Decryption of the two-digit code. Converting numbers to binary, hexadecimal, decimal, octal number systems

22.07.2019 Safety

The set of symbols used to write text is called alphabetically.

The number of characters in the alphabet is power.

The formula for determining the amount of information: N = 2b,

where N is the cardinality of the alphabet (number of symbols),

b is the number of bits (information weight of the symbol).

Almost all the necessary characters can be placed in an alphabet with a capacity of 256 characters. This alphabet is called sufficient.

Because 256 = 2 8 , then the weight of 1 character is 8 bits.

The 8-bit unit of measure has been given a name 1 byte:

1 byte = 8 bits.

The binary code of each character in computer text occupies 1 byte of memory.

How is textual information represented in computer memory?

The convenience of byte-by-byte encoding of characters is obvious, since a byte is the smallest addressable part of memory and, therefore, the processor can access each character separately when performing text processing. On the other hand, 256 characters is quite enough to represent a wide variety of character information.

Now the question arises, which eight-bit binary code to put in correspondence with each character.

It is clear that this is a conditional matter, you can come up with many ways to encode.

All characters of the computer alphabet are numbered from 0 to 255. Each number corresponds to an eight-bit binary code from 00000000 to 11111111. This code is simply the ordinal number of the character in the binary number system.

A table in which all characters of the computer alphabet are assigned serial numbers is called an encoding table.

For different types of computers, different encoding tables are used.

The table has become the international standard for PCs. ASCII(pronounced asci) (American Standard Code for Information Interchange).

The ASCII code table is divided into two parts.

Only the first half of the table is an international standard, i.e. characters with numbers from 0 (00000000), up to 127 (01111111).

Structure of the ASCII encoding table

Serial number	Code	Symbol
0 - 31	00000000 - 00011111	Characters with numbers from 0 to 31 are called control characters. Their function is to control the process of displaying text on the screen or printing, giving a sound signal, marking up text, etc.
32 - 127	00100000 - 01111111	Standard part of the table (English). This includes lowercase and uppercase letters of the Latin alphabet, decimal digits, punctuation marks, all kinds of brackets, commercial and other symbols. Character 32 is a space, i.e. empty position in the text. All the rest are reflected by certain signs.
128 - 255	10000000 - 11111111	Alternative part of the table (Russian). The second half of the ASCII code table, called the code page (128 codes, starting with 10000000 and ending with 11111111), can have different options, each option has its own number. The code page is primarily used to accommodate national scripts other than Latin. In Russian national encodings, characters of the Russian alphabet are placed in this part of the table.

First half of the ASCII code table

I draw your attention to the fact that in the encoding table, letters (uppercase and lowercase) are arranged in alphabetical order, and numbers are sorted in ascending order of values. This observance of the lexicographic order in the arrangement of characters is called the principle of sequential coding of the alphabet.

For the letters of the Russian alphabet, the principle of sequential coding is also observed.

The second half of the ASCII code table

Unfortunately, there are currently five different Cyrillic encodings (KOI8-R, Windows. MS-DOS, Macintosh and ISO). Because of this, problems often arise with the transfer of Russian text from one computer to another, from one software system to another.

Chronologically, one of the first standards for encoding Russian letters on computers was KOI8 ("Information Exchange Code, 8-bit"). This encoding was used back in the 70s on computers of the EC series of computers, and from the mid-80s it began to be used in the first Russified versions of the UNIX operating system.

From the beginning of the 90s, the time of the dominance of the MS DOS operating system, the CP866 encoding remains ("CP" stands for "Code Page", "code page").

Apple computers running the Mac OS operating system use their own Mac encoding.

In addition, the International Organization for Standardization (International Standards Organization, ISO) approved another encoding called ISO 8859-5 as a standard for the Russian language.

The most common encoding currently used is Microsoft Windows, abbreviated as CP1251.

Since the end of the 90s, the problem of standardization of character coding has been solved by the introduction of a new international standard, which is called Unicode. This is a 16-bit encoding, i.e. it has 2 bytes of memory per character. Of course, in this case, the amount of memory occupied increases by 2 times. But such a code table allows the inclusion of up to 65536 characters. The complete specification of the Unicode standard includes all existing, extinct and artificially created alphabets of the world, as well as many mathematical, musical, chemical and other symbols.

Let's try using an ASCII table to imagine how the words will look in the computer's memory.

Internal representation of words in computer memory

Sometimes it happens that the text, consisting of letters of the Russian alphabet, received from another computer, cannot be read - some kind of "abracadabra" is visible on the monitor screen. This is due to the fact that computers use different character encodings of the Russian language.

You can use standard software tools of the Microsoft Windows operating system. To do this, open the "Start" menu on your computer, in the menu that appears, click "All Programs", select the "Accessories" folder and find the "Calculator" application in it. From the calculator's top menu, select View and then Programmer. The calculator form is converted.

Now enter the number to translate. In a special window below the input field, you will see the result of the translation of the code number. So, for example, after entering the number 216, you will get the result 1101 1000.

If you don’t have a computer or a smartphone at hand, you can try the number written in Arabic numerals into binary code yourself. To do this, you must constantly divide the number by 2 until the last remainder remains or the result reaches zero. It looks like this (for example, the number 19):

19: 2 = 9 - remainder 1
9: 2 = 4 - remainder 1
4: 2 = 2 - remainder 0
2: 2 = 1 - remainder 0
1: 2 = 0 - reached 1 (dividend is less than divisor)

Write the balance backwards - from the most recent to the very first. You will get the result 10011 - this is the number 19 in .

To convert a fractional decimal number into a system, you first need to convert the integer part of the fractional number into a binary number system, as shown in the example above. Then you need to multiply the fractional part of the usual number by the binary base. As a result of the product, it is necessary to select the integer part - it takes the value of the first digit of the number in the system after the decimal point. The final of the algorithm comes when the fractional part of the product vanishes, or when the required calculation accuracy is reached.

Sources:

Translation algorithms on Wikipedia

In addition to the usual decimal number system in mathematics, there are many other ways to represent numbers, including in form. For this, only two characters are used, 0 and 1, which makes the binary system convenient when used in various digital devices.

Instruction

Systems in are designed to symbolically display numbers. In the usual one, the decimal system is mainly used, which is very convenient for calculations, including in the mind. In the world of digital devices, including computers, which has now become a second home for many, the most widespread is, followed by decreasing popularity, octal and hexadecimal.

These four systems have one thing in common - they are positional. This means that the value of each sign in the final number depends on the position in which it stands. This implies the concept of capacity, in binary form the unit of capacity is the number 2, in - 10, etc.

There are algorithms for transferring numbers from one system to another. These methods are simple and do not require much knowledge, however, the development of these skills requires some skill, which is achieved by practice.

The conversion of a number from another number system to is carried out in two possible ways: by iterative division by 2 or by writing each individual sign of the number in the form of four characters, which are tabular values, but can also be found independently due to their simplicity.

Use the first method to convert a decimal number to binary. This is all the more convenient because decimal numbers are easier to operate in the mind.

For example, convert the number 39 to binary Divide 39 by 2 - you get 19 and 1 in the remainder. Do a few more iterations of dividing by 2 until it eventually equals zero, and in the meantime write the intermediate remainders on the line from right to left. The final set of ones and zeros will be your number in binary form: 39/2 = 19 → 1; 19/2 = 9 → 1; 9/2 = 4 → 1; 4/2 = 2 → 0; 2/2 = 1 → 0; 1/2 = 0 → 1. So, we got the binary number 111001.

To binarize a number from bases 16 and 8, find or make your own tables of the corresponding designations for each digital and symbolic element of these systems. Namely: 0 0000, 1 0001, 2 0010, 3 0011, 4 0100, 5 0101, 6 0110, 7 0111, 8 1000, 9 1001, A 1010, B 1011, C 1100, D 1101, E 1110, F 11 11 .

Write down each sign of the original number in accordance with the data in this table. Examples: Octal number 37 = = 00110111 in binary; Hexadecimal number 5FEB12 = = 010111111110101100010010 system.

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Sources:

phonegap

Let's figure out how translate texts into digital code? By the way, on our website you can convert any text into decimal, hexadecimal, binary code using the Online Code Calculator.

Text encoding.

According to computer theory, any text consists of individual characters. These characters include: letters, numbers, lowercase punctuation marks, special characters ("", №, (), etc.), they also include spaces between words.

Necessary knowledge base. The set of symbols with which I write down the text is called the ALPHABET.

The number of symbols taken in the alphabet represents its power.

The amount of information can be determined by the formula: N = 2b

N - the same power (set of characters),
b - Bit (weight of the taken symbol).

An alphabet in which there will be 256 can accommodate almost all the necessary characters. Such alphabets are called SUFFICIENT.

If we take an alphabet with a power of 256, and keep in mind that 256 \u003d 28

8 bits is always called 1 byte:
1 byte = 8 bits.

If we translate each character into a binary code, then this computer text code will take 1 byte.

How can textual information look like in computer memory?

Any text is typed on the keyboard, on the keyboard keys, we see signs familiar to us (numbers, letters, etc.). They enter the computer's RAM only in the form of a binary code. The binary code of each character looks like an eight-digit number, such as 00111111.

Since a byte is the smallest addressable memory unit, and the memory is addressed to each character separately, the convenience of such coding is obvious. However, 256 characters is a very convenient amount for any character information.

Naturally, the question arose: Which eight digit code belongs to each character? And how to translate text into digital code?

This process is conditional, and we have the right to come up with various ways to encode characters. Each character of the alphabet has its own number from 0 to 255. And each number is assigned a code from 00000000 to 11111111.

The encoding table is a "cheat sheet" in which the characters of the alphabet are indicated in accordance with the serial number. For different types of computers, different tables are used for encoding.

ASCII (or Asci) has become the international standard for personal computers. The table has two parts.

The first half is for an ASCII table. (It was the first half that became the standard.)

Compliance with the lexicographic order, that is, in the table, the letters (lowercase and uppercase) are indicated in strict alphabetical order, and the numbers in ascending order, is called the principle of sequential coding of the alphabet.

For the Russian alphabet, they also observe sequential coding principle.

Now, in our time, whole five coding systems Russian alphabet (KOI8-R, Windows. MS-DOS, Macintosh and ISO). Due to the number of encoding systems and the lack of one standard, misunderstandings often arise with the transfer of Russian text to its computer form.

One of the first standards for encoding the Russian alphabet and on personal computers they consider KOI8 ("Information exchange code, 8-bit"). This encoding was used in the mid-seventies on a series of ES computers, and since the mid-eighties, it has been used in the first UNIX operating systems translated into Russian.

Since the beginning of the nineties, the so-called time when the MS DOS operating system dominated, the CP866 coding system appeared ("CP" stands for "Code Page", "code page").

Computer giant APPLE, with its innovative system under which they operate (Mac OS), are beginning to use their own system to encode the MAC alphabet.

The International Standards Organization (ISO) appoints another standard for the Russian language alphabet coding system called ISO 8859-5.

And the most common, nowadays, system for coding the alphabet, invented in Microsoft Windows, and is called CP1251.

Since the second half of the nineties, the problem of the standard for translating text into digital code for the Russian language and not only was solved by introducing a system called Unicode into the standard. It is represented by a sixteen-bit encoding, which means that exactly two bytes of RAM are allocated for each character. Of course, with this encoding, memory costs are doubled. However, such a code system allows you to convert up to 65536 characters into an electronic code.

The specificity of the standard Unicode system is the inclusion of absolutely any alphabet, be it existing, extinct, invented. Ultimately, absolutely any alphabet, in addition to this, the Unicode system, includes a lot of mathematical, chemical, musical and general symbols.

Let's use an ASCII table to see what a word might look like in your computer's memory.

It often happens that your text, which is written in letters from the Russian alphabet, is not readable, this is due to the difference in alphabet coding systems on computers. This is a very common problem that is found quite often.

08. 06.2018

Blog of Dmitry Vassiyarov.

Binary code - where and how is it used?

Today I am especially glad to meet you, my dear readers, because I feel like a teacher who, at the very first lesson, begins to introduce letters and numbers to the class. And since we live in a world of digital technologies, I will tell you what the binary code is, which is their basis.

Let's start with the terminology and find out what binary means. For clarification, let's return to our usual calculus, which is called "decimal". That is, we use 10 digits, which make it possible to conveniently operate with various numbers and keep an appropriate record. Following this logic, the binary system provides for the use of only two characters. In our case, it's just "0" (zero) and "1" one. And here I want to warn you that, hypothetically, there could be other symbols in their place, but it is precisely such values, denoting the absence (0, empty) and the presence of a signal (1 or “wand”), that will help us further understand the structure of the binary code.

Why do we need a binary code?

Before the advent of computers, various automatic systems were used, the principle of operation of which was based on receiving a signal. The sensor is triggered, the circuit is closed and a certain device is turned on. No current in the signal circuit - no operation. It was electronic devices that made it possible to make progress in processing information represented by the presence or absence of voltage in the circuit.

Their further complication led to the emergence of the first processors, which also did their job, already processing a signal consisting of pulses alternating in a certain way. We will not now go into the software details, but the following is important for us: electronic devices turned out to be able to distinguish a given sequence of incoming signals. Of course, it is possible to describe the conditional combination in this way: “there is a signal”; "no signal"; "there is a signal"; "there is a signal." You can even simplify the notation: “there is”; "No"; "There is"; "There is".

But it is much easier to indicate the presence of a signal with a unit “1”, and its absence with a zero “0”. Then instead of all this we can use a simple and concise binary code: 1011.

Of course, processor technology has stepped far forward and now chips are able to perceive not just a sequence of signals, but entire programs written by certain commands consisting of individual characters. But for their recording, the same binary code is used, consisting of zeros and ones, corresponding to the presence or absence of a signal. Whether he exists or not, it doesn't matter. For a chip, any of these options is a single piece of information, which is called a “bit” (bit is the official unit of measurement).

Conventionally, a character can be encoded by a sequence of several characters. Two signals (or their absence) can describe only four options: 00; 01;10; 11. This encoding method is called two-bit. But it can also be:

four-bit (as in the example in the paragraph above 1011) allows you to write 2 ^ 4 = 16 character combinations;
eight bits (for example: 0101 0011; 0111 0001). At one time it was of the greatest interest to programming because it covered 2^8 = 256 values. This made it possible to describe all decimal digits, the Latin alphabet and special characters;
sixteen-bit (1100 1001 0110 1010) or higher. But records with such a long length are already for modern, more complex tasks. Modern processors use 32 and 64 bit architectures;

To be honest, there is no single official version, it so happened that it was the combination of eight characters that became the standard measure of stored information, called “bytes”. This could apply even to a single letter written in 8-bit binary code. So, my dear friends, please remember (if anyone did not know):

8 bits = 1 byte.

So accepted. Although a character written as a 2-bit or 32-bit value can also nominally be called a byte. By the way, thanks to the binary code, we can estimate the volume of files measured in bytes and the speed of information transfer and the Internet (bits per second).

Binary encoding in action

To standardize the recording of information for computers, several encoding systems have been developed, one of which is ASCII, based on 8-bit recording, has become widespread. The values in it are distributed in a special way:

the first 31 characters are control characters (from 00000000 to 00011111). Serve for service commands, output to a printer or screen, sound signals, text formatting;
the following from 32 to 127 (00100000 - 01111111) Latin alphabet and auxiliary symbols and punctuation marks;
the rest, up to the 255th (10000000 - 11111111) - alternative, part of the table for special tasks and displaying national alphabets;

The interpretation of the values in it is shown in the table.

If you think that "0" and "1" are located in a chaotic order, then you are deeply mistaken. Using any number as an example, I will show you a pattern and teach you how to read numbers written in binary code. But for this we will accept some conditions:

a byte of 8 characters will be read from right to left;
if in ordinary numbers we use the digits of ones, tens, hundreds, then here (reading in reverse order) for each bit, various powers of “two” are presented: 256-124-64-32-16-8-4-2-1;
now we look at the binary code of a number, for example 00011011. Where there is a “1” signal in the corresponding position, we take the values of this bit and sum them up in the usual way. Accordingly: 0+0+0+32+16+0+2+1 = 51. You can verify the correctness of this method by looking at the code table.

Now, my inquisitive friends, you not only know what a binary code is, but also know how to convert the information encrypted by it.

Language understandable to modern technology

Of course, the algorithm for reading binary code by processor devices is much more complicated. But with its help, you can write anything you want:

text information with formatting options;
numbers and any operations with them;
graphic and video images;
sounds, including those that go beyond our hearing;

In addition, due to the simplicity of the "presentation", various ways of recording binary information are possible: HDD disks;

Complementing the advantages of binary coding is almost unlimited possibilities for transmitting information over any distance. It is this method of communication that is used with spacecraft and artificial satellites.

So, today, the binary system is the language that most of the electronic devices we use can understand. And what is most interesting, no other alternative is foreseen for him yet.

I think that the information I have provided will be enough for you to get started. And then, if such a need arises, everyone will be able to delve into an independent study of this topic. I will say goodbye and after a short break I will prepare for you a new article of my blog, on some interesting topic.

It's better if you tell me yourself ;)

See you soon.

Since it is the simplest and meets the requirements:

The fewer values that exist in the system, the easier it is to make individual elements that operate on these values. In particular, two digits of the binary number system can be easily represented by many physical phenomena: there is current - there is no current, the magnetic field induction is greater than the threshold value or not, etc.
The lower the number of states for an element, the higher the noise immunity and the faster it can work. For example, to encode three states through the magnitude of the magnetic field induction, it will be necessary to enter two threshold values, which will not contribute to noise immunity and reliability of information storage.
Binary arithmetic is pretty simple. Simple are the tables of addition and multiplication - the basic operations on numbers.
It is possible to use the apparatus of the algebra of logic to perform bitwise operations on numbers.

Links

Online calculator for converting numbers from one number system to another

Wikimedia Foundation. 2010 .

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Decryption of the two-digit code. Converting numbers to binary, hexadecimal, decimal, octal number systems

How is textual information represented in computer memory?

Now the question arises, which eight-bit binary code to put in correspondence with each character.

A table in which all characters of the computer alphabet are assigned serial numbers is called an encoding table.

Structure of the ASCII encoding table

Serial number

Code

Symbol

0 - 31

00000000 - 00011111

32 - 127

00100000 - 01111111

128 - 255

10000000 - 11111111