte, kilobyte, megabyte, gigabyte.

Students should be able to:

• give examples of messages carrying 1 bit of information;
• measure the information volume of the text;
• represent the amount of information received in various units (bits, bytes, kilobytes, megabytes, gigabytes).

Lesson plan

1. Org. moment - 1 min.
2. Homework check - 2 min.
3. New material. Measuring information. Alphabetical approach - 25 min.
4. Consolidation of what has been learned - 14 min.
5. Summing up the lesson. - 2 minutes.
6. Homework - 1 min.

I. Org. moment.

II. Homework check.

Workshop problem book No. 1. p. 11 No. 2, 5, 8, 11, 19 *.

III. New material.

1. Introduction.

The process of cognition of the surrounding world leads to the accumulation of information in the form of knowledge.

How do you know if a lot of information has been received or not?

It is necessary to measure the amount of information. And today we will find out how to do this.

Obtaining new information leads to an expansion of knowledge or, as one might say, to a decrease in the uncertainty of knowledge.

If some message leads to a decrease in the uncertainty of our knowledge, then we can say that such knowledge contains information (Figure 1).

2. How you can measure the amount of information.

Reference units are available for measuring various quantities.

For instance:

• Distance is measured in millimeters, centimeters, decimeters ...
• The mass is measured in grams, kilograms, tons ...
• Time is measured in seconds, minutes, days, years ...

Therefore, to measure the information, its own reference unit must be entered.

There are two approaches to measuring information:

b) Alphabetical. It allows you to measure the information volume of a text in any language (natural or formal), when using this approach, the amount of information is not associated with the content of the text, in this case, the volume depends on the information weight of the characters.

3. Alphabetical approach to measuring information.

Let's remember what the alphabet is?

• The alphabet is the entire set of letters, punctuation marks, numbers, brackets and other symbols used in the text.

* Alphabet include space (space between words).

What is the power of the alphabet?

• The cardinality of the alphabet is the total number of characters in the alphabet.

For example: the power of the alphabet of Russian letters and symbols used is 54:

33 letters + 10 numbers + 11 punctuation marks, brackets, space.

The alphabet used in a computer (machine language) has the smallest cardinality; it is called a binary alphabet, since it contains only two characters “0”, “1”.

The information weight of a symbol of the binary alphabet is taken as a unit of information measurement and is called 1 bit.

Try to determine the size of the informational message:

Information written in machine language weighs:

01110 - ... bit

010010 - ... bit

010 - ... bit

0111111011110 - ... bit

With the alphabetical approach, it is considered that each character of the text has informational weight.

The informational weight of the character depends on the power of the alphabet.

With an increase in the power of the alphabet, the informational weight of each character increases.

To measure the amount of information, it is necessary to determine how many times information equal to 1 bit is contained in the determined amount of information.

For instance:

1) Take a four-digit alphabet (invented), (Figure 2).

All characters of the original alphabet can be encoded in all possible combinations using the numbers of the binary alphabet.

Let's get the binary code of each character of the alphabet. In order to encode the characters of the alphabet, the cardinality of which is four, we need two characters of the binary code.

Therefore, each character in the four-digit alphabet weighs 2 bits.

2) Binary code each character in the alphabet whose cardinality is 8 (Figure 3).

Conclusion. The entire alphabet, the cardinality of which is 8, can be encoded in machine language using three characters of the binary alphabet (Figure 4).

What do you think is the information volume of each character in the eight-digit alphabet?

Each character in the eight-digit alphabet weighs 3 bits.

3). Binary code each character in the alphabet that has cardinality 16.

What conclusion can be drawn?

An alphabet of sixteen characters can be encoded using a four-digit binary code.

Solve the problem.

Problem: How much information does 3 characters of a 16-character alphabet contain?

Since each character of an alphabet with a capacity of 16 characters can be encoded using a four-digit binary code, each character in the original alphabet weighs 4 bits.

Since in total we used 3 symbols of the alphabet with a capacity of 16 symbols, therefore: 4 bits 3 = 12 bits

Answer: the amount of information written in 3 characters of the alphabet with a capacity of 16 characters is 12 bits.

Let's write down the table of correspondence between the power of the alphabet (N) and the number of characters in the code (b) - the bit width of the binary code.

Find the pattern (Figure 5)!

What conclusion can be drawn?

The information weight of each symbol, expressed in bits (b), and the power of the alphabet (N) are related by the formula: N = 2 b

The alphabet from which the text (document) is composed on a computer consists of 256 characters.

This alphabet contains symbols: lowercase and uppercase Latin and Russian letters, numbers, signs of arithmetic operations, all kinds of brackets, punctuation marks and other symbols.

Find out how much information is contained in one character of the alphabet, the cardinality of which is 256.

Solution. From the formula N = 2 b it follows 256 = 2 8.

Conclusion. This means that each character of the alphabet used in a computer for printing documents weighs 8 bit.

This value was also taken as a unit of information and gave the name bytes.

8 bits = 1 byte

Task. The article contains 30 pages, each page contains 40 lines, each line contains 50 characters. How much information does the article contain?

Solution progress.

1) On each page 50 40 = 2000 characters;

2) in the entire article 2000 30 = 60,000 characters;

3) since the weight of each character is 1 byte, therefore, the information volume of the entire article is 60,000 1 = 60,000 bytes or 60,000 8 = 480,000 bits.

As you can see from the problem, the byte is a “small” unit of measurement of the information volume of the text, therefore, larger units are used to measure large amounts of information.

Information volume units:

1 kilobyte = 1 KB = 210 bytes = 1024 bytes

1 megabyte = 1 MB = 210 KB = 1024 KB

1 gigabyte = 1 GB = 210 MB = 1024 MB

Try to convert the result of the task into larger units:

60,000 bytes 58.59375 KB

60,000 bytes 0.057 MB

IV. Consolidation of what has been learned.

Workshop problem book No. 1. P. 19 No. 19, 20, 22, 23, 25.

V. Summing up.

Vi. Homework.

Workshop problem book No. 1. p. 20 No. 21, 24, 26.

There are several ways to measure the amount of information. One of them is called alphabetical.

Alphabetical approach allows you to measure the amount of information in a text (symbolic message) composed of characters of a certain alphabet.

Alphabet Is a collection of letters, signs, numbers, brackets, etc.
The number of characters in the alphabet is called it power.

With the alphabetical approach, it is considered that each character of the text has a certain information weight... The informational weight of the character depends on the power of the alphabet.

What is the minimum power of the alphabet with which you can write (encode) information?

Let's call a combination of 2, 3, etc. bit binary code.

How many characters can be encoded with two bits?

Symbol sequence number

1

2

3

4

Two-digit binary code

00

01

10

11

4 characters 2 bits.

How many characters can be encoded with three bits?

Symbol sequence number

1

2

3

4

5

6

7

8

Three-digit binary code

000

001

010

011

100

101

110

111

Hence it follows that in the alphabet with cardinality 8 characters information weight of each character - 3 bits.

It can be concluded that in the alphabet with power 16 characters the information weight of each character will be 4 bits.

Let us denote the power of the alphabet by the letter N, and the informational weight of the symbol by the letter b.

Dependence between the power of the alphabet N and the information weight of the symbol b.

N

2

4

8

16

b

1 bit

The development of high technologies has led to the emergence of a large number of terms and concepts that all users encounter while working with computers. Advanced users have an idea of ​​most of them, however, for beginners, it is very difficult to understand all the terms. One such term that not all even experienced users are aware of is the power of the alphabet. What is meant by this concept and how is it calculated?

Methods for measuring information in electronic form

The power of the alphabet can come in handy for so many users in the process. However, before defining this term and understanding the methods for calculating it, it is necessary to talk a little about how electronic information is measured, since this is the material basis on which further theory is based.

Every person knows that any quantity has its own system of measurements. For example, temperature is measured in degrees, distance is expressed in meters, time intervals are built from seconds, and so on. However, few users know about the values ​​in which text information is measured in electronic form. For these purposes, in computer science, the definition of the power of the alphabet was created.

Definition of the term

Based on the fact that the value of absolutely any quantity known to mankind today is a certain parameter consisting of a set of measuring units, the definition of the concept of the power of the alphabet is easiest to do as follows: the power of the alphabet is the number of characters that is part of any language ...
However, this is just a general definition, which reflects only the superficial meaning of the power of the alphabet, since the definition itself is deeper. To understand its whole essence, it is necessary to understand what the symbols represent from the point of view of high technologies. All symbols used in the computer include letters, numbers, punctuation marks, and a set of special characters. However, this is not all, since in order to determine the cardinality of the alphabet, it is also necessary to take into account the space, which is intended to separate words from each other.

Let's take as an example the Russian keyboard layout, which is used to print Russian-language text and consists of 34 letters, 10 numbers and 11 additional characters, the total number of which is 54, which, in turn, is classified as the power of the alphabet of the Russian keyboard layout ..

Informational weight of characters

Let's move on gradually. The power of the alphabet is not just the number of letters and numbers that are used in the printed text. A deeper approach is needed to determine this parameter.
Let's think for a second about what is the minimum amount of characters included in one letter, number or special character? The correct answer is two. Each character in the computer has its own information weight, thanks to which the machine is able to recognize what information the user has entered. The point is that a machine is not capable of recognizing information in the form in which people represent it. Instead, it uses a special machine language, consisting of zeros and ones, which converts textual information into binary code that can be understood by a computer system.
With regard to information weight, it is expressed in bits and is the standard unit for measuring information in electronic form.

A little about binary code

Now we have a more or less comprehensible definition of the power of the alphabet. However, to understand the full depth of the theory of representation of electronic information by machines, it is necessary to have an understanding of binary code. Let's look at this question using the example of the cardinality of the alphabet, consisting of any four characters, each of which has a weight of two bits.

Following from all of the above, four characters will have all four bits, eight - three, and so on. Based on this principle, the weight of text information expressed in electronic form is calculated by computer systems.

Calculating the power of the alphabet and its practical use

We figured out the terminology and basic theoretical terms, so now let's look at the relationship between the power of the alphabet and its weight. To more clearly draw the relationship between them, let's consider one formula: N = 2b, in which the first variable corresponds to the number of characters, and the second to the number of characters used by computers in machine language.
From this mathematical expression it follows that 21 = 2, 22 = 4, 23 = 8, 24 = 16, and so on. Based on this, a very reasonable and reasonable conclusion can be drawn: the number of characters used in machine language is the weight of a character.

How is the amount of information measured?

The examples considered above are very simple, which can be used to give a general idea of ​​the power of the alphabet. However, in reality, everything looks much more complicated, since each user in the process of typing uses not only lowercase, but also uppercase letters, as well as various fonts, language layout, punctuation marks, special characters, colors and much more. Based on this, we can assume that the total number of all total symbols is 256. Since 256 is 28 in binary code, then in this case the weight of each symbol is 8 bits or one byte.

Thus, having all the necessary parameters, we can calculate the amount of electronic information. For example, we have printed 30 pages of printed information, each containing 50 lines of 60 different characters. Using the formula known to us, we make the necessary calculations:

- informational weight of one line will be equal to: 50 x 60 = 3000 bytes;
- and the entire text will weigh: 3000 x 50 = 150,000 bytes.

It is worth noting that the final result can be expressed not only in bytes, but the standard unit of measurement can be converted to kilobytes, megabytes, and others. To do this, it is necessary to divide the value of the lower order by 1024, since it is exactly how many units of the lower value form the senior unit of measurement.

Conclusion

After reading this article, you got a general idea of ​​what constitutes the power of the alphabet, as well as the methods for calculating it. However, an exclusively mathematical approach was considered, which does not take into account some other parameters, the main of which is the semantic load. This aspect is one of the most important to understand, because regardless of the volume of symbols, if they do not carry any informational value, then its value is zero. However, you can still calculate the weight of a meaningless set of characters.

Generally speaking, the power of the alphabet, as one of the terms of computer science, is not difficult to understand. But many users neglect this term because they consider it useless, however, in practice, everything is completely different. Nowadays, users work mainly with electronic information, which over time can completely replace the printed one, so it is necessary to have an idea of ​​how this information is expressed in machine form and how it is calculated.