1. An information message of 375 bytes consists of 500 characters. What is the information weight of each character in this message? What is the power of the alphabet with which this message was written?
2. A 64-character alphabet was used to record the text. How much information in bytes does 3 pages of text contain if each page contains 40 lines of 60 characters per line?
3. The message takes 6 pages of 40 lines, each line contains 60 characters. The information volume of the entire message is 9000 bytes. What is the information weight of one character? How many characters are in the alphabet of the language in which this message is written?
4. The tribe uses a 32-character alphabet. The code of basic laws of the tribe is stored on 512 clay tablets, each of which contains exactly 256 symbols. How much information is contained on each medium? How much information is contained in the entire code of laws?
5. The message, written in letters of the 8-character alphabet, contains 30 characters. How much information does it carry?
6. The message, written in letters of the 128-character alphabet, contains 20 characters. How much information does it carry?
7. An information message of 1.5 kilobytes contains 3072 characters. How many characters does the alphabet with which this message was written contain?
8. A 4 KB information message consists of 4096 characters. What is the information weight of the symbol of the alphabet used? How many characters does the alphabet with which this message is written contain?
9. Determine the amount of information in a message of K alphabet characters of cardinality N by filling out the table:

Independent work

Option 1

1. Message size – 7 KB. It is known that this message contains 7168 characters. What is the power of the alphabet?
2. A text of 500 characters is given. It is known that the characters are taken from a table measuring 32 by 32. Determine the information volume of the text in bits.
3. The power of the alphabet is 256. How many KB of memory would be required to store 160 pages of text containing an average of 192 characters per page?
4. The message size is 3 KB. The message contains 3072 characters. What is the power of the alphabet?
5. To encode a secret message, 12 special symbols are used. In this case, the characters are encoded with the same minimum possible number of bits. What is the information volume of a message of 256 characters?
6. The power of the alphabet is 32. How many KB of memory would be required to store 256 pages of text containing an average of 128 characters per page?

Option 2

1. The message size is 7.5 KB. It is known that this message contains 7680 characters. What is the power of the alphabet?
2. A text of 600 characters is given. It is known that the characters are taken from a table measuring 16 by 32. Determine the information volume of the text in bits.
3. The power of the alphabet is 128. How many bytes of memory are required to store 8 pages of text containing an average of 4 characters per page?
4. The message size is 11 KB. The message contains 11264 characters. What is the power of the alphabet?
5. To encode a secret message, 18 special symbols are used. In this case, the characters are encoded with the same minimum possible number of bits. What is the information volume of a message of 256 characters?
6. The power of the alphabet is 64. How many KB of memory would be required to store 128 pages of text containing an average of 256 characters per page?

When storing and transmitting information using technical devices, information should be considered as a sequence of symbols - signs (letters, numbers, color codes of image points, etc.).

A set of symbols of a sign system (alphabet) can be considered as various possible states (events).
Then, if we assume that the appearance of symbols in a message is equally probable, the number of possible events N can be calculated as N=2 i
Amount of information in a message I can be calculated by multiplying the number of characters K per information weight of one character i
So, we have the formulas necessary to determine the amount of information in alphabetical approach:

N=2 i	i	Information weight of the symbol, bits
	N	Power of the alphabet
I=K*i	K	Number of characters in text
	I	Information volume of text

The following combinations of known (Given) and sought (Find) quantities are possible:

Type	Given	Find	Formula
1	i	N	N=2 i
2	N	i
3	i,K	I	I=K*i
4	i,I	K
5	I, K	i
6	N, K	I	Both formulas
7	N, I	K
8	I, K	N

If we add to these problems tasks on the ratio of quantities written in different units measurements, using the representation of quantities in the form of powers of two we get 9 types of problems

Let's consider tasks of all types. Let's agree that when moving from one unit of information measurement to another, we will build a chain of values. Then the probability of a computational error decreases.

Problem 1. A message has been received with an information volume of 32 bits. What is this volume in bytes?

Solution: There are 8 bits in one byte.
32:8=4

Answer: 4 bytes. Problem 2

. The volume of the information message is 12582912 bits, expressed in kilobytes and megabytes.
Solution: Since 1Kbyte=1024 bytes=1024*8 bits, then 12582912:(1024*8)=1536 Kbytes and
since 1 MB = 1024 KB, then 1536: 1024 = 1.5 MB

Answer: 1536KB and 1.5MB. Task 3. The computer has RAM

512 MB. The number of bits corresponding to this value is greater:

1) 10,000,000,000bit 2) 8,000,000,000bit 3) 6,000,000,000bit 4) 4,000,000,000bit
Solution: 512*1024*1024*8 bits=4294967296 bits.

Answer: 4. Task 4.
Determine the number of bits in two megabytes, using only powers of 2 for numbers.
Solution: Since 1 byte = 8 bits = 2 3 bits, and 1 MB = 2 10 KB = 2 20 bytes = 2 23 bits. Hence, 2MB = 2 24 bits.

Answer: 2 24 bits. Task 5.
How many megabytes of information does a 2 23 bit message contain?
Solution: Since 1 byte = 8 bits = 2 3 bits, then
2 23 bits=2 23 *2 23 *2 3 bits=2 10 2 10 bytes=2 10 KB=1MB.

Answer: 1MB Task 6.
One character of the alphabet “weighs” 4 bits. How many characters are in this alphabet?
Solution:

i=4	Given: N=2 i According to the formula we find, N=16
N=2 4 N- ?

Find:

Answer: 16 Task 7.
One character of the alphabet “weighs” 4 bits. How many characters are in this alphabet?
Solution:

i=8	Given: N=2 i According to the formula Each character of the alphabet is written using 8 digits of binary code. How many characters are in this alphabet?, N=256
N=2 8 N- ?

Find:

Answer: 256 Task 8.
One character of the alphabet “weighs” 4 bits. How many characters are in this alphabet?
Solution:

N=32	Given: N=2 i The Russian alphabet is sometimes estimated at 32 letters. What is the information weight of one letter of such an abbreviated Russian alphabet? we find 32=, 2 5 =we find 32=,i=5
N=2 4 i- ?

2 i

Answer: 5 Task 9.
One character of the alphabet “weighs” 4 bits. How many characters are in this alphabet?
Solution:

N=100	Given: N=2 i The Russian alphabet is sometimes estimated at 32 letters. What is the information weight of one letter of such an abbreviated Russian alphabet? we find 32=, 2 5 =we find 32=,i=5
N=2 4 i- ?

2 i

The alphabet consists of 100 characters. How much information does one character of this alphabet carry? Problem 10.
One character of the alphabet “weighs” 4 bits. How many characters are in this alphabet?
Solution:

N=24+8=32	Given: N=2 i The Russian alphabet is sometimes estimated at 32 letters. What is the information weight of one letter of such an abbreviated Russian alphabet? we find 32=, 2 5 =we find 32=,i=5
N=2 4 i- ?

2 i

The Chichevok tribe has 24 letters and 8 numbers in its alphabet. There are no punctuation marks or arithmetic signs. What is the minimum number of binary digits they need to encode all the characters? Please note that words must be separated from each other! Problem 11.
One character of the alphabet “weighs” 4 bits. How many characters are in this alphabet?
Solution:

K=360000	The book, typed using a computer, contains 150 pages. Each page has 40 lines, each line has 60 characters. How much information is in the book? Give your answer in kilobytes and megabytes I=K*i Let's determine the number of characters in the book 150*40*60=360000. One character occupies one byte. According to the formula I we find
N=2 4 I- ?

=360000bytes 360000:1024=351KB=0.4MB

Answer: 351KB or 0.4MB The information volume of the book text, typed on a computer using Unicode encoding, is 128 kilobytes. Determine the number of characters in the text of the book.
One character of the alphabet “weighs” 4 bits. How many characters are in this alphabet?
Solution:

I=128KB, i=2bytes	In Unicode, one character takes 2 bytes. From the formula I=K*i let's express K=I/i,K=128*1024:2=65536
N=2 4 K- ?

Answer: 65536

Problem 13. A 1.5 KB information message contains 3072 characters. Determine the information weight of one character of the alphabet used
One character of the alphabet “weighs” 4 bits. How many characters are in this alphabet?
Solution:

I=1.5KB, K=3072	From the formula I=K*i let's express i=I/K,i=1,5*1024*8:3072=4
N=2 4 i- ?

Answer: 4

Problem 14. The message, written in letters from the 64-character alphabet, contains 20 characters. How much information does it carry?
One character of the alphabet “weighs” 4 bits. How many characters are in this alphabet?
Solution:

N=64, K=20	Given: N=2 i we find 64= we find 32=, 2 6 =we find 32=,i=6. According to the formula I=K*i I=20*6=120
N=2 4 I- ?

Answer: 120bit

Problem 15. How many characters does a message written using a 16-character alphabet contain if its size is 1/16 of a megabyte?
One character of the alphabet “weighs” 4 bits. How many characters are in this alphabet?
Solution:

N=16, I=1/16 MB	Given: N=2 i we find 16= we find 32=, 2 4 =we find 32=,i=4. From the formula I=K*i let's express K=I/i, K=(1/16)*1024*1024*8/4=131072
N=2 4 K- ?

Answer: 131072

Problem 16. The size of the message, containing 2048 characters, was 1/512 of a megabyte. What is the size of the alphabet in which the message is written?
One character of the alphabet “weighs” 4 bits. How many characters are in this alphabet?
Solution:

K=2048,I=1/512 MB

From the formula I=K*i let's express i=I/K, i=(1/512)*1024*1024*8/2048=8. According to the formula N=2 i we find N= 2 8 =256

Find: Each character of the alphabet is written using 4 digits of binary code. How many characters are in this alphabet? The alphabet for writing messages consists of 32 characters; what is the information weight of one character? Don't forget to indicate the unit of measurement. The information volume of text typed on a computer using Unicode encoding (each character is encoded by 16 bits) is 4 KB. Determine the number of characters in the text. The volume of the information message is 8192 bits. Express it in kilobytes. How many bits of information does a 4 MB message contain? Give the answer in powers of 2. A message written in letters from the 256-character alphabet contains 256 characters. How much information does it carry in kilobytes?

Modern computer technologies, computer science, the power of the alphabet, number systems and many other concepts have the most direct connections with each other. Very few users today are well versed in these issues. Let's try to clarify what the power of the alphabet is, how to calculate it and apply it in practice. In the future, this, without a doubt, may be useful in practice.

How information is measured

Before we begin to study the question of what the power of the alphabet is, and what it is in general, we should start, so to speak, with the basics.

Surely everyone knows that today there are special systems for measuring any quantities based on reference values. For example, for distances and similar quantities these are meters, for mass and weight - kilograms, for time intervals - seconds, etc.

What is the power of the alphabet: an initial concept

So, if we follow the generally accepted rule that the final value of any quantity is a parameter that determines how many times the reference unit is contained in the measured quantity, we can conclude: the power of the alphabet is the total number of symbols used for a particular language.

To make it clearer, let us leave for now the question of how to find the power of the alphabet aside, and pay attention to the symbols themselves, naturally, from the point of view information technologies. Roughly speaking, full list characters used contains letters, numbers, all kinds of brackets, special characters, punctuation marks, etc. However, if we approach the question of what the power of the alphabet is in a computer way, we should also include a space (a single gap between words or other characters).

Let's take the Russian language, or rather, the keyboard layout, as an example. Based on the above, the complete list contains 33 letters, 10 numbers and 11 special characters. Thus, the total power of the alphabet is 54.

Information weight of characters

However, the general concept of the power of the alphabet does not define the essence of computing information volumes of text containing letters, numbers and symbols. This requires a special approach.

Basically, think about it, well, this is what the minimum set could be from the point of view computer system how many characters can it contain? Answer: two. And that's why. The fact is that each symbol, be it a letter or a number, has its own information weight, by which the machine recognizes what exactly is in front of it. But the computer only understands representation in the form of ones and zeros, which, in fact, is what all computer science is based on.

Thus, any character can be represented as sequences containing the numbers 1 and 0, that is, the minimum sequence denoting a letter, number or symbol consists of two components.

The information weight itself, taken as a standard information unit of measurement, is called a bit (1 bit). Accordingly, 8 bits make 1 byte.

Representation of characters in binary code

So, what is the power of the alphabet, I think, is already a little clear. Now let's look at another aspect, specifically the practical representation of power using binary code. As an example, for simplicity, let's take an alphabet containing only 4 characters.

In a two-digit binary code, the sequence and their information representation can be described as follows:

Serial number
Binary code

Hence the simplest conclusion: with the alphabet power N=4, the weight of a single character is 2 bits.

If you use three-digit binary code for an alphabet with, for example, 8 characters, the number of combinations will be as follows:

Serial number
Binary code

In other words, with the alphabet power N=8, the weight of one symbol for a three-digit binary code will be equal to 3 bits.

How to Find the Power of an Alphabet and Use It in a Computer Expression

Now let's try to look at the relationship expressed by the number of characters in the code and the power of the alphabet. The formula, where N is the alphabetic power of the alphabet, and b is the number of characters in the binary code, will look like this:

That is, 2 1 =2, 2 2 =4, 2 3 =8, 2 4 =16, etc. Roughly speaking, the required number of characters of the binary code itself is the weight of the symbol. In information terms it looks like this:

Measuring information volume

However, these were just the simplest examples, so to speak, for an initial understanding of what the power of the alphabet is. Let's move on to practice.

At this stage of development of computer technology for typing text, taking into account capital, uppercase and lowercase letters, Cyrillic and Latin letters, punctuation marks, brackets, arithmetic symbols, etc. 256 characters are used. Based on the fact that 256 is 2 8, it is not difficult to guess that the weight of each character in such an alphabet is 8, that is, 8 bits or 1 byte.

Based on all known parameters, we can easily obtain the desired information volume of any text. For example, we have a computer text containing 30 pages. One page contains 50 lines of 60 any characters or symbols, including spaces.

Thus, one page will contain 50 x 60 = 3,000 bytes of information, and the entire text will contain 3,000 x 50 = 150,000 bytes. As you can see, measuring even small texts in bytes is inconvenient. What about entire libraries?

In this case, it is better to convert the volume into more powerful units - kilobytes, megabytes, gigabytes, etc. Based on the fact that, for example, 1 kilobyte is equal to 1024 bytes (2 10), and a megabyte is 2 10 kilobytes (1024 kilobytes), it is easy to calculate that the volume of text in information and mathematical expression for our example will be 150000/1024 = 146, 484375 kilobytes or approximately 0.14305 megabytes.

Instead of an afterword

In general, this is briefly all that concerns the consideration of the question of what the power of the alphabet is. It remains to add that in this description a purely mathematical approach was used. It goes without saying that the semantic load of the text is not taken into account in this case.

But, if we approach issues of consideration precisely from a position that gives a person something to comprehend, a set of meaningless combinations or sequences of symbols in this regard will have zero information load, although, from the point of view of the concept of information volume, the result can still be calculated.

In general, knowledge about the power of the alphabet and related concepts is not so difficult to understand and can simply be applied in the sense practical actions. Moreover, any user encounters this almost every day. It is enough to give an example of a popular Word editor or any other of the same level in which such a system is used. But don't confuse it with regular Notepad. Here the power of the alphabet is lower, since typing does not use, say, capital letters.

Solving problems on measuring information

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

N=2b

Task 1:

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

1. 32 = 2 5, which means the weight of one character is b = 5 bits.

Answer: one letter carries 5 bits of information.

Task 2:

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

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

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

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

Task 3:

A 300-bit information message 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 power of the alphabet is N = 8.

Try to solve the following problems yourself.

Task 4:

The volume of a message containing 20 characters was 100 bits. What is the size of the alphabet in which the message is written?

Task 5:

How many characters does a message written using an 8-character alphabet contain if its volume is 120 bits?

Task 6:

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

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 set of letters, signs, numbers, brackets, etc.
The number of characters in the alphabet is called its power.

With the alphabetic approach, it is believed that each character of the text has a specific information weight. The information weight of a symbol depends on the power of the alphabet.

What is the minimum power of the alphabet that can be used to record (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

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

We can conclude that in the alphabet with capacity 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 information weight of the symbol is the letter b.

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

N

2

4

8

16

b

1 bit