Questions and exercises. Disk partitioning is the hard way

Theme of the lesson: Solving the tasks of the section “Measuring information. Units"

Lesson. The solution of the tasks of the section "Measurement of information. Units"

Class: 11
Training Method: explanatory and illustrative.

Lesson Type: combined.

Forms of educational work of students:

· front work

· individual work.

Lesson Objectives:
I. Educational
To form students' ability to solve problems of finding the amount of information.

II. Developing
Develop operational thinking and communicative competence when processing information.
III. Educational
To nurture the perception of the computer as a tool of informational activity of a person and respect for the computer.

Lesson Objectives:

· repeat units of information, concepts: alphabet, power of the alphabet;

· to develop skills for solving problems.

Equipment:

· board,

· computers

· handout.

Software:

· Internet access for online testing

Requirements for knowledge and skills:

Students should know:

· what is the “alphabet”, “the power of the alphabet”, “the alphabetical approach in the measurement of information”, “a meaningful approach to the measurement of information”;

· how to measure information volume;

· how the unit of measurement of bit information is determined;

· what are bytes, kilobytes, megabytes, gigabytes.

Students should be able to:

· measure the information volume of the text;

· represent the amount of information received in various units (bits, bytes, kilobytes, megabytes, gigabytes).

Lesson plan

1. Organizing time.

2. Actualization of knowledge.

3. Safety precautions

4. Online test (warm up)

5. Problem solving.

6. Fizminutka.

7. Knowledge control.

8. Summarizing the lesson.

9. Homework.

10. Reflection.

Key concepts: alphabet, power of the alphabet, information weight of the symbol in the alphabet, derived units of information.

During the classes

1. Organizational moment.

The teacher welcomes the students and notes those who are absent.

2. Updating knowledge

Frontal survey (questions on the presentation slide)

1. What event can be called informative?

(the event is informative provided:

1) at least one of two possible events has occurred;

2) the information is understandable, reliable, objective, useful.).

The coin fell 1 bit tails, from the basket with 8 balls got a red ball -3 bits,

2. What is the amount of information in an uninformative message?

Zero (0), Example: yesterday was Sunday, 2 * 2 \u003d 4

3. What is the uncertainty of knowledge about an event.

Number of possible event results

4. What events are called equiprobable.

Events that do not have the advantage of one over the other.

5. What is the minimum unit used to measure the amount of information?

(1 bit of information is used as the minimum unit of information.)

6. Define bat from the point of view of the uncertainty of knowledge and from the point of view of equiprobable events.

A message that reduces the uncertainty of knowledge in half 1 bit information.

The message that one event out of two equally probable occurred 1 bit information.

7. What is the formula used to determine the amount of information in a message that one of two equally probable events has occurred.

It is determined from the solution of the exponential equation 2 i \u003d N

(To find the amount of information using the formula:

2 i \u003d N,

where N - the number of all possible events;

I - the amount of information contained in this message.)

8. What is a meaningful approach to measuring information?

(The informative approach considers the informativeness of equiprobable events.)

9. What is the alphabetical approach to measuring information? ( Alphabetical approach to measuring information allows you to determine the amount of information contained in the text. The alphabetical approach is objectivethose. it does not depend on the subject (person) perceiving the text. )

3. Safety

1. When working at a computer, you must remember: life-threatening voltage is connected to each workstation. Therefore, during operation, you must be extremely careful and comply with all safety requirements.

2. To work at the computer is not harmful to health, it is necessary to take precautions and monitor the proper organization of their workplace.

Remember the rules of working at a computer

Sit at the computer directly, without straining.

Press the keys on the keyboard gently and do not use foreign objects for this.

Do not touch the connecting wires or touch the rear walls. system unit and monitor.

In the event of an unusual situation with the computer (flashing, abnormal sounds, smell), immediately inform the teacher about it.

Keep a safe eye distance to the monitor screen - at least 50 cm.

The time of continuous work at the computer is no more than 30 minutes.

Do not keep objects that are not required during the assignment at the workplace.

Before doing work, carefully study the progress of its implementation.

During work with computers it is forbidden to move around the class. Avoid jerky movements

Online test:http: // fominyh.ucoz.ru/tests/1-59-0

4. Problem solving for a meaningful approach:

Teacher analysis of the task:

1. In the class 32 student. Which amount of information contained in the message that Kolya Sidorov will go to the board.

2 i \u003d N

N \u003d 32 \u003d 2 i \u003d\u003e i \u003d 5 bits

The solution to the problem at the blackboard student.

2. Message that from a basket with colorful balloons (all balls of different colors) got it green ball contains 4 bits information. How many balls were in the basket?

2 i \u003d N

N \u003d 4 \u003d 2 i \u003d\u003e i \u003d 2 bits

Independent work:

3. In the gymnasium class of the school, several students from 128 applicants. Which number of students was selected if the message of who was selected contains 140 bits information?

2 i \u003d N

N \u003d 128 \u003d 2 i =>i \u003d 7 bit - information on the number of students selected

140/7 \u003d 20 students - quantityselected pupils

4 . From the NEW folder, it was simultaneously deleted 10 files and message names deleted files contains 80 bit of information. How many files were there in the folder?

80/10 \u003d 8 bits - the average number of bits contains information about one file

2 i \u003d N

N \u003d 2 8 =>N \u003d 256 files

5. In home 4 entrances, in each of which 16 floors. How much information is contained in the message that Ivan lives on fifthfloor in thirdporch

2 i \u003d N

16 * 4 \u003d 64 - carries a message that in the house 4 entrances, in each of which 16 floors

N \u003d 64 \u003d 2 i =>i \u003d 6 bit - contained in the message that Ivan lives on fifthfloor in thirdporch

5. A little bit.

Solving problems with an alphabetical approach to measuring information:

Parsing by teacher:

1. How many characters are in the text, if the power of the alphabet is 64 characters, and the amount of information contained in it is 1.5 Kbytes.

Answer: in the text 2048 characters

Board Solution:

The message occupies 3 pages of 25 lines. Each line contains 60 characters. How many characters are in the alphabet used if the entire message contains 1125 bytes?

K pages \u003d 3 pages

K lines \u003d 25 lines

K characters \u003d 60 characters

I \u003d 1125 bytes

i \u003d I / K \u003d (1125 * 8bit) / (3 * 25 *60) =
= 9000 / 4500 = 2 bit

N \u003d 2 i ¦ N \u003d 2 2 \u003d 4character

N -?

Answer:in used alphabet 4 characters

7. Knowledge control

Online test: http://ege.yandex.ru/

8. Lesson summary.

The teacher gives marks to students completing assignments at the blackboard, commenting on them.

9. Homework.

1. Multi tribe alphabet consists of 32 letters. Which amount of information carries one letter of this alphabet?

2. Message written in letters from 16 character alphabet contains 50 characters. Which amount of information does it carry?

3. How much characters contains a message recorded using 16 character alphabet, if its volume amounted to 1/16 part Megabytes?

4. How much kilobytes compose a message from 384 characters 16 character the alphabet?

Additionally, Problem number 1 . A book typed using a computer contains 150 pages; on each page - 40 lines, b in each line - 60 characters. How much information is in the book?

Decision. The power of the computer alphabet is 256. One character carries 1 byte of information. This means that the page contains 40 x 60 \u003d 2400 bytes of information. The amount of all information in the book (in different units):

2400 * 150 \u003d\u003d 360,000 bytes. 360000/1024 \u003d 351.5625 Kbytes. 351.5625 / 1024 \u003d 0.34332275 MB.

Task number 2.On a 100 MB disk, information is prepared for display on the display screen: 24 lines of 80 characters each, this information fills the entire screen. What part of the disk does it occupy?

Decision.

The code of one character takes 1 byte.

24 * 80 \u003d 1920 (bytes)

Disk capacity 100 * 1024 * 1024 bytes \u003d 104857600 bytes

1920/104857600 \u003d 0.000018 (part of the disk)

10. Reflection.

Laboratory work No. 2.

Purpose of work:

Methodical instructions.

Tasks for measuring information

1. Measure the informational volume of the message “Hurray! New Years is soon!" in bits, bytes, kilobytes (KB), megabytes (MB).

Note: it is believed that the text is typed using a computer, one character of the alphabet carries 1 byte of information. Space is also a character in an alphabet with a capacity of 256 characters.

2. Measure the approximate information capacity of one page of any of your textbook, the entire textbook.

Indication: To complete the task, take a textbook on your favorite subject, count the number of lines on the page, the number of characters per line, including spaces. Remember that one character of the alphabet carries 1 byte of information. Multiplying the obtained values, you will find the information capacity of one page of the textbook (in bytes).

3. How many such textbooks can fit on a 1.44 MB diskette, on a 1 GB hard drive.

4. In the children's game “Guess the Number”, the first participant makes up an integer from 1 to 32. The second participant asks questions: “Is the hidden number greater than the number ___?”. How many questions with the right strategy guarantee guessing?

Indication: Ask the question in such a way that information uncertainty (the number of options) is halved.

5. The poison is in one of 16 glasses. How many pieces of information will a poison glass message contain?

6. How many bits of information does a message say that a “Queen of Spades” was taken from a deck of 32 cards?

7. Spend two lotteries: “4 of 32” and “5 of 64” A message about the results of which of the lotteries carries more information?

8. The information message of 1.5 KB contains 3072 characters. How many characters does the alphabet with which this message was written contain? (An explanation of the solution to the problem on the board).

10. The speed of the information stream is 20 bits / sec. How long does it take to transfer information of 10 kilobytes.

11. Compare (put a sign of relationship)

o 200 bytes and 0.25 KB.

o 3 bytes and 24 bits.

o 1536 bits and 1.5 KB.

o 1000 bits and 1 KB.

o 8192 bytes and 1 KB.

12. There are 32 balls in the lottery drum. How much information does the message about the first number drawn out (for example, the number 15 appear)?

13. When playing dice, a die with six faces is used. How many bits of information does a player receive each time he rolls a die?

14. A book typed using a computer contains 150 pages; on each page - 40 lines, in each line - 60 characters. How much information is in the book?

15. Count the amount of information contained in the novel by A. Dumas “Three Musketeers”, and determine how many similar works can be placed on a single laser disc? (590 pages, 48 \u200b\u200blines per page, 53 characters per line).

16. On a 100 MB disk, information is prepared for display on the display screen: 24 lines of 80 characters each, this information fills the entire screen. What part of the disk does it occupy?

17. In the school library 16 shelving with books. There are 8 shelves on each rack. The librarian informed Petya that the book he needed was on the fifth rack on the third shelf from above. How much information did the librarian pass on to Pete?

18. In the box are 7 colored pencils. How much information does a message say that a red pencil was taken out of the box?

19. How much information does the message carry: “The meeting is scheduled for September.”

20. The message takes 3 pages of 25 lines. Each line contains 60 characters. How many characters are in the alphabet used if the entire message contains 1125 bytes?

21. Eustace needs to convey the following message:

Dear Alex! I heartily congratulate you on

Successful passing the exam in computer science.

Laboratory work No. 2.

Information Measurement

Purpose of work:teach solving problems on quantitative measurement information volume of textual information.

Methodical instructions.

In connection with different approaches to the definition of information there are two approaches to measuring information.

Subjective (substantial) approach

With this approach, information is information, knowledge that a person receives from various sources. Thus, a message is informative (contains non-zero information) if it enhances a person’s knowledge.

With a subjective approach, the information content of a message is determined by the presence in it new knowledge and understandability for this person (definition 1) Different people who receive the same message differently evaluate the amount of information contained in it. This is because the knowledge of people about these events, phenomena before receiving the message was different. A message is informative for a person if it contains new information, and not informative if the information is old, known. Thus, the amount of information in the message depends on how new this message is to the recipient and is determined by the amount of knowledge that this message carries to the person who receives it.

From the point of view of information as novelty, we cannot estimate the amount of information contained in a new discovery, musical style, new theory of development.

The subjective approach is based on the fact that the receipt of information, its increase, means a decrease ignorance or information uncertainty (definition 2).

The unit of measurement of the amount of information is called bit (bit - binarydigit), which means binary bit.

The amount of information is the number of bits in the message.

A message that reduces information uncertainty (knowledge uncertainty) by half carries for him 1 bit information.

What is "information uncertainty"?

Information uncertainty about an event is the number of possible results of the event.

Example_1: The book lies on one of two shelves - top or bottom. The message that the book is on the top shelf reduces the uncertainty by exactly half and carries 1 bit of information.

The message that one event of two equally probable occurred 1 bit information.

Example_2: Nesterov lives on Leningradskaya Street. We received a message that his house number is an even number, which reduced the uncertainty. After receiving such information, we began to know more, but information uncertainty remained, although it decreased by half.

Example_3:Your friend lives in a 16-story building. How much information does a message say that a friend lives on the 7th floor.

Decision : Information uncertainty (the number of possible outcomes of the event) is 16. We will ask questions that can only be answered with “yes” or “no”. We will pose the question so that each answer brings 1 bit of information, i.e. reduced information uncertainty by half.

We ask questions: - Does a friend live above the 8th floor?

After this answer, the number of options was halved, therefore, information uncertainty was halved. 1 bit of information received.

Does a friend live above the 4th floor?

The number of options has halved, another 1 bit of information has been received.

Does a friend live above the 6th floor?

After this answer, two options remained: a friend lives on either the 7th floor, or on the 8th floor. 1 more bit of information received.

Does a friend live on the 8th floor?

All clear. A friend lives on the 7th floor.

Each response reduced information uncertainty by half. A total of 4 questions were asked. Received 4 bits of information. The message that a friend lives on the 7th floor of a 16-storey building carries 4 bits of information.

A scientific approach to evaluating communications was proposed back in 1928 by R. Hartley.

Let some message contain information that one of the N equally probable events has occurred ( equiprobability indicates that no event has advantages over others). Then the amount of information contained in this message is x bits and the number N is related by the formula:

where x is the amount of information or the information content of the event (in bits);

N is the number of equally probable events (the number of possible choices).

This formula is an exponential equation for unknown x. Solving the equation, we obtain the formula for determining the amount of information contained in the message that one of the N equally probable events has occurred, which has the form:

x \u003d log 2 N

base 2 logarithm of N.

If N is equal to an integer power of two, then such an equation is solved easily, otherwise the logarithm table will help to cope with the solution.

If N \u003d 2 (a choice of two possibilities), then x \u003d 1 bit.

returning to example_3, if you use the formula to calculate the amount of information in a message that a friend lives on the 7th floor of a 16-story building, then x \u003d log 2 16 \u003d 4 bits.

Example_4: How much information does the message that the meeting is scheduled for July carry?

Decision : There are 12 months in a year, therefore, the number of equally probable events or the number of possible choices is N \u003d 12. Then the amount of information x \u003d log 2 12. To solve this equation, we use the table of logarithms or a calculator.

Answer: x \u003d 3.58496 bits.

Example_5: When guessing an integer in the range from 1 to N, 8 bits of information were received. What is equal to N?

Decision: To find the number, it is enough to solve the equation N \u003d 2 x, where x \u003d 8. Since 2 8 \u003d 256, then N \u003d 256. Therefore, when guessing any integer in the range from 1 to 256, we get 8 bits of information.

Situations in which the value of N is precisely known are rare. Try by this principle to calculate the amount of information obtained when reading a page of a book. This is impossible to do.

Questions and exercises

Test yourself. Test "Coding Information. Difficulty 1"

Test yourself. Test "Coding Information. Difficulty 2"

Questions and exercises

1. What is coding?
2. What are some ways to encode textual information?
3. What information coding systems do you know?
4. What is the number system?
5. What number systems do you know?
6. What is the difference between positional and non-positional number systems?
7. Come up with several positional number systems.
8. Bring the table of numbers to different systems numbering up to 50.
9. Represent numbers 18099, 896, 1349, 2478 in the Roman numeral system.
10. Why is the binary system convenient for a computer?
11. What are the disadvantages of a positional number system?
12. What is the minimum basis a number system should have if numbers are written in it:
a) 10, 31, 231, 101
b) 400, 2561, 616, 124
c) 12, 684, 1016, A519?
13. In which number systems the equalities are true:
a) 2 * 2 \u003d 10
b) 2 * 3 \u003d 11
c) 3 * 3 \u003d 13
14. What is the sum of binary numbers 111011 + 100011?
15. What is the value of the difference of binary numbers 101100 - 11101?
16. Make tables of addition and multiplication in the ternary number system and perform the steps:
a) 12 + 22 b) 211 + 102 c) 2 * 21 g) 22 * \u200b\u200b11
17. Make tables of addition and multiplication in the quaternary number system and perform the steps:
a) 342 + 23 b) 213 + 3 c) 213 - 32
18. Follow the steps:
110011+1110
11100+10111
11011+110001
100110-11000
1010100-1010
10000-101
100111. 10110
11010. 1101
10010:11
1111:101
19. What number systems are considered related to binary?
20. Tell us the algorithm for converting numbers from the decimal number system to any other positional number systems.
21. Convert numbers to the specified number systems:

22. Translate the decimal numbers 173,347 into the binary system; 124.25; 215.78.
23. Translate the decimal numbers into the octal system: 469,347; 8.73; 79.132.
24. Translate the decimal numbers into the hexadecimal system: 426.55; 68.19; 153.98.
25. Tell us the algorithms for converting numbers from the binary number system to systems related to the binary, and vice versa.
26. Convert the binary numbers 1100011101,11101 and 100101100001,1011101 to the quaternary, octal and hexadecimal systems.
27. Translate in the binary system numbers

28. Translate the numbers into the indicated systems:

29. Convert to the decimal system numbers:

30. For numbers given in various number systems:

31. Follow the translation scheme for the number 156.75:

32. Children collected 100 mushrooms - 44 ceps and 23 boletus. In which number system are mushrooms calculated? How many mushrooms did the children collect if counted in decimal?
33. In the class of 100 people: 23 boys and 22 girls. In which number system is class documentation maintained?
34. In the garden of 100 bushes of raspberries - 28 black and 61 red. In which number system are the bushes calculated?
35. Over the 5 years of study, Vasya’s dummy student completed his homework 1000 times: 122 times in Russian and 101 times in mathematics. In what number system did Vasya count his successes? How many times did he please his teachers in our usual number system?
36. Which character sequences are called binary codes?
37. Can a bit be called a binary bit?
38. What range of decimal numbers can be represented with one byte:
a) excluding sign discharge; b) taking into account the sign discharge?
39. How much information does one character have?
40. What is the information volume of a message?
41. List the 5 main standards for coding Russian letters.
42. How many bytes will the phrase “Invitation to Windows” occupy in the Unicode system and in the CP-1251 system?
43. How does the keyboard and screen driver program work?
44. What is resolution?
45. List the most common screen resolutions.
46. \u200b\u200bList the basic units for measuring the amount of information.
47. What is a bitmap?
48. What is the unit of information transfer rate?
49. On a disk with a capacity of 100 MB, information is prepared for display on the display screen: 24 lines of 80 characters. This information occupies the entire screen. How many times information given volume can be located on the disk?
50. The printing device prints 100 characters in 1 second. How long will it take to print a page of text of 50 lines, 60 characters in each line?
51. Eustace needs to convey in plain text the following message:
Dear Alex! I sincerely wish you a Happy New Year. I wish you happiness, health and success in your work. Your Eustace.
The direction finder determines the place of transmission, if it lasts at least 3 minutes. At what speed (in bauds) should Eustace transmit a radiogram.
52. The memory capacity of a 3.5-inch floppy disk is 1.44 MB. CD-ROM drive may contain 640 MB of information. Determine how many floppy disks you need to place information from one CD-ROM drive?
53. If we write one character in each cell in a notebook in a box of 12 sheets, how many notebooks can be written to one floppy disk with a memory capacity of 1.44 MB?
54. Notice how long it will take you to count the number of letters “a” in the first 10 lines of the page you are reading. To accurately calculate the number of letters “a” in the text of the textbook, the computer would need about 5 seconds. How many times is this faster than what you could do manually without a computer?
55. If the image on the screen contains 128x64 pixels, and each dot can have one of 256 shades, then the minimum amount of memory required to store this image is: a) 1KB, b) 4KB, c) 8KB, d) 16KB, e) 32KB?
56. Estimate how many school essays the size of 2 typewritten pages (in one page 40 lines of 50 characters per line) can fit on a floppy disk with a capacity of 1.44 MB?
57. Let hDD has a capacity of 80 GB. The speech recognition device receives information at a maximum speed of 200 letters per minute. How long does it take to fill 5% of the hard drive’s memory? 58. Suppose that in some computer the distance between the processor and the memory is 30 cm, and each operation requires the transfer of information from the processor to the memory and vice versa. Prove that such a computer can not work with a speed of 600 million opt./sec. (the speed of light is about 300 million m / s).
59. Determine the amount of memory to store the digital audio file, the playing time of which is 2 minutes at a sampling frequency of 44.1 kHz and a sound depth of 16 bits. Take into account stereo sound.
60. Determine the size of the digital mono audio file (in bytes), the playing time of which is 10 seconds with a sampling frequency of 22 kHz and a sound depth of 8 bits.

Control tasks

The tasks below are control task. Decisions must be made in electronic form and submitted to the teacher for verification.