How to write letters in binary. Binary codes. Horner transformation

Binary code is a form of recording information in the form of ones and zeros. This is positional with a base 2. Today, the binary code (the table presented a little below contains some examples of writing numbers) is used in all digital devices without exception. Its popularity is due to the high reliability and simplicity of this form of recording. Binary arithmetic is very simple, and accordingly, it is easy to implement on the hardware level. components (or as they are also called - logical) are very reliable, since they operate in only two states: a logical unit (there is a current) and a logical zero (no current). Thus, they compare favorably with analog components, the operation of which is based on transient processes.

How is the binary notation made up?

Let's see how such a key is formed. One bit of a binary code can contain only two states: zero and one (0 and 1). When using two digits, it becomes possible to write four values: 00, 01, 10, 11. A three-digit record contains eight states: 000, 001 ... 110, 111. As a result, we get that the length of the binary code depends on the number of digits. This expression can be written using the following formula: N = 2m, where: m is the number of digits, and N is the number of combinations.

Types of binary codes

In microprocessors, such keys are used to record a variety of processed information. The bit depth of a binary code can significantly exceed its built-in memory. In such cases, long numbers take up several storage locations and are processed with multiple commands. In this case, all memory sectors that are allocated for a multibyte binary code are considered as one number.

Depending on the need to provide this or that information, the following types of keys are distinguished:

unsigned;
direct integer character codes;
signed backs;
iconic additional;
Gray code;
Gray-Express code .;
fractional codes.

Let's consider each of them in more detail.

Unsigned binary

Let's see what this type of recording is. In unsigned integer codes, each digit (binary) represents a power of two. In this case, the smallest number that can be written in this form is equal to zero, and the maximum can be represented by the following formula: M = 2 p -1. These two numbers completely define the key range that can be used to express such a binary code. Let's consider the possibilities of the mentioned form of registration. When using this type of unsigned key, consisting of eight bits, the range of possible numbers will be from 0 to 255. A sixteen-bit code will have a range from 0 to 65535. In eight-bit processors, two memory sectors are used to store and write such numbers, which are located in adjacent destinations ... Working with such keys is provided by special commands.

Direct integer signed codes

In this kind of binary keys, the most significant bit is used to record the sign of a number. Zero is positive and one is negative. As a result of the introduction of this bit, the range of encoded numbers is shifted to the negative side. It turns out that an eight-bit signed integer binary key can write numbers in the range from -127 to +127. Sixteen-bit - in the range from -32767 to +32767. In eight-bit microprocessors, two adjacent sectors are used to store such codes.

The disadvantage of this form of notation is that the signed and digital digits of the key must be processed separately. The algorithms of programs working with these codes are very complex. To change and highlight the sign bits, it is necessary to use masking mechanisms for this symbol, which contributes to a sharp increase in the size of the software and a decrease in its performance. In order to eliminate this drawback, a new type of key was introduced - a reverse binary code.

Signed reverse key

This form of notation differs from direct codes only in that a negative number in it is obtained by inverting all the digits of the key. In this case, the digital and sign digits are identical. Due to this, the algorithms for working with this type of code are greatly simplified. However, the reverse key requires a special algorithm to recognize the character of the first digit, to calculate the absolute value of the number. And also the restoration of the sign of the resulting value. Moreover, in reverse and forward codes of numbers, two keys are used to write zero. Although this value has no positive or negative sign.

Signed's complement binary number

This type of record does not have the listed disadvantages of the previous keys. Such codes allow direct summation of both positive and negative numbers. In this case, the analysis of the sign discharge is not carried out. All of this is made possible by the fact that complementary numbers represent a natural ring of symbols, not artificial formations such as forward and backward keys. Moreover, an important factor is that it is extremely easy to perform binary's complement computations. To do this, it is enough to add a unit to the reverse key. When using this type of sign code, consisting of eight digits, the range of possible numbers will be from -128 to +127. A sixteen-bit key will have a range of -32768 to +32767. In eight-bit processors, two adjacent sectors are also used to store such numbers.

Binary additional code interesting by the observed effect, which is called the sign propagation phenomenon. Let's see what this means. This effect is that in the process of converting a one-byte value to a two-byte value, it is enough to assign each bit of the high byte to the values of the sign bits of the low byte. It turns out that the most significant bits can be used to store the signed. In this case, the key value does not change at all.

Gray Code

This form of recording is, in fact, a one-step key. That is, in the process of moving from one value to another, only one bit of information changes. In this case, an error in reading data leads to a transition from one position to another with a slight offset in time. However, obtaining a completely incorrect result for the angular position in such a process is completely ruled out. The advantage of such a code is its ability to mirror information. For example, by inverting the most significant bits, you can simply change the direction of the sample. This is due to the Complement control input. In this case, the output value can be either increasing or decreasing with one physical direction of rotation of the axis. Since the information recorded in the Gray key is exclusively encoded in nature, which does not carry real numerical data, then before further work it is required to first convert it to the usual binary notation. This is done using a special converter - the Gray-Binar decoder. This device It is easily implemented on elementary logic gates both in hardware and software.

Gray Express Code

The standard one-step key Gray is suitable for solutions that are represented as numbers, two. In cases where it is necessary to implement other solutions, only the middle section is cut out and used from this form of recording. As a result, one-step key is preserved. However, in such code, the start of the numeric range is not zero. It is shifted by the specified value. During data processing, half the difference between the initial and reduced resolution is subtracted from the generated pulses.

Fixed-point binary fractional representation

In the process of work, one has to operate not only with whole numbers, but also with fractional ones. Such numbers can be written using forward, backward and complementary codes. The principle of construction of the mentioned keys is the same as for integers. Until now, we have assumed that the binary comma should be to the right of the least significant bit. But this is not the case. It can be located both to the left of the most significant bit (in this case, only fractional numbers can be written as a variable), and in the middle of a variable (mixed values can be written).

Floating point binary code representation

This form is used to write, or vice versa - very small. An example is interstellar distances or the size of atoms and electrons. When calculating such values, one would have to use a binary code with a very large bit depth. However, we do not need to take into account cosmic distance with millimeter precision. Therefore, the fixed-point form is ineffective in this case. Algebraic form is used to display such codes. That is, the number is written as the mantissa multiplied by ten to the power that reflects the desired order of the number. You should know that the mantissa should not be more than one, and zero should not be written after the comma.

Binary calculus is believed to have been invented in the early 18th century by the German mathematician Gottfried Leibniz. However, as scientists recently discovered, long before the Polynesian island, Mangareva used this type of arithmetic. Despite the fact that colonization almost completely destroyed the original numbering systems, scientists have restored complex binary and decimal forms of counting. In addition, Cognitive scholar Nunez argues that binary coding was used in ancient China as early as the 9th century BC. e. Other ancient civilizations, such as the Maya Indians, also used complex combinations of decimal and binary systems to track time intervals and astronomical phenomena.

Since it is the most simple and meets the requirements:

The fewer values exist in the system, the easier it is to manufacture individual elements operating with these values. In particular, two digits of the binary number system can be easily represented by many physical phenomena: there is a current - there is no current, induction magnetic field more than the threshold value or not, etc.
How less quantity states of 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, you will need to enter two threshold values, which will not contribute to noise immunity and reliability of information storage.
Binary arithmetic is pretty straightforward. The tables of addition and multiplication, the basic operations on numbers, are simple.
It is possible to use the apparatus of logic algebra to perform bitwise operations on numbers.

Links

Online calculator for converting numbers from one number system to another

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See what "Binary Code" is in other dictionaries:

2 bit Gray code 00 01 11 10 3 bit Gray code 000 001 011 010 110 111 101 100 4 bit Gray code 0000 0001 0011 0010 0110 0111 0101 0100 1100 1101 1111 1110 1010 1011 1001 1000 Gray code is a number system in which two adjacent values ... ... Wikipedia

Signal Point Code (SPC) of signal system 7 (SS7, OKS 7) is unique (in home network) node address used at the third level of MTP (routing) in telecommunication SS7 networks for identification ... Wikipedia

In mathematics, a number that is not divisible by any square except for 1. For example, 10 is squareless, but 18 is not, since 18 is divisible by 9 = 32. The beginning of a sequence of squareless numbers is: 1, 2, 3, 5, 6, 7, ... ... Wikipedia

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In the narrow sense of the word, at present, the phrase means "Attempt on the security system," and tends more towards the meaning of the next term Cracker attack. This happened due to the distortion of the meaning of the word "hacker". Hacker ... ... Wikipedia

Binary translator is a tool to translate binary code into text for reading or printing. You can translate a binary file to English using two methods; ASCII and Unicode.

Binary number system

The binary decoder system is based on the number 2 (radix). It consists of only two numbers as base-2: 0 and 1.

Although the binary system was used for various purposes in ancient Egypt, China and India, it became the language of electronics and computers. modern world... It is the most effective system for detecting off (0) and on (1) electrical signal states. It is also a binary code-to-text framework that is used by computers to compose data. Even the digital text you are currently reading consists of binary numbers... But you can read this text because we have decoded the binary code of the translation file using the binary code of the word.

What is ASCII?

ASCII is the character encoding standard for electronic communication, short for American Standard Code for Information Interchange. In computers, telecommunications equipment, and other devices, ASCII codes represent text. Although many additional characters are supported, most modern character encoding schemes are based on ASCII.

ASCII is the traditional name for a coding system; The Internet Assigned Numbers Authority (IANA) prefers the updated US-ASCII name, which clarifies that the system was developed in the United States and is based on predominantly used typographic characters. ASCII is one of the highlights of the IEEE.

Binary to ASCII

Originally based on the English alphabet, ASCII encodes 128 specified seven-bit integer characters. 95 coded characters can be printed, including numbers 0 to 9, lowercase letters a to z, uppercase letters A through Z and punctuation characters. In addition, 33 non-printable control codes produced by Teletype machines were included in the original ASCII specification; most of them are now deprecated, although some are still widely used, such as carriage returns, line feeds, and tab codes.

For example, binary 1101001 = hex 69 (i is the ninth letter) = decimal 105 would represent an ASCII lowercase I.

Using ASCII

As mentioned above, using ASCII, you can translate computer text into human text. Simply put, it is a binary to English translator. All computers receive messages in binary, 0 and 1 series. However, just as English and Spanish can use the same alphabet, but for many similar words they have completely different words, computers also have their own language version. ASCII is used as a method that allows all computers to exchange documents and files in the same language.

ASCII is important because computers were given a common language in development.

In 1963, ASCII was first commercially used as a seven-bit teleprinter code for the American Telephone & Telegraph's TWX (Teletype Writer eXchange) network. TWX originally used the previous five-bit ITA2, which was also used by the competing Telex teleprinter system. Bob Bemer introduced features such as escape sequence. According to Boemer, his British colleague Hugh McGregor Ross helped popularize this work - "so much so that the code that became ASCII was first called the Boehmer-Ross Code in Europe." Because of his extensive ASCII work, Boemer has been called the "father of ASCII".

Until December 2007, when UTF-8 was superior, ASCII was the most common character encoding in The world wide web; UTF-8 is backward compatible with ASCII.

UTF-8 (Unicode)

UTF-8 is a character encoding that can be as compact as ASCII, but can also contain any Unicode characters (with some increase in file size). UTF is the Unicode Transformation Format. "8" means to represent a character using 8-bit blocks. The number of blocks a character must represent ranges from 1 to 4. One of the really nice things about UTF-8 is that it is compatible with null-terminated strings. When encoded, no character will have a nul (0) byte.

Unicode and the Universal Character Set (UCS) ISO / IEC 10646 have a much wider range of characters, and their various forms of encoding began to quickly replace ISO / IEC 8859 and ASCII in many situations. Although ASCII is limited to 128 characters, Unicode and UCS support more characters by separating unique concepts of identification (using natural numbers called code points) and encoding (up to the binary formats UTF-8, UTF-16, and UTF-32-bit).) ...

Difference between ASCII and UTF-8

ASCII was included as the first 128 characters in the set Unicode characters(1991) so 7-bit ASCII characters both sets have the same numeric codes. This allows UTF-8 to be compatible with 7-bit ASCII, since a UTF-8 file with only ASCII characters is identical to an ASCII file with the same character sequence. More importantly, forward compatibility is ensured because software which recognizes only 7-bit ASCII characters as special and does not change the bytes with the highest bit set (as is often done to support 8-bit ASCII extensions such as ISO-8859-1) will retain UTF-8 data unmodified.

Binary code translator apps

The most common application for this number system can be seen in computer technology. After all, the backbone of all computer language and programming is the two-digit number system used in digital coding.

This is what constitutes the digital encoding process, taking data and then displaying it with limited bits of information. Limited information consists of zeros and ones in the binary system. The images on your computer screen are examples of this. To encode these images, a binary string is used for each pixel.

If the screen uses 16-bit code, each pixel will be instructed on which color to display based on which bits are 0 and 1. The result is over 65,000 colors represented by 2 ^ 16. In addition to this, you will find the use of binary the number system in the mathematical branch known as Boolean algebra.

The values of logic and truth belong to this area of mathematics. In this application, statements are assigned 0 or 1 depending on whether they are true or false. You can try Binary to Text Conversion, Decimal to Binary, Binary to Decimal Conversion if you are looking for a tool that helps in this application.

The advantage of the binary number system

The binary number system is useful for a number of things. For example, the computer clicks switches to add numbers. You can stimulate the addition of a computer by adding binary numbers to the system. Currently, there are two main reasons for using this computer number system. First, it can ensure the reliability of the safety range. Secondary and most importantly, it helps to minimize the required circuits. This reduces space requirements, energy consumption and costs.

You can encode or translate binary messages written in binary numbers. For instance,

(01101001) (01101100011011110111011001100101) (011110010110111101110101) is the decoded message. When you copy and paste these numbers into our binary translator, you will receive the following text in English:

I love you

It means

(01101001) (01101100011011110111011001100101) (011110010110111101110101) = I love you

tables

binary	hexadecimal

If you are curious about how to read binary numbers, it is important to understand how binary numbers work. The binary system is known as the "base 2" numbering system, which means there are two possible numbers for each digit; one or zero. Large numbers are written by adding additional binary ones or zeros.

Understanding binary numbers

Knowing how to read binaries is not critical to using computers. But it is good to understand the concept in order to better understand how computers store numbers in memory. It also allows you to understand terms like 16-bit, 32-bit, 64-bit and memory dimensions like bytes (8 bits).

"Reading" binary code usually means converting the binary number to the base 10 (decimal) number that people are familiar with. This transformation is easy enough to do in your head once you understand how a binary language works.

Each digit in a binary number has a specific meaning if the digit is not zero. Once you've determined all of these values, you simply add them together to get the 10-digit decimal value of a binary number. To see how this works, take the binary number 11001010.

1. The best way read a binary number - start from the very right digit and move to the left. The strength of this first location is zero, that is, the value for that digit, if it is not zero, is two powers of zero or one. In this case, since the digit is zero, the value for that location will be zero.

2. Then move on to the next digit. If it is one, then calculate two to the power of one. Make a note of this value. In this example, the value is a power of two, equal to two.

3. Continue repeating this process until you reach the left-most digit.

4. To finish, all you have to do is add all these numbers together to get the total decimal value of the binary number: 128 + 64 + 0 + 0 + 8 + 0 + 2 + 0 = 202 .

The note: Another way to see this whole process in the form of an equation is as follows: 1 x 2 7 + 1 x 2 6 + 0 x 2 5 + 0 x 2 4 + 1 x 2 3 + 0 x 2 2 + 1 x 2 1 + 0 x 2 0 = 20.

Binary numbers with signature

The above method works for basic unsigned binary numbers. However, computers need a way to represent negative numbers using binary code as well.

Because of this, computers use signed binary numbers. In this type of system, the left-most digit is known as the sign bit, and the remaining digits are known as amplitude bits.

Reading a signed binary number is almost the same as reading an unsigned one, with one slight difference.

1. Follow the same procedure as described above for an unsigned binary number, but stop as soon as you reach the leftmost bit.

2. Look at the left-most bit to determine the sign. If it is one, then the number is negative. If it is zero, then the number is positive.

3. Now do the same calculations as before, but apply the appropriate sign to the number indicated by the leftmost bit: 64 + 0 + 0 + 8 + 0 + 2 + 0 = -74 .

4. The signed binary method allows computers to represent numbers that are positive or negative. However, it consumes the start bit, which means that large numbers require slightly more memory than unsigned binary numbers.

Binary code decoding is used to translate from machine language to ordinary. Online tools work quickly, although it's easy to do it manually.

Binary or binary code is used to transmit information in digital form. A set of only two characters, for example 1 and 0, allows you to encrypt any information, be it text, numbers or an image.

How to encrypt with binary code

For manual translation of any symbols into a binary code, tables are used in which each symbol is assigned a binary code in the form of zeros and ones. The most common encoding system is ASCII, which uses 8-bit code notation.

The base table contains binary codes for the Latin alphabet, numbers and some symbols.

A binary interpretation of the Cyrillic alphabet and additional characters has been added to the extended table.

To translate from a binary code into text or numbers, it is enough to select the desired codes from the tables. But, naturally, it takes a long time to do such work manually. And mistakes, moreover, are inevitable. The computer copes with decryption much faster. And we don’t even think when typing on the screen that at this moment the text is being translated into a binary code.

Converting a binary number to decimal

To manually convert a number from a binary number system to decimal, you can use a fairly simple algorithm:

Below the binary number, starting with the rightmost digit, write the digit 2 in increasing powers.
Multiply the powers of the number 2 by the corresponding digit of the binary number (1 or 0).
Add the resulting values.

This is how the algorithm looks on paper:

Online services for binary decryption

If you still need to see the decrypted binary code, or, conversely, translate the text into binary form, the easiest way is to use online services designed for this purpose.

Two windows, usual for online translations, allow you to see both versions of the text in normal and binary form almost simultaneously. And decryption is carried out in both directions. Entering text is done by simple copying and pasting.