Minimum amount of bits for recording numbers. Coding information. The amount of information. Working with various systems
Above, we considered examples of binary coding numbers, letters, colors. However, since any information presented in the computer has a binary nature, very often the need to compare binary codes and other types of information.
When encoding, information is written using characters. For example, the usual text is information encoded by a set of characters, such as the Russian alphabet. A set of characters used for data encoding is called alphabet . The number of characters in the alphabet is called the power of the alphabet. The sequence of symbols in the alphabet is called in short .
If there are two different alphabets and is given a rule conversion rule from one alphabet in the words of another alphabet, then the transformation process is called coding .
The most common coding alphabet consisting of 2 characters 0 and 1. It is encoded with all information in the computer.
In general, the coding task is set as: "There is some set of values \u200b\u200b(data set). It is necessary to compare each value binary code that meets the following requirements:
· Firstly, all codes must be the same length - consist of the same amount of bits. This is necessary to calculate the volume of encoded information and correct code recognition.
· Secondly, the length of the binary code must be minimal necessary for encoding all values \u200b\u200bfrom the set.
The minimum number of bits required for encoding n sets is determined from the following inequality
2 K.-1 < N. ≤ 2 K., (5)
where k is the number of bits required for coding.
From inequality it can be seen to determine the number of bits, it is necessary to find a degree 2, greater or equal to N, but the closest to this number.
Another (reverse) setting of tasks related to the coding of the data set sounds like this: "What a maximum number of binary codes can be made up to bits." The answer is expressed by Formula
N. = 2 K.. (6)
Analysis of tasks from demo options
E1.1.(2004, A3) Chessboard consists of 64 fields: 8 columns on 8 lines. What is the minimum amount of bits to coding the coordinates of a single chess field?
E1.3.(2005, A3) The usual road traffic lights without additional sections gives six types of signals (continuous red, yellow and green, blinking yellow and green, red and yellow at the same time). An electronic traffic control device sequentially reproduces recorded signals. A 100 traffic light signals are recorded in a row. In bytes, this information volume is
E1.5.(2007, A2) The light scoreboard consists of light bulbs, each of which can be in two states ("enabled" or "off"). What the smallest number of light bulbs should be on the scoreboard so that with it can be transferred to 50 different signals?
E1.7.(2008, A3) To transmit the secret message, use code consisting of decimal numbers. In this case, all the numbers are encoded by the same (minimum possible) amount of bits. Determine the information volume of the message in 150 characters.
E1.9.(2010, A2) in some country car room Consists of 7 characters. As symbols, 18 different letters and decimal numbers are used in any order. Each such number in computer Program It is recorded as the minimum possible and identical whole number of bytes, while uses the villain coding and all the characters are encoded by the same and minimally possible amount of bits. Determine the amount of memory allocated by this program for recording 60 numbers.
From the analysis of demo tasks, it can be concluded that the tasks associated with encoding a data set are included in the EGE on computer science every year. The most simple are the tasks for determining the number of binary codes of the same length, which were offered in 2005 (A2) and 2006 (A2). Most tasks are associated with the definition of the minimum number of bits necessary to encode a data set, and further counting the information volume of a certain message. The main complexity of these tasks is that they have a wide variety of specific performances. This is due to the fact that coding may be required for almost any data sets. The main thing in these tasks correctly define the data set to be encoded.
Examples of typical tasks
P1.1.To transmit signals, sequences from the characters "+" and "-" 6 characters long. How many different signals can be encoded with their help? Choose the correct answer.
Decision
1. First of all, we note that since only 2 characters are used for coding, then we have a binary coding space, and the sequences consisting of "+" and "-" signs are similar to binary codes from zeros and units. Thus, one character in such code can also be considered a bit.
2. We define how many different binary codes 6 bits can be made up. To do this, use the formula n \u003d 2k, where k \u003d 6. Consequently, n \u003d 64.
Let us explain on this example why from 6 bits you can create 64 different combinations of binary codes. The biggest binary number Of the 6 bits are 1111112. If you translate this number in the decimal code it turns out the number
1 × 26 + 1 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 1 × 21 + 1 × 20 \u003d 6310
At first glance it may seem that from 6 bits, you can create 63 different binary code, ranging from the code corresponding to 110 \u003d 0 and ending with the code corresponding to 6310 \u003d 1111112. But you must not forget that there is another binary code of 6 bits - this is the number 0000002. Thus, it is possible to make 64 different code.
Answer:
P1.2.For accounting, each student is assigned a binary code of the same length. Is 9 bits enough for coding all school students if 1000 people study at school? Calculate the difference between the maximum possible number of binary codes from 9 bits and the number of schoolchildren. Choose the correct answer.
Decision
1. We define how many different binary codes 9 bits long can be compiled. To do this, use the formula n \u003d 2k, where k \u003d 9. Consequently, n \u003d 512. We received that 512 binary codes of 9 bits can be made. Obviously, this quantity is not enough to coding all 1000 school students. Choose the correct answer.
2. According to the condition of the task, we find the difference between the number of binary codes and the number of students 512 - 1000 \u003d -448.
Answer: 3 (3rd option from the proposed).
P1.3.To highlight the numbers in electronic clockThis uses a rectangular light scoreboard from 7 oblong bulbs, which are located on it like a number 8, folded from matches. Each light bulb may be in the "enabled" or "off" state. How many combinations from the on and off light bulbs are superfluous? Choose the correct answer.
Decision
1. First of all, we note that since the light bulbs on the scoreboard can only be in two states, then we have a space with binary coding, and the combinations of the on and off light bulbs are similar to binary codes from zeros and units. Thus, one light bulb on the scoreboard is an analogue of the 1st bit.
2. It is not necessary to represent how from 7 matches can be added to the figure 8, although indeed such electronic scoreboards are found quite often, not only in hours, but also in other electronic devices.
3. Of the 7 light bulbs, you can make up 27 \u003d 128 different light signals. And to highlight the numbers you only need 10 light signals.
4. Consequently, 128 - 10 \u003d 118 light signals will be unsupened.
Answer: 4 (4th option from the proposed).
P1.4.The light board consists of light bulbs, each of which can be in two states ("enabled", "off"). What the smallest number of light bulbs should be on the scoreboard so that with it can be transferred 20 different signals? Choose the correct answer.
Decision
1. As well as in the previous task, light signals are scoreboards with binary codes. However, by setting this task is the reverse previous one.
2. To determine how much the lights are required for encoding 20 signals, we will find degree 2, close to 20, but large. It is 25 \u003d 32. Therefore, it will take 5 light bulbs for encoding 20 signals.
Answer: 1 (1st option from the proposed).
P1.5.The following data is applied to the magnetic map to pass through the turnstile in the subway: the following data is applied: the date of purchase of the card, the number of trips and the room tariff planwhich reflects the features of the use of the card. In the date the number, month and two are encoded latest numbers of the year. Metro uses 8 different tariff plans. No more than 60 trips can be entered on the map. Each information element is encoded by the minimum required bit. Calculate the information data encoded on the magnetic card in the bits. Choose the correct answer.
Decision
1. We define the number of bits necessary for encoding each data element - day of the month, month, year, tariff plan and the number of travel. In the month, the maximum can be 31 numbers.
2. Select degree 2, greater than 31, but the closest to this number is 32 \u003d 25. Therefore, for coding, therefore, 5 bits need for coding of the sequence numbers of the month.
3. Similarly, determine the number of bits necessary to encode other data items. Below in the table shows the number of values \u200b\u200band the number of bits.
Note. In this task, it is impossible to fold all possible values, and then determine the overall minimum number of bits necessary for coding, since it is necessary to clearly know how many bits occupies each individual data item. So, if in this problem, it turns out the total number of values \u200b\u200bto be encoded, then it turns out 213. For encoding 213 values, there are enough 8 bits, but the codes thus obtained will not allow to allocate separate elements data.
4. In the bottom line of the table, the information data on the magnetic map is calculated - 25 bits.
Answer: 3 (3rd option from the proposed).
P1.6.For the delivery of the EGE on computer science, groups of 30 people or less are formed. Each participant of the exam is assigned binary code. On the exam, each participant can dial the maximum 40 points. An exam results are introduced into the e-examination file: the binary code of the participant and the binary code of the number of scored balls. Determine the information file if 16 people came to the exam. Choose the correct answer.
Decision
1. Since there may be no more than 30 people in the group, then it will require 5 bits to coding each participant, since 25 \u003d 32 - the nearest degree 2. Thus, no matter how many people come to the exam, everyone will be assigned to everyone 5 bit code.
2. Determine the number of bits necessary for encoding scored points. You can dial 40 points. The nearest, but large 40 degree 2 is 26 \u003d 64. Therefore, for encoding scored balls, we will use a 6-bit code.
3. The data of one participant in the electronic statement occupy 5 + 6 \u003d 11 bits.
4. A total of 16 people came to the exam, so 11 * 16 \u003d 176 bits were submitted to the statement.
Answer:
P1.7.In the Russian Football Championship in the Higher League, 16 teams participate. Each team during the season plays with each team 2 times - once in his field and 1 time on the opponent's field. The results of the match are made to the file - the date (day and month is encoded separately, the year is not coded), binary codes of teams of participants and the codes of the number of heads scored by commands to which 1 byte is given to the result of each command. For simplicity of coding months, we will assume that the football season lasts all 12 months (although in fact it is not so). What is the information of the file in bytes after half the season passed - half of all matches played. Choose the correct answer.
Decision
1. We define the minimum number of bits required for the command encoding. Since teams 16, we find degree 2, close to 16 (or equal). This will be the number 16 \u003d 24. Therefore, it is necessary to 4 bits for encoding the command.
2. Determine the number of bits required for the date encoding (see table).
3. Determine how many bits contains a record of the results of one match. To encode goals, it takes 1 byte for each command, i.e., 8 bits. Total need to be folded
· 5 bits (day of the day);
· 4 bits (code of the month);
· 4 bits (single command code);
· 4 bits (other command code);
· 8 bits (single command head number);
· 8 bits (number of head numbers of another command).
Thus, one record occupies 33 bits.
4. Determine how many matches the teams are played in the season. It is convenient to put the grid of matches, as is usually done.
At the bottom of the table, matches of the 1st half of the season are indicated, at the top of the matches of the second half of the season. The cells that are not filled with gray, since the team itself does not play with it.
In table 16 columns and 16 lines with the results of matches less than the painted cells - they are also 16.
Thus, the entire matches for the season 16 * 16 - 16 \u003d 256 - 16 \u003d 240.
Over half of the season, 120 matches play.
5. The information volume of the file with the results after 120 of the played matches is 120 * 33 (bits). To transfer to bytes, this number should be divided into * 33/8 \u003d 15 * 33 \u003d 495 bytes.
Answer: 2 (2nd option from the proposed).
Tasks for self solutions
C1.5.For encoding characters in ASCII encoding, 1 byte is used. How many characters (the power of the alphabet) can be encoded with 1 byte? Choose the correct answer.
C1.7.What is the minimum amount of bits (binary discharges) to coding 4 arithmetic operations: addition, subtraction, multiplication, division? Choose the correct answer.
C1.9.How many characters contains a message recorded using a 16-thicker alphabet if its information volume was 1/16 KB. Choose the correct answer.
C1.11.Only Russian lowercase letters used to encode information. What information volume in bytes will have a message consisting of 16 characters? Choose the correct answer.
C1.13.To communicate the MUMBO-Yumbo tribe uses a language containing 24 basic concepts and 3 bundles (OK) that allow you to combine these concepts. Messages are transmitted using drum drums by portions: concept + bunch. All concepts are encoded by the same number of shocks and ligaments are encoded by the same number of shocks. How many drum beats is used in each portion of messages?
C1.14.To communicate in the Mumbo-Yumbo tribe language, 13 basic concepts and 4 bundles are used to combine these concepts. To transfer messages, the tribe uses a binary code: a combination of bell and deaf drum sounds. Messages are transmitted by portions - the concept + bunch. How many shocks will be required to encode each portion of the message?
A computer, as a computing machine (device), processes and stores information converted (recoded) to binary code - sequence "0" and "1".When recoding information into binary code, there is a need to determine the amount of information (information) required to store this type of information.
One bit can be expressed (encoded) two concepts:
If the number of bits increase to two, then you can encode four different events:
Three bits can encode eight different events:
By increasing the number of discharges in binary code per unit, the number of encoded events is twice.
What describes the formula:
N \u003d 2 i,
where n is the number of independent encoded events;
I - the discharge of the binary code.
Degree decets reflect, the number of E events encoded with i [Bit]:
N, events |
Task 1.
The light scoreboard consists of light bulbs. Each light bulb can be in one of two states ("enabled", "off"). What the smallest amount of light bulbs should be on the scoreboard so that with it can be transferred 18 different signals?Task 2.
The light scoreboard consists of light bulbs. Each light bulb can be in one of the three states ("on", "turned off", "flashing"). What the smallest amount of light bulbs should be on the scoreboard so that with it can be transferred 18 different signals?for n \u003d 18 it will be 27
What follows that i \u003d 3.
Answer: 3 light bulbs.
Task 3.
119 athletes participate in Velocross. A special device registers passing by each of the participants in the intermediate finish, recording its number using the minimum possible number of bits equal to each athlete. What is the information of the message recorded by the device after the intermediate finish passed 70 cyclists?Task 4.
In some country, a car number of 7 characters is made up of capital letters (26 letters are used) and decimal digits in any order. Each symbol is encoded in the same and minimally possible amount of bits, and each number is the same and minimally possible by bytes. Determine the amount of memory required for storing 20 car numbers.Task 5.
The meteorological station is monitored by air humidity. The result of one measurement is an integer from 0 to 100 percent, which is recorded using the minimum possible number of bits. Station made 80 measurements. Determine the information volume of observation results.Homework
1 Chessboard consists of 8 columns and 8 lines. What a minimum amount of bits will be required to encode the coordinates of a single chess field.2 What is the minimum amount of bits to be created for encoding positive numbers smaller than 60?
3 To coding a secret message, 12 special characters icons are used. At the same time, the characters are encoded by the same minimally possible amount of bits. What is the information volume of 256 characters long?
4 To encode a tank record, 7 notes are used. Each note is encoded by the same minimum possible amount of bits. What is the information of the message consisting of 180 notes?
5 in Velocross participate 678 athletes. A special device registers passing by each of the participants in the intermediate finish, recording its number using the minimum possible number of bits equal to each athlete. What is the information of the message recorded by the device after the intermediate finish passed 200 cyclists?
6 In some country, a car number of 6 characters is made up of capital letters (12 letters are used) and decimal digits in any order. Each symbol is encoded in the same and minimally possible amount of bits, and each number is the same and minimally possible by bytes. Determine the amount of memory required for storing 32 car numbers.
7 How many different sequences are from the symbols "plus" and "minus", long exactly in five characters?
8 Some alphabet contains 4 different symbols. How many three-letter words can be made from the characters of this alphabet, if the characters in the Word can repeat?
9 The light scoreboard consists of luminous elements, each of which can burn with one of three different colors. How many different signals can be transmitted using a scoreboard consisting of four such elements (provided that all elements should burn)?
10 To transmit signals on a fleet, special signal flags hanging in one line are used (the sequence is important). How many different signals can pass the ship using four signal flags if there are three flags on the ship different species (Each type of flags unlimited number)?
11 To transmit signals on the fleet, special signal flags hanging in one line are used (the sequence is important). How many different signals can pass the ship using five signal flags if there are flags of four different types on the ship (each species flags of an unlimited number)?
12 Some signaling device in one second transmits one of the three signals. How many different messages in a length of four seconds can be transferred using this device.
13 Vasya and Petya transmit each other messages using blue, red and green lanterns. This is what they do, including one lantern at the same short time in some sequence. The number of flashes in one message is 3 or 4, between messages - pauses. How many different messages can the boys transmit?
14 For encoding 300 different messages, 5 consecutive color flashes are used. Flashing of the same duration, one light bulb is used for each flash. How many colors should be used when transmitted (specify the minimum possible number)?
15 Teacher, exposing the fourth grades in biology for the third quarter (3, 4, 5), noted that a combination of three fourth estimates on this subject in all students is different. What can be the maximum number of students in this class?
16 Some alphabet contains four different symbols. How many words in length exactly in 4 characters can be made up of words of this alphabet (symbols in the word can be repeated)?
17 Square Light Table 2x2 consists of glowing elements, each of which can burn as one of four different colors. How many different signals can be transmitted using a scoreboard consisting of four such elements (provided that all elements should burn)?
18 The light scoreboard consists of luminous elements, each of which can burn with one of the eight different colors. How many different signals can be transmitted using a scoreboard consisting of three such elements (provided that all elements should burn)?
Each cell of the computer memory operating in a tricious number system can take three different values.(-1, 0, 1). For storage of some magnitude, 4 memory cells took. How many different values \u200b\u200bcan this value take?
Decision:
Another example of task:
The school database stores records containing information about students:
<Фамилия>
<Имя> - 12 characters: Russian letters (first uppercase, other lowercase),
<Отчество> - 16 characters: Russian letters (first uppercase, other lowercase),
<Год рождения> - Numbers from 1992 to 2003.
Each field is recorded using the minimum possible number of bits. Determine the minimum number of bytes required to encode one entry if the letters E and E are considered to be coinciding.
1) 282) 293)464)56
Decision:
obviously, it is necessary to determine the minimum possible sizes in bits for each of the four fields and fold them;
important! It is known that the first letters of the name, patronymic and surname are always capital, so you can store them in the form of lowercase and make the title only when displaying on the screen (but it does not care anymore)
thus, for symbolic fields, it is enough to use the alphabet of 32 characters (Russian lowercase letters, "E" and "ё" coincide, no spaces are needed)
to coding each character of a 32-character alphabet, you need 5 bits (32 \u003d 2555 5), so it is necessary to store the name, patronymic and surname (16 + 12 + 16) 5 \u003d 220 bits
for year of birth, there are 12 options, so it is necessary to remove 4 bits for it (2 4 \u003d 16 ≥ 12)
thus, 224 bits or 28 bytes are required.
the correct answer is 1.
Tasks for training3:
The light scoreboard consists of light bulbs. Each light bulb can be in one of the three states ("enabled", "off" or "flashing"). What the smallest amount of light bulbs should be on the scoreboard so that with it can be transferred 18 different signals?
1) 6 2) 5 3) 3 4) 4
The meteorological station is monitored by air humidity. The result of one measurement is an integer from 0 to 100 percent, which is recorded using the minimum possible number of bits. Station made 80 measurements. Determine the information volume of observation results.
1) 80 bits 2) 70 bytes 3) 80 bytes 4) 560 byte
The usual road traffic light without additional sections serves six types of signals (continuous red, yellow and green, blinking yellow and green, red and yellow at the same time). An electronic traffic control device sequentially reproduces recorded signals. A 100 traffic light signals are recorded in a row. In bytes, this information volume is
1) 37 2) 38 3) 50 4) 100
(The condition is incorrect, meaning the number of entire bytes.)
How many different sequences are from the symbols "plus" and "minus", the length of exactly five characters?
1) 64 2) 50 3) 32 4) 20
Chessboard consists of 8 columns and 8 lines. What is the minimum amount of bits to coding the coordinates of a single chess field?
1) 4 2) 5 3) 6 4) 7
Two texts contain the same number of characters. The first text is made in an alphabet with a capacity of 16 characters, and the second text is in the alphabet of 256 characters. How many times are the amount of information in the second text more than in the first?
1) 12 2) 2 3) 24 4) 4
What is the minimum amount of bit to coding positive numbers smaller than 60?
1) 1 2) 6 3) 36 4) 60
Two playing in "Noliki" on the field 4 on 4 cells. What amount of information received the second player by learning the course of the first player?
1) 1 bit 2) 2 bits 3) 4 bits 4) 16 bits
Message volume - 7.5 KB. It is known that this message contains 7680 characters. What is the power of the alphabet?
1) 77 2) 256 3) 156 4) 512
Dan text from 600 characters. It is known that the characters are taken from the table size 16 to 32. Determine the information of the text in the bits.
1) 1000 2) 2400 3) 3600 4) 5400
The power of the alphabet is 256. How much does the memory of the memory be required to save 160 pages of text containing an average of 192 characters on each page?
1) 10 2) 20 3) 30 4) 40
The volume of the message is 11 KB. The message contains 11264 characters. What is the power of the alphabet?
1) 64 2) 128 3) 256 4) 512
To coding a secret message, 12 special characters icons are used. At the same time, the characters are encoded by the same minimally possible amount of bits. What is the information volume of 256 characters long?
1) 256 bits 2) 400 bits 3) 56 bytes 4) 128 byte
The power of the alphabet is 64. How many kb of memory will need to save 128 pages of text containing an average of 256 characters on each page?
1) 8 2) 12 3) 244)36
7 icons - notes are used to encode music. Each note is encoded by the same minimum possible amount of bits. What is the information of the message consisting of 180 notes?
1) 180 bits 2) 540 bits 3) 100 bytes 4) 1 KB
The basket contains 8 black balls and 24 white. How many information is the message that the black ball took?
1) 2 bits 2) 4 bits 3) 8 bits 4) 24 bits
In the box lie 64 color pencils. The message that the white pencil has taken out, is 4 bits of information. How many white pencils were in the box?
1) 4 2) 8 3) 16 4) 32
For a quarter of Vasily Pupkin received 20 ratings. The message that he received four yesterday, carries 2 bits of information. How many fours got Vasily for a quarter?
1) 2 2) 4 3) 5 4) 10
In the basket lie black and white balls. Among them are 18 black balls. The message that the white ball was taken, carries 2 bits of information. How many balls in the basket?
1) 18 2) 24 3) 36 4) 48
IN closed box There are 32 pencils, some of them are blue. At random is taken out one pencil. The message "This pencil is not blue" carries 4 bits of information. How many blue pencils in the box?
1) 16 2) 24 3) 30 4) 32
Some alphabet contains 4 different symbols. How many three-letter words can be made from the characters of this alphabet, if the characters in the Word can repeat?
1) 4 2) 16 3) 64 4) 81
In some country, the car number of 6 characters is made up of capital letters (12 letters are used) and decimal digits in any order. Each symbol is encoded in the same and minimally possible amount of bits, and each number is the same and minimally possible by bytes. Determine the amount of memory required for storing 32 car numbers.
1) 192 byte 2) 128 bytes 3) 120 byte 4) 32 byte
1) 100 byte 2) 150 bytes 3) 200 bytes 4) 250 bytes
The light scoreboard consists of glowing elements, each of which can burn with one of three different colors. How many different signals can be transmitted using a scoreboard consisting of four such elements (provided that all elements should burn)?
1) 4 2) 16 3) 64 4) 81
In some country, the car number of 6 characters is made up of capital letters (in total 19 letters) and decimal digits in any order. Each symbol is encoded in the same and minimally possible amount of bits, and each number is the same and minimally possible by bytes. Determine the amount of memory required for storing 40 car numbers.
1) 120 byte 2) 160 bytes 3) 200 bytes 4) 240 bytes
In some country, the car number of 6 characters is made up of capital letters (26 letters are used) and decimal digits in any order. Each symbol is encoded in the same and minimally possible amount of bits, and each number is the same and minimally possible by bytes. Determine the amount of memory required for storing 20 car numbers.
1) 160 byte 2) 120 bytes 3) 100 bytes 4) 80 byte
To transmit signals on the fleet, special signal flags are used in one line (the sequence is important). How many different signals can send a ship using four signal flags if there are flags of three different species on the ship (each type of unlimited flags)?
To transmit signals on the fleet, special signal flags are used in one line (the sequence is important). How many different signals can pass the ship using five signal flags if there are flags of four different types on the ship (each species flags of an unlimited number)?
678 athletes participate in Velocross. A special device registers passing by each of the participants in the intermediate finish, recording its number using the minimum possible number of bits equal to each athlete. What is the information of the message recorded by the device after the intermediate finish passed 200 cyclists?
1) 200 bits 2) 200 bytes 3) 220 bytes 4) 250 bytes
In some country, a car number of 7 characters is made up of capital letters (only 18 letters are used) and decimal digits in any order. Each symbol is encoded in the same and minimally possible amount of bits, and each number is the same and minimally possible by bytes. Determine the amount of memory required for storing 60 car numbers.
1) 240 bytes 2) 300 bytes 3) 360 bytes 4) 420 byte
Some signaling device in one second transmits one of the three signals. How many different messages in length in four seconds can be transmitted using this device?
The database stores records containing dates information. Each entry contains three fields: year (number from 1 to 2100), number of the month (number from 1 to 12) and the number of the day in the month (number from 1 to 31). Each field is recorded separately from other fields using the minimum possible number of bits. Determine the minimum number of bits required to encode one entry.
Vasya and Petya transmit each other messages using blue, red and green lanterns. This is what they do, including one lantern at the same short time in some sequence. The number of flashes in one message is 3 or 4, between messages - pauses. How many different messages can the boys transmit?
For encoding 300 different messages, 5 consecutive color flashes are used. Flashing of the same duration, one light bulb is used for each flash. How many colors should be used when transmitted (specify the minimum possible number)?
Each cell of the 8 × 8 field is encoded by the minimum possible and identical number of bits. Solving the problem of passing the "horse" field is recorded by a sequence of codes visited cells. What is the amount of information after 11 moves made? (The record of the decision begins with the initial position of the horse).
1) 64 bits 2) 9 bytes 3) 12 bytes 4) 96 byte
Each cell of the 5 × 5 field is encoded by the minimum possible and identical number of bits. Solving the problem of passing the "horse" field is recorded by a sequence of codes visited cells. What is the amount of information after 15 shallows? (The record of the decision begins with the initial position of the horse).
1) 10 byte 2) 25 bits 3) 16 byte 4) 50 bytes
Teacher, putting into the journal of the fourth grades on biology for the third quarter (3, 4, 5), noted that a combination of three fourth estimates on this subject in all students is different. What can be the maximum number of students in this class?
Some alphabet contains four different symbols. How many words in length exactly in 4 characters can be made up of words of this alphabet (symbols in the word can be repeated)?
In some country, a car number of 10 characters is made up of capital letters (21 letters are used) and decimal digits in any order. Each symbol is encoded in the same and minimally possible amount of bits, and each number is the same and minimally possible by bytes. Determine the amount of memory required for storing 81 car number.
1) 810 byte 2) 567 bytes 3) 486 byte 4) 324 byte
The square light scoreboard 22 consists of luminous elements, each of which can burn with one of four different colors. How many different signals can be transmitted using a scoreboard consisting of four such elements (provided that all elements should burn)?
The light scoreboard consists of luminous elements, each of which can burn with one of the eight different colors. How many different signals can be transmitted using a scoreboard consisting of three such elements (provided that all elements should burn)?
In some country, a car number of 5 characters is made up of capital letters (30 letters are used) and decimal digits in any order. Each symbol is encoded in the same and minimally possible amount of bits, and each number is the same and minimally possible by bytes. Determine the amount of memory required for storing 50 car numbers.
1) 100 byte 2) 150 bytes 3) 200 bytes 4) 250 bytes
In some country, a car number of 7 characters is made up of capital letters (30 letters are used) and decimal digits in any order. Each symbol is encoded in the same and minimally possible amount of bits, and each number is the same and minimally possible by bytes. Determine the amount of memory required for storing 32Automotor numbers.
1) 160 byte 2) 96b 3) 224bb 4) 192b
In some country, the car number of 5 characters is made up of capital letters (26 letters are used) and decimal digits in any order. Each symbol is encoded in the same and minimally possible amount of bits, and each number is the same and minimally possible by bytes. Determine the amount of memory required for storing 40 car numbers.
1) 160 byte 2) 200 bytes 3) 120 bytes 4) 80 bytes
In some country, a car number of 7 characters is made up of capital letters (22 letters are used) and decimal numbers in any order. Each symbol is encoded in the same and minimally possible amount of bits, and each number is the same and minimally possible by bytes. Determine the amount of memory required for storing 50 car numbers.
1) 350 byte 2) 300 bytes 3) 250 bytes 4) 200AB
The light board consists of color indicators. Each indicator can be painted in four colors: white, black, yellow and red. What the smallest number of light bulbs should be on the scoreboard so that it is possible to transfer 300 different signals with it?
1) 4 2) 5 3) 6 4) 7
One cell memory cell (one trit) It can take one of three possible values: 0, 1 or -1. For some kind of magnitude in memory, such a computer has been given 4 cells. How many different values \u200b\u200bcan this value take?
1) 8 2) 16 3) 64 4) 81
The volume of the message is 11 KB. The message contains 11264 characters. What is the maximum power of the alphabet used in the transmission of the message?
1) 64 2) 128 3) 256 4) 512
1000 people live in some country. Individual taxpayer numbers (INN) contain only numbers 0, 1, 2 and 3. What should be the minimum STI length, if all the inhabitants have different numbers?
There are 200 people in some country. Individual taxpayer numbers (INN) contain only numbers 2, 4, 6 and 8. What should be the minimum STI length if all residents have different numbers?
Two watchdogs located at a high distance from each other, it was agreed to transmit each other messages using a red and green signal missile. How many different messages can be transferred, run exactly 3 rockets?
How many messages could transmit the traffic light if he had three "eyes" at the same time, and each of them could change the color and become red, yellow or green?
Some device transmits one of the seven signals per second. How many different messages in 3 C can be transmitted using this device?
To transmit signals on the fleet, special signal flags are used in one line (the sequence is important). What number of different types of flags should have, so that with the help of a sequence of three flags, 8 different signals can be transferred (each species flags of an unlimited number)?
At school 800 students, students' codes are recorded in school information system With the minimum number of bits. What is the information about codes of 320 students present at the conference?
1) 2560 bits 2) 100 bytes 3) 6400 bits 4) 400 byte
In some country, the car number consists of 8 characters. The first character is one of the 26 Latin letters, the other seven - decimal numbers. Sample number - A1234567. Each symbol is encoded by the minimum possible amount of bits, and each number is the same and minimally possible byte. Determine the amount of memory required for storing 30 car numbers.
1) 180 byte 2) 150 bytes 3) 120 bytes 4) 250bb
To register on the site of some country, you need to come up with a password with a length of exactly 11 characters. In the password, you can use decimal numbers and 12 different symbols of the local alphabet, and all letters are used in two strokes - line and uppercase. Each symbol is encoded the same and minimally possible amount of bits, and each password is the same and minimum possible byte. Determine the amount of memory required for storage 60 passwords.
1) 720 byte 2) 660 byte 3) 540 byte 4) 600B
To encode messages, it is decided to use sequences of different lengths consisting of "+" and "-" characters. How many different messages can be encoded using at least 2 or no more than 6 characters in each of them?
To encode messages, it is decided to use sequences of different lengths consisting of "+" and "-" signs. How many different messages can be encoded using at least 3 and no more than 7 characters in each of them?
To register on the site of some country, you need to come up with a password for a length of exactly 15 characters. In the password, you can use decimal numbers and 11 different symbols of the local alphabet, and all letters are used in two strokes - line and uppercase. Each symbol is encoded the same and minimally possible amount of bits, and each password is the same and minimum possible byte. Determine the amount of memory required for storing 30 passwords.
1) 360 byte 2) 450 bytes 3) 330 byte 4) 300B
To register on the site of some country, you need to come up with a password with a length of exactly 11 characters. In the password you can use decimal numbers and 32 different symbols of the local alphabet, and all letters are used in two designs - line and uppercase. Each symbol is encoded the same and minimally possible amount of bits, and each password is the same and minimum possible byte. Determine the amount of memory required for storing 50 passwords.
1) 450 byte 2) 400 bytes 3) 550 byte 4) 500B
1 Cylobyte is denoted by "KB", and megabytes - "MB", but in demo tests, the developers of the EGE led just such designations.
2 This is not another method of solution, and more severe justification of the previous algorithm.
Task Systems:
Demonstration esmer options 2004-2011
Guseva I.Yu. Ege. Computer science: distribution material training tests. - St. Petersburg: Trigon, 2009.
Yakushkin P.A., Leschinner V.R., Kiriyenko D.P. EGE 2010. Informatics. Typical test tasks. - M.: Exam, 2010.
Krylov S.S., Ushakov D.M. EGE 2010. Informatics. Thematic workbook. - M.: Exam, 2010.
Yakushkin P.A., Ushakov D.M. The most complete edition model options Real assignments of EGE 2010. Informatics. - M.: Astrel, 2009.
Abramyan M.E., Mikhalkovich S.S., Rusanova Ya.M., Cherdyntseva M.I. Informatics. Ege step by step. - M.: School Technology Research Institutes, 2010.
Churkina i.e. EGE 2011. Informatics. Thematic training tasks. - M.: Eksmo, 2010.
Krylov S.S., Leschinner V.R., Yakushkin P.A. EGE 2011. Informatics. Universal materials to prepare students. - M.: Intellect Center, 2011.
13th task: "Number of information"
The level of complexity is elevated,
Maximum score - 1,
Approximate execution time - 3 minutes.
Solution 13. the tasks of the ege By computer science (K. Poles, in. 4):
Message volume - 7.5 KB. It is known that this message contains 7680 characters. What is the power of the alphabet?
Answer: 256
✍ Show Solution:
- We use the formula:
I \u003d 7.5 KB \u003d 7.5 * 2 13 bits
\\ [K \u003d \\ FRAC (7.5 * 2 ^ (13)) (7680) \u003d \\ FRAC (7.5 * 2 ^ (13)) (15 * 2 ^ 9) \u003d \\ FRAC (7.5 * 16 ) (15) \u003d 8 \\]
2 8 = 256
Different characters
(according to the formula Q \u003d 2 N)
Solution 13 of the tasks of the EGE on computer science (K. Polekov, in. 6):
The power of the alphabet is equal 256 . How many kb memory will need to save 160 pages of texton average 192 Symbol On each page?
Answer: 30
✍ Show Solution:
- We find the total number of characters on all pages (for convenience we will use de-degree degrees):
\\ [I \u003d (15 * 2 ^ (11)) * 2 ^ 3 bits \u003d \\ FRAC (15 * 2 ^ (14)) (2 ^ (13)) KBIT \u003d 30 KB \\]
I \u003d. 30 Krib
Solution 13 of the task of the EGE on computer science (K. Polekov, p. 3):
Two texts contain the same number of characters. The first text is made in the alphabet 16 characters, and the second text - in the alphabet from 256 characters.
How many times are the amount of information in the second text more than in the first?
Answer: 2
✍ Show Solution:
- Formula is needed Q \u003d 2 n
- Calculate the required number of bits for storing one character for both texts:
Working with various systems
Ege 2017 Collection D.M. Ushakov "10. training options…" option 1:
The cable network holds a vote among the audience about which of the four films they would like to see in the evening. Use the cable network 2000
person. In the voting participated 1200
person.
What is the amount of information ( in bytes), recorded automated system voting?
Answer: 300
✍ Show Solution:
- Since the numbers of four films are stored in computer systemYou can find the number of bits required for storing the movie number:
Ege 2017 Collection D.M. Ushakov "10 training options ..." Option 10:
Rent a rehearsal exam in school 105 person. Each of them is distinguished by a special number identifying it in automatic system Replies checks. When registering a participant to record its number system uses the minimum possible amount bit, the same for each participant.
What is the amount of information in bitsrecorded by the device after registration 60
participants?
Answer: 420
✍ Show Solution:
Solution 13 of the tasks of the EGE on computer science (K. Polekov, in. 17):
The database stores records containing dates information. Each entry contains three fields: year (number from 1 to 2100), number of month (number from 1 to 12) and day number in the month (number from 1 to 31). Each field is recorded separately from other fields using the minimum possible number of bits.
Determine the minimum number of bits required to encode one entry.
Answer: 21
✍ Show Solution:
- Formula is needed Q \u003d 2 n.
- Calculate the required number of bits for the storage of each item of the entire record:
Solution 13 of the task of the EGE on computer science (test version of the examination work, the simulator of 2018, S.S. Krylov, D.M. Ushakov):
Rehearsal exam pass 9
Flows in 100
Man in each. Each of them allocate a special code consisting of the flow number and the number in the stream. When encoding these numbers of participants, the inspection system uses the minimum possible amount bit, the same for each participant, separately for the flow number and the number in the stream. In this case, the minimum possible and equally integer is used to record the code. byte.
What is the amount of information in bytes recorded by the device after registration 80
participants?
Answer: 160
✍ Show Solution:
- The code consists of two components: 1. The flow number (in bits) and 2. The number in order (in bits). We find the number of bits necessary for storing them:
Computer systems and car numbers
Solution 13 of the task of the EGE on computer science (K. Polekov, p. 33):
The car number consists of several letters (the number of letters is the same in all rooms), followed by three digits. At the same time used 10 digits only 5 letters: N, o, m, e and R. Need to have no less 100 000 different numbers.
What the smallest number of letters should be in the car room?
Answer: 3
✍ Show Solution:
- Formula is needed Q \u003d M n.
13 task. DEVEROVIYS EGE 2018 Informatics:
10 Symbols. As symbols, the capital letters of the Latin alphabet use, i.e. 26 Different characters. In the database for storing each password, the same and minimum possible integer byte bit.
Determine the amount of memory ( in bytes) required to store data on 50
users.
In response, write down only an integer - the number of bytes.
Answer: 350
✍ Show Solution:
- The main formula for solving this task is:
- To find the number of bits required to store one password, first need to find the number of bits required for storing 1 symbol in the password. By the formula we get:
where Q. - Number of characters that can be encoded using N. bit.
Solution 13 of the tasks of the EGE on computer science (diagnostic version of the examination work, EGE 2018 simulator, S.S. Krylov, D.M. Ushakov):
In some country, the car number consists of 7 characters. Each symbol can be one of 18 Different letters or decimal digital.
Each such number in the computer program is recorded as the minimum possible and identical integer byteAt the same time use inventive coding and each symbol is encoded the same and the minimum possible amount. bit.
Determine the amount of memory in bytesassigned to this program for recording 50
rooms.
In response, specify only the number.
Answer: 250
✍ Show Solution:
- Since the room can use either one letter from 18 or one digit from 10 , just one of the symbol in the room can be used one of 28 Symbols:
Ege 2017 Collection D.M. Ushakov "10 training options ..." Option 6:
15 12 -Simvolny set A, b, c, d, e, f, g, h, i, k, l, m, n. In the database for storing information about each user, the same and minimum possible integer byte. At the same time, the inventive coding of passwords is used, all symbols are encoded the same and the minimum possible amount. bit. In addition to the password itself, additional information is stored for each user in the system, for which it is assigned 12 Byte per user.
Determine the amount of memory ( in bytes) required for storing information about 30
users.
In response, write down only an integer - the number of bytes.
Answer: 600
✍ Show Solution:
Ege of computer science 2017 Task 13 FIPI Option 1 (S. Krylov, Churkina ie):
When registering in a computer system, each user is issued a password consisting of 7 characters and containing only characters from 33 -Simvol alphabet. In the database for storing information about each user, the same and minimum possible integer byte. At the same time, the inventive coding of passwords is used, all symbols are encoded the same and the minimum possible amount. bit. In addition to your own password, for each user, the system stores additional information, for which a whole number of bytes is allocated; This number is the same for all users.
For storing information about 60 users needed 900 byte.
How much byte is allocated for storage additional information About one user?
In response, write down only an integer - the number of bytes.
Answer: 9
✍ Show Solution:
- First decide with a password. According to the formula Q \u003d M n We get:
Solution 13 of the task of the EGE on computer science (K. Polekov, p. 58):
When registering in a computer system, each user is issued a password consisting of 9 characters. As characters use capital and lowercase Latin alphabet letters (in it 26 characters), and decimal numbers. In the database to store information about each user, the same and the minimum possible integer byte is assigned. In this case, the inventive coding of passwords is used, all symbols are encoded the same and minimally possible amount of bits. In addition to the password itself, additional information is stored for each user, for which it is allocated. 18 bytes per user. In the computer system allocated 1 KB For storing information about users.
About what the greatest quantity Can users be saved in the system? In response, write down only the integer - the number of users.
Answer: 40
✍ Show Solution:
- Since both capital and lowercase letters are used, we will get the entire options for encoding characters:
