The double code is a form of recording information in the form of ones and zeros. This is a positional basis 2. Today, a two-code code (table, presented below, try to write down the numbers) is victorious in all digital extensions. This popularity is explained by the high arrogance and simplicity of the form given to the record. Double arithmetic is rather simple, apparently it is easy to implement on the hardware level. components (otherwise they are called - logical) are even more superfluous, stink shards operate with robots with only two camps: logical one (є strum) and logical zero (no strum). Tim himself stinks visibly in the form of analog components, the work of which is based on transitional processes.

How is the double form of the record formed?

Let's figure out how such a key is formed. One bit of a two-code code can only take two places: zero and one (0 and 1). When two ranks are different, it is possible to write down a number of values: 00, 01, 10, 11. This virase can be written down for an additional offensive formula: N = 2m, de: m is the number of rows, and N is the number of combinations.

See two codes

In microprocessors, such keys are assigned to record various information that is being processed. The size of the two-code code can significantly override the mind of the awakened memory. At the same time, the numbers are taken up by a small amount of the middle ones, and they are processed with an additional number of teams. When all sectors of memory, seeing a rich byte double code, are seen as one number.

Depending on the need for data, these other information, different types of keys:

• unsigned;
• direct cylindric codes;
• sign turnaround;
• sign additions;
• Gray code;
• Gray Express code;
• dry code.

Let's take a closer look at some of them.

Unsigned two code

Let's figure out what kind of record is this. In whole unsigned skin codes, the category (dviykovy) is the step of the number two. With the smallest number, which can be written in such a form, equal to zero, and the maximum can be represented by the offensive formula: M = 2 n -1. Tsі two numbers again designate the range of the key, which can be used to show such a two code. Let's look at the feasibility of the conceived form of the record. When choosing this type of unsigned key, which is composed of eight ranks, the range of possible numbers is set to 0 to 255. Sixteen-digit code of the matime range of 0 to 65535. suidnіh addressees. The robot with such keys will be secured by special commands.

Straight line character codes

At whom two keys are seen, the senior order is scored to record the number. Zero is a plus, and one is a minus. As a result of the introduction of this order, the range of encoded numbers is shifted in the negative beak. It turns out that an eight-digit signed binary key can write numbers in the range of -127 to +127. Sixteen-rank - in the range of -32767 to +32767. Eight-bit microprocessors have two land sectors to store similar codes.

A small amount of such a form of the record is those that sign and digital digits of the key need to be processed okremo. Algorithms of the programs, as they work with these codes, appear even more collapsible. In order to change that vision of symbolic divisions, it is necessary to set up a mechanism for masking that symbol, which will lead to a sharp increase in software security and a change in its code. With the method of using this shortfall, a new type of key was provided - a double code.

iconic gate key

The given form is written in the form of direct codes only, that a negative number in a new way comes out in a way of inverting all the ranks of the key. With which digital and sign ranks are identical. Zavdyaki tsomu robotic algorithms with this type of code can be easily forgiven. Prote zvorotny key vmagaє special algorithm for recognizing the symbol of the first order, calculating the absolute value of the number. And also restore the sign of the resulting value. Moreover, the reverse and direct codes of numbers for writing zero have two keys. Regardless of those that have no positive or negative sign.

Signed additional code of a two number

This type of record does not have a lot of listings of small forward keys. Such codes allow you to carry out the summation of both positive and negative numbers without intermediary. For whom there is no analysis of the sign category. Everything became possible because of the fact that the supplementary numbers are a natural ring of symbols, and not piecework, such as straight those turning keys. More than that, an important factor is those that calculate the additional calculation in two codes is super simple. For whom it is enough to add one to the gate key. When choosing the type of sign code, which is composed of eight digits, the range of possible numbers becomes -128 to +127. Sixteen digit key matime range of input -32768 to +32767. In eight-bit processors, two separate sectors are also used to store such numbers.

The double supplementary code has an effect, which one is afraid of, which is called a manifestation of a wider sign. Let's figure out what it means. The effect is that the process of converting a single-byte value of a two-byte value is enough for the skin bit of the high byte to recognize the value of the sign bits of the young byte. Come out, scho zberіgannya sign can be quickened by senior bits. For whom the key value is not changed.

Gray code

I write down the form, in a vlasne, є with a single key. Therefore, in the process of transition from one value to another, only one bit of information is changed. In case of any mistake, when reading data, bring it up to the transition from one to the next position with an insignificant sound in an hour. However, the rejection of an absolutely incorrect result of the final position for such a process is again turned off. The advantage of such a code is the ability to mirror information. For example, inverting older bits, you can simply change directly to the right. Tse vіdbuvaєtsya zavdyaki input Complement, scho control. With this value, it seems that it can be both growing, and falling off at one physical direction wrapping the axis. Oskіlki іnformatsija, written down in Gray's key, may be an exclusive coding character, which carries real numerical data, before a distant robot, it is necessary to transform it in front of the original binary form of the notation. It works for the help of a special convertor - the Grey-Binar decoder. Danish attachments are easily implemented on elementary logical elements in both hardware and software ways.

Gray Express Code

The standard single-key key Grey is suitable for solutions, as represented by the numbers, two. In vipadkah, it is necessary to implement other solutions, with such a form, the record is victorious, it’s more than an average plot. As a result, the singleton of the key is taken. However, such a code does not have zero on the cob of the numerical range. Vіn zm_shchuєtsya on the set value. In the process of processing these types of impulses that are generated, half of the difference between cob and reduction permits is taken into account.

Giving a fractional number to a double key with a fixed coma

At the process of work, it is necessary to operate both in whole numbers, and in fractional ones. Such numbers can be written down for the help of direct, reverse and additional codes. The principle of prompting the guessing of keys is the same, like in whole. Dosi mi vazhali, scho dviykova coma can be right-handed in the young category. But not so. It can be roztashovuvatisya and levoruch in the senior order (for this time, you can write fractional numbers on the switch), and in the middle of the change (you can write down the change in value).

Submission of a double code with a floating coma

Such a form is zastosovuetsya for recording chi navpaki - more small. As a butt, you can bring in the midst of the world to see the difference between atoms and electrons. When such values ​​were counted, it would be possible to win the binary code with even greater rank. However, it is not necessary for us to protect the cosmic measurements to the nearest millimeter. Therefore, the form of recording with a fixed coma in different ways is not effective. A form of algebra is used to represent such codes. That number is written as a mantis, multiplied by ten steps, which reflects the required order of the number. It should be known that the mantis is not guilty of being greater than one, and if the komi is not guilty of writing zero.

It is important that the double calculation was found on the cob of the 18th century by Gottfried Leibniz, a mathematician from Nimechi. Prote, as recently vіdkrіl vchenі, back before the Polynesian island of Mangarov vikorovuvali tsey type of arithmetic. Irrespective of those that the colonization practically failed the original system of counting for the most part, they have inspired folding doubles and dozens of rahunka. In addition, the teachings of the Cognitivist Nunes affirm that coding with a two-code code was stagnant in ancient China in the 9th century BC. e. Other ancient civilizations, for example, the Maya Indians, also victorious combinations of dozens and binary systems for the observation of hourly intervals and astronomical phenomena.

08. 06.2018

Blog of Dmitry Vassiyarov.

Double code - how to get stuck?

Today, I am especially radiant with my readers, my dear readers, even if I feel like a teacher, who at the first lesson starts to know the class with letters and numbers. And if we live in the world of digital technologies, then I will tell you what a two-code code is, which is its basis.

Let's look at the terminology and understand that it means two. For clarification, let's turn to the zodiac count for us, as it is called "ten". Tobto, we win 10 characters-digits, to give the ability to manually operate with different numbers and keep a record.

Dorimuyuchis tsієї logics, dvіykovy system of transferring vikoristannya only two signs. In our opinion, the whole is “0” (zero) and “1” one. And here I want to get ahead of you, that hypothetically in this world they could have but and іnshі intelligible signs, but the same meaning, which means the number of days (0, empty) and the presence of the signal (1 or “stick”), help us to understand the structure of the two code.

Need a second code?

Before the advent of EOM, various automatic systems were victorious, the principle of such foundations on an otrimann signal. Spratsovuє sensor, lancet flickering and mikkaє singing attachment. No struma in the signal lance - no spratsovuvannya. The electronic device itself was allowed to reach progress in the processing of information, presented either in a clear way or in the daytime of the voltage of the lancet.

Farther away, this aggravation led to the appearance of the first processors, as if they were victorious over their own work, shaping the signal already, which is composed of impulses, which are sung by a song rank. We will not delve into the details of the program at once, but it is important for us to step forward: the electronic attachments appeared to be different from the given sequence of signals that need to be received. Obviously, you can describe the mental combination in this way: є signal; "no signal"; "є signal"; "є signal". Navit can prostiti record: є; "nі"; "є"; "є".

But it’s even easier to designate the presence of a signal as a unit “1”, like a day – as a zero “0”. To do this, we can replace a simple and concise double code: 1011.

Insanely, the processor technology churned the krok far ahead and at the same time, the chips of the building capture not just a sequence of signals, but a whole series of programs, written down by singing commands, that add up to a lot of symbols.

And for their record, the very same two code is written, which is composed of zeros and ones, which confirms the obviousness or the presence of the signal. Є він, otherwise yoga is dumb - it doesn’t have a meaning. For a chip, whether it be one of these options, it is one piece of information that took away the name “bit” (bit is the official unit of the world).

Mentally, a symbol can be encoded by a sequence of decal characters. Two signals (or їх vidsutnіstyu) can describe more or less options: 00; 01; ten; 11. This way of coding is called double. Ale wine can be:

• Chotyrokhbitny (as in the application to paragraph 1011) allows you to write 2 ^ 4 = 16 character combinations;
• Eight bits (for example: 0101 0011; 0111 0001). At their hour of the day, representing the greatest interest for programming, the shards have 2 ^ 8 = 256 values. Tse gave the ability to describe all the dozens of digits, the Latin alphabet and special characters;
• Sixteen days (1100 1001 0110 1010) and more. Ale records with such a long time - tse already for today's folding tasks. Modern processors victorious 32-bit and 64-bit architecture;

To be honest, there is no single official version, it so happened that the combination of eight characters itself became the standard entry for information, what is called, what is called “byte”. Taka could zastosovuvatisya up to one letter, written in 8 bit two code. So, my dear friends, remember to be kind (as if you didn’t know):

8 bits = 1 byte.

So accepted. If you want a symbol, records of 2 or 32 bit values, you can nominally call it a byte. Before speech, for two code we can evaluate the size of the files that are stored in bytes and the speed of transmission of information and the Internet (bits per second).

Binary coding at diї

To standardize the recording of information for computers, a few coding systems were split, one of which is ASCII, which is based on an 8-bit recording, with a wide width. The meaning of this rozpodіleni is distinguished by the rank:

• the first 31 characters are control characters (from 00000000 to 00011111). Serve for service commands, display on the printer or screen, sound signals, text formatting;
• advances from 32 to 127 (00100000 – 01111111) Latin alphabet and additional symbols and symbols;
• reshta, up to 255th (10000000 - 11111111) - alternative, part of the table for special tasks and variation of national alphabets;

Deciphering the meaning of it is shown in the table.

If you care that 0 and 1 are sorted in a chaotic order, then you will be deeply merciful. On the example of any number, I will show you the law and teach you how to read the numbers written in a double code. Ale for whom is it possible to take action of intelligence:

• Byte of 8 characters readable right-handed;
• Even though we have victorious numbers of singles, tens, hundreds, in the highest numbers, then here (reading in reverse order) for the skin bit, the different degrees of the “two” are presented: 256-124-64-32-16-8-4-2-1;
• Now we marvel at the double code of the number, for example 00011011. There, where the second position is the signal "1" - the value of the second order is taken and subsumed in the same way. Valid: 0+0+0+32+16+0+2+1 = 51. You can change the correctness of this method by looking at the table of codes.

Now, my drunken friends, you don’t even know what a two-code code is, but you can transform the information encrypted with it.

Mova, I understood modern technology

Obviously, the algorithm for reading the double code by processor attachments is richly foldable. Ale yoga, with the help of you, you can write down everything for sure:

• Text information with formatting parameters;
• The numbers are the kind of operations with them;
• Graphic and video images;
• Sounds, including those that go beyond our strangeness;

Krym tsgogo, zavdyaki simplicity and vikladu zhliva raznі ways to record binary information:

Additional advantages of dual coding are practically unimaginable for the possibility of transmitting information on any country. The very same way to communicate with space ships and piece satellites.

Otzhe, today's double number system is my own, sensible for more electronic attachments, like victorious ones. І scho naytsіkavishe, hodnoї іnshoyї alternatives for the new one are not yet available.

I think that the information I have provided for the beginning will be enough for you. And further, as if it were such a need, the skin could be buried at the self-sufficiency of the tsієї those.

Well, I’ll say goodbye and after a small interruption, I’m preparing a new article for you on my blog, on a spicy topic.

In short, you yourself can tell me;)

To zustrіchi.

Here you can convert two numbers into ASCII characters, which is often easy to get at your head.

1 - Convert skin 4 double digits into one single digit.

Here is a conversion diagram for double format:

0001 = 1 0010 = 2 0011 = 3 0100 = 4 0101 = 5 0110 = 6 0111 = 7 1000 = 8 1001 = 9 1010 = a (the hex number a1 = 1 =0 1110 = e 1111 = f

(Sixteen numbers in a to f є tens of numbers from 10 to 15. Those that are sixteen, or "base 16", - instead of that, so that the skin number of the code represents 10 different numbers, for example, dozens or "base 10", the skin number is which can be represented by 16 different numbers.)

Just as you know this diagram, the transformation of a row of two digits into a row of sixteen digits is simple.

For example,

01000100 = 0100 0100 = 44 hex 1010001001110011 = 1010 0010 0111 0011 = a273 hex

It's easy to drink, isn't it? Just a transformation of a two-digit number, whether it be a dozhini, into a sixteenth equivalent.

(Tse pratsyuє, to that the 16th digit base is 16, and the dvіykova is the base 2, and 16 is the 4th step 2, to remove 1 16th digit, 4 digits are needed. 10, on the other side, not є step 2, not we can convert the 2nd code to the 10th one so very easily.)

2 - Split a row of sixteen numbers on the bet.

When converting numbers to ASCII, skin two sixteen digits are symbols. In this order, split the sixteenth row into two numbers.

You added a sixteenth number, for example 7340298b392, for 6 pairs, for example:

7340298b392 = 07 34 02 98 b3 92

There are 6 pairs of sixteen digits, that will be 6 letters. (Because of the fact that I understand that 98, b3 and 92 are not in letters. I will explain why through the hvilina.)

3 - Turn the skin of a pair of sixteen digits into a tenth number.

Zrobitse by multiplying (the tenth equivalent) of the left digit by 16 and adding another.

For example, b3 hex \u003d 11 * 16 + 3, which is 110 + 66 + 3, which becomes 179. (b hex is old 11 tens.)

4 - Convert tens numbers to ASCII characters.

Now, to remove the ASCII letters for decimals, just type in that ASCII 65 is an uppercase "A" and 97 is an inline "a".

Father, like letter 68?

68 - 4 letters of the alphabet in upper case, right-handed?
65=A, 66=B, 67=C, 68=D.

Otzhe, 68 - tse D.

You take the tenth number, consider 64 for great letters, if the number is less than 97 or 96 for small letters, if the number is more than 97 or more, and the number of letters of the alphabet, connected with it by a set of 2 sixteen digits.

As an alternative, since you're not afraid of a little bit of simple hex arithmetic, you can skip 3 and just go from hex to ASCII, guessing, for example, that

Hex 41 = "A" hex 61 = "a"

Also, apparently, 40 hex for great letters or 60 hex for small letters, and we can convert those that are missing up to the tenth, so that we take the number of the letter into the alphabet.

For example

01101100 = 6c, 6c - 60 = c = 12 decimal = "l" 01010010 = 52, 52 - 40 = 12 hex = 18 decimal = "R"

(If you remember carefully, "m" (or "M") is 13 letters of the alphabet. In this way, you can expand uphill or down from 13, in order to know the sheet, which is closer to the middle, lower to or drop.)

I dipped it on my shirt once and could read it near my head:

01000100 01000001 01000100

I hacked it like this:

01000100 = 0100 0100 = 44 hex, - 40 hex = ucase letter 4 = D 01000001 = 0100 0001 = 41 hex, - 40 hex = ucase letter 1 = A 0100010 0 = 4 D

The T-shirt said "DAD", like, how I got it, I was cool, the shards were bathed by a female woman. Її a person can be similar to me.

How can I realize that 92, b3 and 98 were not letters?

The ASCII code for lowercase "z" is 96 + 26 = 122, which is 122, which looks like 7a. 7a is the largest sixteen number for a letter. Anything greater than 7a is not a letter.

Otzhe, as you can tse robiti like a person.

How to roble computer programs?

For a skin set of 8 double digits, convert yogo to a number and find yogo in the ASCII table.

(To reach the obvious and direct route. A typical programmer can think of 10 or 15 other ways to stretch the details. Details lie in the middle of the computer's easy interface.)

Computers don't understand words and numbers like people do. Today's software security allows you to ignore the end of the line, but on the lowest levels your computer operates with a two-way electrical signal, which maybe only two stands: є strum chi no strum In order to "understand" collapsible data, your computer is guilty of coding them in a double format.

The dual system is based on two digits - 1 and 0, which means that your computer can understand. Ymovіrno, you know the tenth system. There are ten digits - from 0 to 9, and then move on to the offensive order to form two-digit numbers, and the number from the skin offensive order is ten times larger, lower in front. The double system is similar, moreover, the skin number double is larger, lower in front.

Pidrahunok in double format

The first digit of the double expression is equal to 1 from the tenth system. The other figure is equal to 2, the third - 4, the fourth - 8, then - to be won by the next. Adding all the values ​​will give you the number in the tenth format.

1111 (for double format) = 8 + 4 + 2 + 1 = 15 (for tenth system)

Appearance 0 gives 16 possible values ​​for some double battles. Change to 8 bits, and you will take 256 possible values. Tse borrows a lot more space for presentation, shards of chotir numbers in the tenth form give us 10,000 possible values. Obviously, the binary code takes up more space, but the computers can understand two files more quickly, lower than a dozen systems. І for deyaky speeches, such as a logical processing, two code shortening for ten.

Let me tell you, there is one more basic system that is being played in programming: shestnadtsyatkov. If computers don't work in hexadecimal format, the programmers can use the code to present the binary address in manual format when writing the code. This is due to the fact that two digits of a sixteenth number can be a whole byte, so that they replace all digits in a two-digit format. The sixteenth system of victorious digits 0-9, as well as letters from A to F, to select the additional six digits.

Why do computers hack two files

Short note: hardware security and the laws of physics. The skin symbol on your computer is an electrical signal, and in the first days, calculate the reduction of electrical signals in a richer way. It was more reasonable to distinguish between “turned on” camps, representations with a negative charge, and “unplugged” camps, representations with a positive charge.

For those who do not know why "wired" is represented by a positive charge, it is connected with the fact that the electrons have a negative charge, and more electrons have more struma with a negative charge.

In this manner, early computers rose from the room twin files for the creation of their systems, and although the stench victorious over the old, cumbersome possession, the stench worked on the same fundamental principles. Modern computers win so many ranks, transistor for vikonanny rozrahunkіv іz dvіykovy code.

Axis diagram of a typical transistor:

As a matter of fact, the wine allows the stream to flow from the dzherel to the drain, as if at the gate there is a stream. Tse form a double key. Virobniki can create digital transistors as small as 5 nanometers apart from two strands of DNA. Therefore, as modern processors work, and stink, they can suffer from problems with the differences between the included and the closed state (even if it is connected with their unrealistic molecular rozmіrom, sila up to wonders of quantum mechanics).

Why only two systems

So you might think: “Why is it 0 and 1? Why not add one more number? If it is often associated with the traditions of the creation of computers, natomist, adding one more number would mean that it would be necessary to see one camp of the strum, and not just “switched off” or “switched off”.

The problem here is that if you want to beat the cost of equal voltages, you will need a way to easily calculate the cost of them, but now the hardware is safe, building on the price, not zhittєzdatnym as a replacement of two counts. For example, I use so titles, second hand computer, Razrobleniy in the 1950s, but rozrobleniya on that i stuck. Ternary logic more efficient, lower dviykov, but still there is no effective replacement of the binary transistor or, prinaymni, no transistor on the scales and critical scales, scho and dviykov.

The reason, through which we can't reverse logic, lies in the way transistors are wired in a computer and how the stench is reversed for mathematical calculations. The transistor takes information for two inputs, vikonu operation and rotates the result for one output.

In this way, binary mathematics is simpler for a computer, no matter what. Double logic is easily converted to double systems, moreover, True and False match the On and Wimk stans.

Binary truth table, which works on dual logic, may be used for skin fundamental surgery. Ale oskіlki potrіynі gate vikoristovuyut three entrances, potrіyna table of truth is small b 9 or more. In that hour, a binary system can have 16 possible operators (2^2^2), a triple system is small b 19683 (3^3^3). Scaling becomes a problem, shards, even though it’s trifecta efficient, it’s also exponentially folding.

Who know? In the future, it is possible to have three parts of the computer, but the binary logic shards are confused with the problems of miniaturization. For the time being, the world continues to practice in the dual mode.

The term "binary" behind the coin - what is made up of two parts, components. In this order, bіnarnі kodi tse kodi, yakі fold only from two symbolic stanіv, for example, black or white, light or dark, conductor or insulator. A binary code in digital technology is a way of presenting data (numbers, slive and others) as a combination of two characters, which can be assigned as 0 and 1. The characters of a single BC are called bits. One of the reasons for stosuvannya BC is the simplicity and superficiality of the accumulated information in the presence of a combination of the entire two physical states, for example, in view of the change or the strength of the light stream when reading from an optical code disk.
Іsnuyut different possibilities of coding information.

Double code

In digital technology, the way of presenting data (numbers, slive and others) as a combination of two characters, which can be set as 0 and 1. The characters of a single DC are called bits.

One of the reasons for stosuvannya DK is the simplicity and superficiality of the accumulated information in a way that looks like a combination of all two physical states, for example, when you look at a change or the strength of a magnetic flux in a given middle of a magnetic record.

The most, as if you could be pronounced by a double code, to lay a lot of vicarious rows, that is. in the number of battles in the combination, which turns the number. For example, for the expression of numerical values ​​from 0 to 7, a 3-bit or 3-bit code is enough for the mother:

It can be seen that for numbers greater than 7 with a 3-digit code, there are no code combinations of 0 and 1.

Transitioning from numbers to physical values, we can formulate a stronger hardening in a more general way: the largest number of values ​​m, whether it be a value (temperature, voltage, flow, etc.) = 2n. For example, n=3, as for the examined butt, 8 values ​​are taken, including the leading 0.
Two code is a rich code. Tse means that from the transition from one position (value) to another, the kilka bit can change overnight. For example, the number 3 in the double code = 011. The number 4 in the double code = 100. It is necessary to change your camp to the opposite lane 3 beats at the same time when switching from 3 to 4. The reading of such a code from the code disk would lead to the point that, through the inevitable removal (tolerance) of the code disk, changes in the information on the skin from the tracks would not be seen overnight. Tse, in his line, would cause it to happen that when you go from one number to the next, you will see the wrong information for a short time. So, in case of a visceral transition from the number 3 to 4, it is possible to have a short time to see the number 7 if, for example, the senior bit of the hour of the transition, changing its value of the troch earlier lower later. In order to get away from it, it will become so ranks of a single code, for example, so the ranks of the Gray code.

Gray code

Gray code is what we call a one-bit code, that is. when passing from one number to the next one, only one of the last bits of information is changed. The error in reading the information from the mechanical code disk when moving from one number to the next one will lead to less than three shifts per hour, which will lead to an absolutely incorrect value of the key position when moving from one position to the next
Perevagou Gray-code є yogo zdatnіst mirror image of information. So, inverting the senior bit, you can simply change the rahunka directly by a simple rank and by such a rank pick up the actual (physical) straight wrapping of the axis. Changing directly the rahunka in such a rank can easily be changed by the so-called Complement entrance. The meaning, as you can see, can be growing in such a rank or decreasing with the same physical direct wrapping of the axis.
Oskіlki іnformatsіya expressed in Gray-code may purely coding character is not carrying real numeric information, wine is guilty of far more transformations to the standard binary code. It works for the help of rewriting the code (Gray-Binar decoder), which is easily implemented for the help of the language with logical elements, which “turns on or off” (XOR) as a software and hardware way.

Validity of decimal numbers in the range from 0 to 15 of two code and Gray code

The conversion of the Gray code to the primary binary code can be done by using a simple circuit with inverters and logical elements “on or off” as shown below:

Gray-Excess code

The splendid one-color Gray code is suitable for permissions, as it can be represented by the number of stars in steps 2. In case of need to implement it, it is allowed to use the splendid Gray code, the middle lot is visible and victorious. This rank saves the "one-tailedness" of the code. However, the numerical range does not start from zero, but shifts to a single value. When processing information on the signal that is generated, half of the difference between cob and reduction permissions is visible. So let me, like, for example, 360? for expression, kuta are often implemented in this way. So a 9-bit Gray-code is equal to 512 kroki, urizations from both sides by 76 kroki in 360°.