Why is information called encoded? Coding information in a computer. Audio coding standards

3. Coding of graphic information4

4. Encoding of audio information8

5. Conclusion10

References11

Introduction

A modern computer can process numerical, text, graphic, sound and video information. All these types of information in a computer are presented in binary code, that is, an alphabet of power two is used (only two characters 0 and 1). This is due to the fact that it is convenient to represent information in the form of a sequence of electrical impulses: there is no impulse (0), there is an impulse (1). Such coding is usually called binary, and the logical sequences of zeros and ones themselves are called machine language. Each digit of machine binary code carries an amount of information equal to one bit. This conclusion can be made by considering the numbers of the machine alphabet as equally probable events. When writing a binary digit, you can choose only one of two possible states, which means it carries an amount of information equal to 1 bit. Therefore, two digits carry 2 bits of information, four digits carry 4 bits, etc. To determine the amount of information in bits, it is enough to determine the number of digits in the binary machine code.

Encoding text information

Currently, most users use a computer to process text information, which consists of symbols: letters, numbers, punctuation marks, etc.

Traditionally, in order to encode one character, an amount of information equal to 1 byte is used, i.e. I = 1 byte = 8 bits. Using a formula that connects the number of possible events K and the amount of information I, you can calculate how many different symbols can be encoded (assuming that symbols are possible events): K = 2I = 28 = 256, i.e. to represent text information, you can use an alphabet with a capacity of 256 characters.

The essence of encoding is that each character is assigned a binary code from 00000000 to 11111111 or a corresponding decimal code from 0 to 255.

Currently, five different code tables are used to encode Russian letters (KOI - 8, CP1251, CP866, Mac, ISO), and texts encoded using one table will not be displayed correctly in another encoding. This can be visually represented as a fragment of a combined character encoding table. Different symbols are assigned to the same binary code.

However, in most cases, the user takes care of transcoding text documents, and special programs are converters that are built into applications. Since 1997, the latest versions of Microsoft Windows & Office support the new Unicode encoding, which allocates 2 bytes for each character, and therefore, you can encode not 256 characters, but 65536 different characters.

To determine the numeric code of a character, you can either use a code table, or, working in the text editor Word 6.0 / 95. To do this, select “Insert” - “Symbol” from the menu, after which the Symbol dialog panel appears on the screen. A character table for the selected font appears in the dialog box. The characters in this table are arranged line by line, sequentially from left to right, starting with the Space symbol (upper left corner) and ending with the letter “I” (lower right corner).

To determine the numeric code of a character in Windows encoding (CP1251), you need to use the mouse or cursor keys to select the desired character, then click on the Key button. After this, the Settings dialog box appears on the screen, which contains the decimal numeric code of the selected character in the lower left corner.

Encoding graphic information

Graphic information can be presented in two forms: analog or discrete. A painting whose color changes continuously is an example of an analog representation, while an image printed using an inkjet printer and consisting of individual dots of different colors is a discrete representation. By splitting a graphic image (sampling), graphic information is converted from analogue form to discrete form. In this case, coding is performed - assigning a specific value to each element in the form of a code. When encoding an image, it is spatially discretized. It can be compared to constructing an image from a large number of small colored fragments (mosaic method). The entire image is divided into separate points, each element is assigned a color code.

In this case, the quality of encoding will depend on the following parameters: dot size and the number of colors used. The smaller the dot size, which means the image is made up of a larger number of dots, the higher the encoding quality. The more colors are used (i.e., an image point can take on more possible states), the more information each point carries, and, therefore, the encoding quality increases. Creation and storage of graphic objects is possible in several types - in the form of a vector, fractal or raster image. A separate subject is 3D (three-dimensional) graphics, which combines vector and raster methods of image formation. She studies methods and techniques for constructing three-dimensional models of objects in virtual space. Each type uses its own method of encoding graphic information.

Raster image. Using a magnifying glass, you can see that a black and white graphic image, for example from a newspaper, consists of tiny dots that make up a certain pattern - a raster. In France in the 19th century, a new direction in painting arose - pointillism. His technique was to apply a drawing on the canvas with a brush in the form of multi-colored dots. This method has also long been used in printing for encoding graphic information. The accuracy of the drawing depends on the number of dots and their size. After dividing the drawing into dots, starting from the left corner, moving along the lines from left to right, you can code the color of each dot. In what follows, we will call one such point a pixel (the origin of this word is related to the English abbreviation “picture element”). The volume of a raster image is determined by multiplying the number of pixels (by the information volume of one point, which depends on the number of possible colors. The image quality is determined by the resolution of the monitor. The higher it is, that is, the greater the number of raster lines and dots per line, the higher the image quality. In modern PCs generally use the following screen resolutions: 640 by 480, 800 by 600, 1024 by 768 and 1280 by 1024. Since the brightness of each point and its linear coordinates can be expressed using integers, we can say that this encoding method allows you to use binary code to process graphics data.

If we talk about black and white illustrations, then if you do not use halftones, the pixel will take one of two states: glowing (white) and not glowing (black). And since information about the color of a pixel is called the pixel code, one bit of memory is enough to encode it: 0 - black, 1 - white. If illustrations are considered in the form of a combination of dots with 256 shades of gray (and these are the ones that are currently generally accepted), then an eight-bit binary number is enough to encode the brightness of any dot. Color is extremely important in computer graphics. It acts as a means of enhancing the visual impression and increasing the information richness of the image. How is the human brain's sense of color formed? This occurs as a result of analyzing the light flux entering the retina from reflecting or emitting objects.

Color models. If we talk about coding color graphic images, then we need to consider the principle of decomposition of an arbitrary color into its main components. Several coding systems are used: HSB, RGB and CMYK. The first color model is simple and intuitive, i.e. convenient for humans, the second is most convenient for computers, and the last CMYK model is for printing houses. The use of these color models is due to the fact that the luminous flux can be formed by radiation that is a combination of “pure” spectral colors: red, green, blue or their derivatives. There are additive color reproduction (typical for emitting objects) and subtractive color reproduction (typical for reflective objects). An example of an object of the first type is a cathode ray tube of a monitor, and an example of the second type is a printing print.

1) The HSB model is characterized by three components: color hue (Hue), color saturation (Saturation) and color brightness (Brightness).

2) The principle of the RGB method is as follows: it is known that any color can be represented as a combination of three colors: red (Red, R), green (Green, G), blue (Blue, B). Other colors and their shades are obtained due to the presence or absence of these components.

3) The principle of the CMYK method. This color model is used when preparing publications for printing. Each of the primary colors is associated with an additional color (complementing the main one to white). An additional color is obtained by summing a pair of other primary colors.

There are several modes for presenting color graphics: full color (True Color); High Color; index.

In full-color mode, 256 values ​​(eight binary bits) are used to encode the brightness of each component, that is, 8 * 3 = 24 bits must be spent on encoding the color of one pixel (in the RGB system). This allows 16.5 million colors to be uniquely identified. This is pretty close to the sensitivity of the human eye. When encoding using the CMYK system, to represent color graphics you need to have 8*4=32 binary bits. High Color mode is encoding using 16-bit binary numbers, that is, the number of binary digits is reduced when encoding each point. But this significantly reduces the range of encoded colors. With index color coding, only 256 color shades can be transmitted. Each color is encoded using eight bits of data. But since 256 values ​​do not convey the entire range of colors accessible to the human eye, it is understood that a palette (lookup table) is attached to the graphic data, without which the reproduction will be inadequate: the sea may turn out to be red, and the leaves may turn out to be blue. The raster point code itself in this case does not mean the color itself, but only its number (index) in the palette. Hence the name of the mode - index.

The correspondence between the number of displayed colors (K) and the number of bits for encoding them (a) can be found by the formula: K = 2 a.

The binary code of the image displayed on the screen is stored in video memory. Video memory is an electronic volatile storage device. The size of video memory depends on the resolution of the display and the number of colors. But its minimum volume is determined so that one frame (one page) of the image fits, i.e. as a result of the product of resolution and pixel code size.

Vmin = M * N * a.

Binary code of the eight-color palette.

Color Components

Red 1 0 0

Green 0 1 0

Blue 0 0 1

Blue 0 1 1

Purple 1 0 1

Yellow 1 1 0

White 1 1 1

Black 0 0 0

The sixteen-color palette allows you to increase the number of colors used. Here we will use a 4-bit pixel encoding: 3 bits of primary colors + 1 bit of intensity. The latter controls the brightness of three basic colors simultaneously (the intensity of three electron beams). By separately controlling the intensity of the primary colors, the number of colors produced increases. So, to obtain a palette with a color depth of 24 bits, 8 bits are allocated for each color, that is, 256 intensity levels are possible (K = 28).

A vector image is a graphic object consisting of elementary segments and arcs. The basic element of imagery is line. Like any object, it has properties: shape (straight, curved), thickness, color, style (dotted, solid). Closed lines have the property of being filled (either with other objects or with the selected color). All other vector graphics objects are made up of lines. Since the line is described mathematically as a single object, the amount of data for displaying the object using vector graphics is much less than in raster graphics. Information about a vector image is encoded as ordinary alphanumeric and processed by special programs.

Software tools for creating and processing vector graphics include the following GR: CorelDraw, Adobe Illustrator, as well as vectorizers (tracers) - specialized packages for converting raster images into vector ones.

Fractal graphics are based on mathematical calculations, just like vector graphics. But unlike vector, its basic element is the mathematical formula itself. This leads to the fact that no objects are stored in the computer's memory and the image is constructed only using equations. Using this method, you can build the simplest regular structures, as well as complex illustrations that imitate landscapes.

Encoding of audio information

Computers are now widely used in various fields. The processing of sound information and music was no exception. Until 1983, all recorded music was released on vinyl records and compact cassettes. Currently, CDs are widely used. If you have a computer with a studio sound card installed, with a MIDI keyboard and microphone connected to it, then you can work with specialized music software. Conventionally, it can be divided into several types: 1) all kinds of utilities and drivers designed to work with specific sound cards and external devices; 2) audio editors, which are designed to work with sound files, allow you to perform any operations with them - from breaking them into parts to processing them with effects; 3) software synthesizers, which appeared relatively recently and work correctly only on powerful computers. They allow you to experiment with creating different sounds; and others.

The first group includes all operating system utilities. For example, win 95 and 98 have their own mixer programs and utilities for playing/recording sound, playing CDs and standard MIDI files. After installing the sound card, you can use these programs to check its functionality. For example, the Phonograph program is designed to work with wave files (sound recording files in Windows format). These files have the extension .WAV. This program provides the ability to play, record and edit sound recordings using techniques similar to those used with a tape recorder. It is advisable to connect the microphone to the computer to work with the Phonograph. If you need to make a sound recording, then you need to decide on the sound quality, since the duration of the sound recording depends on it. The higher the recording quality, the shorter the possible sound duration. With average recording quality, you can record speech satisfactorily, creating files up to 60 seconds long. Approximately 6 seconds will be the recording duration, which has the quality of a music CD.

In order to record sound on any medium, it must be converted into an electrical signal. This is done using a microphone. The simplest microphones have a membrane that vibrates under the influence of sound waves. A coil is attached to the membrane, moving synchronously with the membrane in a magnetic field. An alternating electric current occurs in the coil. Voltage changes accurately reflect sound waves. The alternating electrical current that appears at the output of the microphone is called an analog signal. When applied to an electrical signal, “analog” means that the signal is continuous in time and amplitude. It accurately reflects the shape of the sound wave as it travels through the air.

Audio information can be represented in discrete or analog form. Their difference is that with a discrete representation of information, a physical quantity changes abruptly (“ladder”), taking on a finite set of values. If information is presented in analog form, then a physical quantity can take on an infinite number of values ​​that are continuously changing.

Let's briefly look at the processes of converting sound from analog to digital and vice versa. Having a rough idea of ​​what's going on in your sound card can help you avoid some mistakes when working with audio. Sound waves are converted into an analog alternating electrical signal using a microphone. It passes through the audio path and enters an analog-to-digital converter (ADC), a device that converts the signal into digital form. In a simplified form, the operating principle of an ADC is as follows: it measures the signal amplitude at certain intervals and transmits further, via a digital path, a sequence of numbers carrying information about changes in amplitude. Digital audio is output using a digital-to-analog converter (DAC), which, based on incoming digital data, generates an electrical signal of the required amplitude at appropriate times.

If you graph the same sound at 1 kHz (the note up to the seventh octave of a piano roughly corresponds to this frequency), but sampled at different frequencies (the bottom of the sine wave is not shown in all graphs), then the differences will be visible. One division on the horizontal axis, which shows time, corresponds to 10 samples. The scale is taken the same (see Appendix Figure 1.13). You can see that at 11 kHz there are approximately five sound wave oscillations for every 50 samples, meaning one sine wave period is represented with just 10 values. This is a rather inaccurate rendering. At the same time, if we consider the digitization frequency of 44 kHz, then for each period of the sinusoid there are already almost 50 samples. This allows you to get a good quality signal.

The bit depth indicates the accuracy with which changes in the amplitude of the analog signal occur. The accuracy with which the signal amplitude value at each instant of time is transmitted during digitization determines the quality of the signal after digital-to-analog conversion. The reliability of waveform reconstruction depends on the bit depth.

To encode the amplitude value, the principle of binary coding is used. The sound signal must be presented as a sequence of electrical pulses (binary zeros and ones). Typically, 8, 16-bit, or 20-bit representations of amplitude values ​​are used. When binary coding a continuous audio signal, it is replaced by a sequence of discrete signal levels. The quality of encoding depends on the sampling frequency (the number of signal level measurements per unit time). As the sampling frequency increases, the accuracy of the binary representation of information increases. At a frequency of 8 kHz (number of samples per second 8000), the quality of the sampled audio signal corresponds to the quality of a radio broadcast, and at a frequency of 48 kHz (number of samples per second 48000) - the sound quality of an audio CD.

If you use 8-bit encoding, you can achieve an analog signal amplitude accuracy of up to 1/256 of the dynamic range of a digital device (28 = 256).

If you use 16-bit encoding to represent the amplitude values ​​of the audio signal, the measurement accuracy will increase by 256 times.

Modern converters typically use 20-bit signal encoding, which allows for high-quality audio digitization.

Conclusion

A code is a set of conventions (or signals) for recording (or communicating) some predefined concepts.

Information coding is the process of forming a specific representation of information. In a narrower sense, the term “coding” is often understood as a transition from one form of information representation to another, more convenient for storage, transmission or processing.

Typically, each image is represented by a separate character when encoding. A sign is an element of a finite set of elements distinct from each other. A sign together with its meaning is called a symbol. The code length is the number of characters used for encoding.

The code can be of constant or non-constant length. To represent information in computer memory, a binary coding method is used.

An elementary computer memory cell is 8 bits long. Each byte has its own number. The largest sequence of bits that a computer can process as a single unit is called a machine word. The length of a machine word depends on the processor bit depth and can be 16, 32 bits, etc. Another way to represent integers is with two's complement code. The range of value values ​​depends on the number of memory bits allocated for their storage. The complementary code of a positive number is the same as its direct code.

Bibliography

1.Computer science and information technology. Ed. Yu.D. Romanova, 3rd edition, M.: EKSMO, 2008

2. Kostrov B.V. Fundamentals of digital transmission and coding of information. - TechBook, 2007, 192 pages.

3. Makarova N.V. “Informatics”: Textbook. - M.: Finance and Statistics, 2005 - 768 p.

4. Stepanenko O. S. Personal computer. Self-instruction manual Dialectics. 2005, 28 pp.

Encoding text information in a computer is sometimes an essential condition for the correct operation of a device or the display of a particular fragment. How this process occurs during the operation of a computer with text and visual information, sound - we will analyze all this in this article.

Introduction

An electronic computer (which we call a computer in everyday life) perceives text in a very specific way. For her, encoding text information is very important, since she perceives each text fragment as a group of symbols isolated from each other.

What are the symbols?

Not only Russian, English and other letters act as symbols for a computer, but also punctuation marks and other characters. Even the space we use to separate words when typing on a computer is perceived by the device as a symbol. In some ways it is very reminiscent of higher mathematics, because there, according to many professors, zero has a double meaning: it is both a number and at the same time does not mean anything. Even for philosophers, the question of white space can be a pressing issue. A joke, of course, but, as they say, there is some truth in every joke.

What kind of information is there?

So, to perceive information, the computer needs to start processing processes. What kind of information is there anyway? The topic of this article is the encoding of textual information. We will pay special attention to this task, but we will also deal with other micro-topics.

Information can be text, numeric, audio, graphic. The computer must run processes that encode textual information in order to display on the screen what we, for example, type on a keyboard. We will see symbols and letters, this is understandable. What does the machine see? She perceives absolutely all information - and now we are not just talking about text - as a certain sequence of zeros and ones. They form the basis of the so-called binary code. Accordingly, the process that converts the information received by the device into something it can understand is called “binary encoding of text information.”

Brief principle of operation of binary code

Why is it that binary coding of information is most widespread in electronic machines? The text base, which is encoded using zeros and ones, can be absolutely any sequence of symbols and signs. However, this is not the only advantage that binary text encoding of information has. The thing is that the principle on which this coding method is based is very simple, but at the same time quite functional. When there is an electrical impulse, it is marked (conditionally, of course) with a unit. There is no impulse - marked with zero. That is, text coding of information is based on the principle of constructing a sequence of electrical impulses. A logical sequence made up of binary code symbols is called machine language. At the same time, encoding and processing text information using binary code allows operations to be carried out in a fairly short period of time.

Bits and bytes

A number perceived by a machine contains a certain amount of information. It is equal to one bit. This applies to every one and every zero that make up one or another sequence of encrypted information.

Accordingly, the amount of information in any case can be determined simply by knowing the number of characters in the binary code sequence. They will be numerically equal to each other. 2 digits in the code carry 2 bits of information, 10 digits - 10 bits, and so on. The principle of determining the information volume that lies in a particular fragment of binary code is quite simple, as you can see.

Coding text information in a computer

Right now you are reading an article that consists of a sequence, as we believe, of letters of the Russian alphabet. And the computer, as mentioned earlier, perceives all information (and in this case too) as a sequence not of letters, but of zeros and ones, indicating the absence and presence of an electrical impulse.

The thing is that you can encode one character that we see on the screen using a conventional unit of measurement called a byte. As written above, binary code has a so-called information load. Let us recall that numerically it is equal to the total number of zeros and ones in the selected code fragment. So, 8 bits make 1 byte. Combinations of signals can be very different, as can be easily seen by drawing a rectangle on paper consisting of 8 cells of equal size.

It turns out that text information can be encoded using an alphabet with a capacity of 256 characters. What's the point? The meaning lies in the fact that each character will have its own binary code. Combinations “tied” to certain characters start from 00000000 and end with 11111111. If you move from the binary to the decimal number system, then you can encode information in such a system from 0 to 255.

Do not forget that now there are various tables that use the encoding of letters of the Russian alphabet. These are, for example, ISO and KOI-8, Mac and CP in two variations: 1251 and 866. It is easy to make sure that text encoded in one of these tables will not be displayed correctly in an encoding other than this one. This is due to the fact that in different tables different symbols correspond to the same binary code.

This was a problem at first. However, nowadays programs already have built-in special algorithms that convert text, bringing it to the correct form. 1997 was marked by the creation of an encoding called Unicode. In it, each character has 2 bytes at its disposal. This allows you to encode text with a much larger number of characters. 256 and 65536: is there a difference?

Graphics coding

Coding text and graphic information has some similarities. As you know, a computer peripheral device called a “monitor” is used to display graphic information. Graphics now (we are talking about computer graphics now) are widely used in a variety of fields. Fortunately, the hardware capabilities of personal computers make it possible to solve quite complex graphics problems.

Processing video information has become possible in recent years. But the text is much “lighter” than the graphics, which, in principle, is understandable. Because of this, the final size of graphics files must be increased. Such problems can be overcome by knowing the essence in which graphical information is presented.

Let's first figure out what groups this type of information is divided into. Firstly, it is raster. Secondly, vector.

Raster images are quite similar to checkered paper. Each cell on such paper is painted over with one color or another. This principle is somewhat reminiscent of a mosaic. That is, it turns out that in raster graphics the image is divided into separate elementary parts. They are called pixels. Translated into Russian, pixels mean “dots”. It is logical that the pixels are ordered relative to the lines. The graphic grid consists of just a certain number of pixels. It is also called a raster. Considering these two definitions, we can say that a raster image is nothing more than a collection of pixels that are displayed on a rectangular grid.

Monitor raster and pixel size affect image quality. The larger the monitor's raster, the higher it will be. Raster sizes are screen resolution, which every user has probably heard of. One of the most important characteristics that computer screens have is resolution, not just resolution. It shows how many pixels there are per unit of length. Typically, monitor resolution is measured in pixels per inch. The more pixels per unit length, the higher the quality will be, since the “grain” is reduced.

Audio stream processing

Coding of text and audio information, like other types of coding, has some features. We will now talk about the last process: encoding audio information.

The representation of an audio stream (as well as an individual sound) can be produced using two methods.

Analogue form of audio information representation

In this case, the quantity can take on a truly huge number of different values. Moreover, these same values ​​do not remain constant: they change very quickly, and this process is continuous.

Discrete form of representation of audio information

If we talk about the discrete method, then in this case the quantity can take only a limited number of values. In this case, the change occurs spasmodically. You can discretely encode not only audio, but also graphic information. As for the analog form, by the way.

Analog audio information is stored on vinyl records, for example. But the CD is already a discrete way of presenting audio information.

At the very beginning, we talked about the fact that the computer perceives all information in machine language. To do this, information is encoded in the form of a sequence of electrical impulses - zeros and ones. Encoding audio information is no exception to this rule. To process sound on a computer, you first need to turn it into that very sequence. Only after this can operations be performed on a stream or a single sound.

When the encoding process occurs, the stream is subject to time sampling. The sound wave is continuous; it develops over small periods of time. The amplitude value is set for each specific interval separately.

Conclusion

So, what did we find out during this article? Firstly, absolutely all information that is displayed on a computer monitor is encoded before appearing there. Secondly, this coding involves translating information into machine language. Thirdly, machine language is nothing more than a sequence of electrical impulses - zeros and ones. Fourthly, there are separate tables for encoding different characters. And, fifthly, graphic and sound information can be presented in analog and discrete form. Here, perhaps, are the main points that we have discussed. One of the disciplines that studies this area is computer science. Coding of textual information and its basics are explained at school, since there is nothing complicated about it.

General concepts

Definition 1

Coding- this is the transformation of information from one form of representation to another, the most convenient for its storage, transmission or processing.

Definition 2

Code called the rule for displaying one set of characters in another.

Definition 3

Binary code is a way of representing information using two symbols - $0$ and $1$.

Definition 4

Code length– the number of characters used to represent the encoded information.

Definition 5

Bit is one binary digit $0$ or $1$. One bit can encode two values: $1$ or $0$. With two bits you can encode four values: $00$, $01$, $10$, $11$. Three bits encode $8$ different values. Adding one bit doubles the number of values ​​that can be encoded.

Picture 1.

Types of information encoding

There are the following types of information coding:

• color coding;
• coding of numerical information;
• coding of audio information;
• video encoding.

Encoding text information

Any text consists of a sequence of characters. Symbols can be letters, numbers, punctuation marks, mathematical symbols, round and square brackets, etc.

Text information, like any other information, is stored in computer memory in binary form. To do this, each is assigned a certain non-negative number, called character code, and this number is written into the computer memory in binary form. The specific relationship between symbols and their codes is called coding system. Personal computers typically use the ASCII (American Standard Code for Informational Interchange) encoding system.

Note 1

Software developers have created their own $8$-bit text encoding standards. Due to the additional bit, the encoding range in them was expanded to $256$ characters. To avoid confusion, the first $128$ characters in such encodings, as a rule, correspond to the ASCII standard. The remaining $128$ implements regional language features.

Note 2

Eight-bit encodings common in our country are KOI8, UTF8, Windows-1251 and some others.

Color coding

To store a photograph in binary code, it is first virtually divided into many small colored dots called pixels(something like a mosaic). Once broken down into dots, the color of each pixel is encoded into a binary code and stored on a storage device.

Example 1

If an image is said to be, for example, $512 x 512 pixels in size, this means that it is a matrix formed of $262,144 pixels (the number of vertical pixels multiplied by the number of horizontal pixels).

Example 2

The device that “breaks” images into pixels is any modern camera (including a webcam, phone camera) or scanner. And if the camera’s characteristics say, for example, “$10$ Mega Pixels,” then the number of pixels into which this camera divides the image for recording in binary code is 10 million. The more pixels the image is divided into, the more realistic the photo looks in decoded form (on the monitor or after printing).

However, the quality of encoding photographs into binary code depends not only on the number of pixels, but also on their color diversity. Algorithms for recording color in binary code there are several. The most common one is RGB. This abbreviation is the first letters of the names of three primary colors: red - EnglishRed, green – English Green, blue – English Blue. By mixing these three colors in different proportions, you can get any other color or shade.

This is what the RGB algorithm is based on. Each pixel is written in binary code by indicating the amount of red, green and blue involved in its formation.

The more bits allocated to encode a pixel, the more options for mixing these three channels can be used and the greater the color saturation of the image.

Definition 6

The color variety of pixels that make up an image is called color depth.

Encoding graphic information

The technique described above for forming images from small dots is the most common and is called raster . But in addition to raster graphics, computers also use the so-called Vector graphics .

Vector images are created only using a computer and are formed not from pixels, but from graphic primitives (lines, polygons, circles, etc.).

Vector graphics are drawing graphics. It is very convenient for computer “drawing” and is widely used by designers in the graphic design of printed materials, including the creation of huge advertising posters, as well as in other similar situations. A vector image in binary code is written as a collection of primitives indicating their sizes, fill color, location on the canvas and some other properties.

Example 3

To record a vector image of a circle on a storage device, the computer only needs to encode in binary code the type of object (circle), the coordinates of its center on the canvas, the length of the radius, the thickness and color of the line, and the fill color.

In a raster system, the color of each pixel would have to be encoded. And if the image size is large, it would require significantly more storage space to store it.

However, the vector encoding method does not allow realistic photos to be written in binary code. Therefore, all cameras work only on the principle of raster graphics. The average user rarely has to deal with vector graphics in everyday life.

Encoding numerical information

When encoding numbers, the purpose for which the number was entered into the system is taken into account: for arithmetic calculations or simply for output. All data encoded in the binary system is encrypted using ones and zeros. These symbols are also called bits. This encoding method is the most popular, because it is the easiest to organize technologically: the presence of a signal is $1$, the absence is $0$. Binary encryption has only one drawback - the length of the symbol combinations. But from a technical point of view, it is easier to operate a bunch of simple, similar components than a small number of more complex ones.

Note 3

Integers are encoded simply by converting numbers from one number system to another. To encode real numbers, $80$-bit encoding is used. In this case, the number is converted to standard form.

Encoding of audio information

Definition 7

Any sound heard by a person is an air vibration, which is characterized by two main indicators: frequency and amplitude. Oscillation amplitude- this is the degree of deviation of the air state from the initial one with each oscillation. It is perceived by us as the volume of sound. Oscillation frequency is the number of deviations of air states from the initial one per unit of time. It is perceived as the pitch of the sound.

Example 4

Thus, a quiet mosquito squeak is a sound with a high frequency, but with a small amplitude. The sound of a thunderstorm, on the contrary, has a large amplitude but a low frequency.

The way a computer works with sound can be described in general terms as follows. The microphone converts air vibrations into electrical vibrations with similar characteristics. A computer's sound card converts electrical vibrations into binary code, which is stored on a storage device. When playing such a recording, the reverse process (decoding) occurs - the binary code is converted into electrical vibrations that enter the audio system or headphones. Speakers or headphones have the opposite effect of a microphone. They convert electrical vibrations into air vibrations.

The principle of dividing a sound wave into small sections is the basis of binary audio coding. The computer's audio card divides the sound into very small time segments and encodes the intensity of each of them into a binary code. This splitting of sound into parts is called sampling. The higher the sampling frequency, the more accurately the geometry of the sound wave is recorded and the better the quality of the recording.

Definition 8

The quality of the recording also depends heavily on the number of bits used by the computer to encode each section of audio resulting from sampling. The number of bits used to encode each section of audio resulting from sampling is called depth of sound.

Video encoding

Video recording consists of two components: sound And graphic .

Encoding the audio track of a video file into binary code is carried out using the same algorithms as encoding regular audio data. The principles of video encoding are similar to raster graphics encoding (discussed above), although they have some features. As you know, video recording is a sequence of rapidly changing static images (frames). One second of video can consist of $25$ or more pictures. At the same time, each next frame differs only slightly from the previous one.

Given this feature, video encoding algorithms, as a rule, provide for recording only the first (base) frame. Each subsequent frame is formed by recording its differences from the previous one.

Vector and fractal images.

Vector image is a graphic object consisting of elementary segments and arcs. The basic element of imagery is line. Like any object, it has properties: shape (straight, curved), thickness, color, style (dotted, solid). Closed lines have the property of being filled (either with other objects or with the selected color). All other vector graphics objects are made up of lines. Since the line is described mathematically as a single object, the amount of data for displaying the object using vector graphics is much less than in raster graphics. Information about a vector image is encoded as ordinary alphanumeric and processed by special programs.

Software tools for creating and processing vector graphics include the following GR: CorelDraw, Adobe Illustrator, as well as vectorizers (tracers) - specialized packages for converting raster images into vector ones.

Fractal graphics is based on mathematical calculations, like vector. But unlike vector, its basic element is the mathematical formula itself. This leads to the fact that no objects are stored in the computer's memory and the image is constructed only using equations. Using this method, you can build the simplest regular structures, as well as complex illustrations that imitate landscapes.

Tasks.

It is known that the video memory of a computer has a capacity of 512 KB. Screen resolution is 640 by 200. How many screen pages can be simultaneously placed in video memory with a palette
a) from 8 colors;
b) 16 colors;
c) 256 colors?

How many bits are required to encode information about 130 shades? It is not difficult to calculate that 8 (that is, 1 byte), since with 7 bits you can store the hue number from 0 to 127, and 8 bits store from 0 to 255. It is easy to see that this encoding method is not optimal: 130 is noticeably less than 255. Think about it , how to condense information about a drawing when writing it to a file, if it is known that
a) the drawing simultaneously contains only 16 color shades out of 138 possible;
b) the drawing contains all 130 shades at the same time, but the number of dots painted with different shades varies greatly.

A) it is obvious that 4 bits (half a byte) are enough to store information about 16 shades. However, since these 16 shades are selected from 130, they may have numbers that do not fit into 4 bits. Therefore, we will use the palette method. Let’s assign the 16 shades used in our drawing their “local” numbers from 1 to 15 and encode the entire drawing at the rate of 2 points per byte. And then we will add to this information (at the end of the file containing it) a correspondence table consisting of 16 pairs of bytes with shade numbers: 1 byte is our “local” number in this picture, the second is the real number of this shade. (when instead of the latter, encoded information about the hue itself is used, for example, information about the brightness of the glow of the “electronic guns” Red, Green, Blue of the cathode ray tube, then such a table will be a color palette). If the drawing is large enough, the gain in the resulting file size will be significant;
b) let's try to implement the simplest algorithm for archiving information about a drawing. Let's assign codes 128 - 130 to the three shades with which the minimum number of points are painted, and codes 1 -127 to the remaining shades. We will write into a file (which in this case is not a sequence of bytes, but a continuous bit stream) seven-bit codes for shades with numbers from 1 to 127. For the remaining three shades in the bit stream we will write a sign number - seven-bit 0 - and immediately followed by a two-bit “local” number, and at the end of the file we will add a table of correspondence between “local” and real numbers. Since shades with codes 128 - 130 are rare, there will be few seven-bit zeros.

Note that posing questions in this problem does not exclude other solutions, without reference to the color composition of the image - archiving:
a) based on identifying a sequence of points painted with the same shades and replacing each of these sequences with a pair of numbers (color), (quantity) (this principle underlies the PCX graphic format);
b) by comparing pixel lines (recording the shade numbers of the points of the first page as a whole, and for subsequent lines recording the shade numbers of only those points whose shades differ from the shades of points located in the same position in the previous line - this is the basis of the GIF format);
c) using a fractal image packaging algorithm (YPEG format). (IO 6,1999)

The world is filled with a wide variety of sounds: the ticking of clocks and the hum of engines, the howling of the wind and the rustling of leaves, the singing of birds and the voices of people. People began to guess about how sounds are born and what they represent a very long time ago. Even the ancient Greek philosopher and scientist - encyclopedist Aristotle, based on observations, explained the nature of sound, believing that a sounding body creates alternating compression and rarefaction of air. Thus, an oscillating string either discharges or compresses the air, and due to the elasticity of the air, these alternating effects are transmitted further into space - from layer to layer, elastic waves arise. When they reach our ear, they impact the eardrums and cause the sensation of sound.

By ear, a person perceives elastic waves having a frequency somewhere in the range from 16 Hz to 20 kHz (1 Hz - 1 vibration per second). In accordance with this, elastic waves in any medium, the frequencies of which lie within the specified limits, are called sound waves or simply sound. In the study of sound, such concepts as tone And timbre sound. Any real sound, be it the playing of musical instruments or a human voice, is a peculiar mixture of many harmonic vibrations with a certain set of frequencies.

The vibration that has the lowest frequency is called main tone, other - overtones.

Timbre- a different number of overtones inherent in a particular sound, which gives it a special coloring. The difference between one timbre and another is determined not only by the number, but also by the intensity of the overtones accompanying the sound of the fundamental tone. It is by timbre that we can easily distinguish the sounds of a piano and a violin, a guitar and a flute, and recognize the voice of a familiar person.

Musical sound can be characterized by three qualities: timbre, i.e. the color of the sound, which depends on the shape of the vibrations, pitch, determined by the number of vibrations per second (frequency), and volume, depending on the intensity of the vibrations.

Computers are now widely used in various fields. The processing of sound information and music was no exception. Until 1983, all recorded music was released on vinyl records and compact cassettes. Currently, CDs are widely used. If you have a computer with a studio sound card installed, with a MIDI keyboard and microphone connected to it, then you can work with specialized music software.

Conventionally, it can be divided into several types:

1) all kinds of utilities and drivers designed to work with specific sound cards and external devices;
2) audio editors, which are designed to work with sound files, allow you to perform any operations with them - from breaking them into parts to processing them with effects;
3) software synthesizers, which appeared relatively recently and work correctly only on powerful computers. They allow you to experiment with creating different sounds;
and others.

The first group includes all operating system utilities. For example, win 95 and 98 have their own mixer programs and utilities for playing/recording sound, playing CDs and standard MIDI files. After installing the sound card, you can use these programs to check its functionality. For example, the Phonograph program is designed to work with wave files (sound recording files in Windows format). These files have the extension .WAV. This program provides the ability to play, record and edit sound recordings using techniques similar to those used with a tape recorder. It is advisable to connect the microphone to the computer to work with the Phonograph. If you need to make a sound recording, then you need to decide on the sound quality, since the duration of the sound recording depends on it. The higher the recording quality, the shorter the possible sound duration. With average recording quality, you can record speech satisfactorily, creating files up to 60 seconds long. Approximately 6 seconds will be the recording duration, which has the quality of a music CD.

How does audio encoding work? Since childhood, we have been exposed to recordings of music on different media: records, cassettes, CDs, etc. Currently, there are two main ways to record sound: analog and digital. But in order to record sound on any medium, it must be converted into an electrical signal.

This is done using a microphone. The simplest microphones have a membrane that vibrates under the influence of sound waves. A coil is attached to the membrane, moving synchronously with the membrane in a magnetic field. An alternating electric current occurs in the coil. Voltage changes accurately reflect sound waves.

The alternating electric current that appears at the output of the microphone is called analog signal. When applied to an electrical signal, “analog” means that the signal is continuous in time and amplitude. It accurately reflects the shape of the sound wave as it travels through the air.

Audio information can be represented in discrete or analog form. Their difference is that with a discrete representation of information, a physical quantity changes abruptly (“ladder”), taking on a finite set of values. If information is presented in analog form, then a physical quantity can take on an infinite number of values ​​that are continuously changing.

A vinyl record is an example of analog storage of sound information, since the sound track changes its shape continuously. But analog recordings on magnetic tape have a big drawback - the aging of the media. Over the course of a year, a phonogram that had a normal level of high frequencies may lose them. Vinyl records lose quality several times when played. Therefore, preference is given to digital recording.

In the early 80s, compact discs appeared. They are an example of discrete storage of audio information, since the audio track of a CD contains areas of varying reflectivity. In theory, these digital discs can last forever if they are not scratched, i.e. their advantages are durability and resistance to mechanical aging. Another advantage is that there is no loss of sound quality when dubbing digitally.

On multimedia sound cards you can find an analog microphone preamp and mixer.

Digital-to-analog and analog-to-digital conversion of audio information.

Let's briefly look at the processes of converting sound from analog to digital and vice versa. Having a rough idea of ​​what's going on in your sound card can help you avoid some mistakes when working with audio.

Sound waves are converted into an analog alternating electrical signal using a microphone. It passes through the audio path (see appendix figure 1.11, diagram 1) and enters an analog-to-digital converter (ADC) - a device that converts the signal into digital form.

In a simplified form, the operating principle of the ADC is as follows: it measures the signal amplitude at certain intervals and transmits further, along the digital path, a sequence of numbers carrying information about changes in amplitude (see Appendix Figure 1.11, Scheme 2).

During analog-to-digital conversion, no physical conversion occurs. It is as if a fingerprint or sample is taken from the electrical signal, which is a digital model of voltage fluctuations in the audio path. If this is depicted in the form of a diagram, then this model is presented as a sequence of columns, each of which corresponds to a specific numerical value. A digital signal is by its nature discrete - that is, intermittent - so the digital model does not exactly match the shape of the analog signal.

Sample is the time interval between two measurements of the amplitude of an analog signal.

Sample is literally translated from English as “sample”. In multimedia and professional audio terminology, this word has several meanings. In addition to a period of time, a sample is also called any sequence of digital data that is obtained through analog-to-digital conversion. The transformation process itself is called sampling. In Russian technical language they call it sampling.

Digital audio is output using a digital-to-analog converter (DAC), which, based on incoming digital data, generates an electrical signal of the required amplitude at appropriate times (see appendix figure 1.11, diagram 3).

Options sampling

Important parameters sampling are frequency and bit depth.
Frequency- number of analog signal amplitude measurements per second.

If the sampling frequency is not more than twice the frequency of the upper limit of the audio range, then loss will occur at high frequencies. This explains why the standard frequency for an audio CD is 44.1 kHz. Since the oscillation range of sound waves is from 20 Hz to 20 kHz, the number of signal measurements per second must be greater than the number of oscillations over the same period of time. If the sampling frequency is significantly lower than the frequency of the sound wave, then the amplitude of the signal has time to change several times during the time between measurements, and this leads to the fact that the digital fingerprint carries a chaotic set of data. During digital-to-analog conversion, such a sample does not transmit the main signal, but only produces noise.

In the new Audio DVD format, the signal is measured 96,000 times in one second, i.e. A sampling frequency of 96 kHz is used. To save hard disk space in multimedia applications, lower frequencies are often used: 11, 22, 32 kHz. This leads to a decrease in the audible frequency range, which means there is a strong distortion of what is heard.

If you graph the same sound at 1 kHz (the note up to the seventh octave of a piano roughly corresponds to this frequency), but sampled at different frequencies (the bottom of the sine wave is not shown in all graphs), then the differences will be visible. One division on the horizontal axis, which shows time, corresponds to 10 samples. The scale is taken the same (see Appendix Figure 1.13). You can see that at 11 kHz there are approximately five sound wave oscillations for every 50 samples, meaning one sine wave period is represented with just 10 values. This is a rather inaccurate rendering. At the same time, if we consider the digitization frequency of 44 kHz, then for each period of the sinusoid there are already almost 50 samples. This allows you to get a good quality signal.

Bit depth indicates with what accuracy changes in the amplitude of the analog signal occur. The accuracy with which the signal amplitude value at each instant of time is transmitted during digitization determines the quality of the signal after digital-to-analog conversion. The reliability of waveform reconstruction depends on the bit depth.

To encode the amplitude value, the principle of binary coding is used. The sound signal must be presented as a sequence of electrical pulses (binary zeros and ones). Typically, 8, 16-bit, or 20-bit representations of amplitude values ​​are used. When binary coding a continuous audio signal, it is replaced by a sequence of discrete signal levels. The quality of encoding depends on the sampling frequency (the number of signal level measurements per unit time). As the sampling frequency increases, the accuracy of the binary representation of information increases. At a frequency of 8 kHz (number of samples per second 8000), the quality of the sampled audio signal corresponds to the quality of a radio broadcast, and at a frequency of 48 kHz (number of samples per second 48000) - the sound quality of an audio CD.

If you use 8-bit encoding, you can achieve an analog signal amplitude accuracy of up to 1/256 of the dynamic range of a digital device (2 8 = 256).

If you use 16-bit encoding to represent the amplitude values ​​of the audio signal, the measurement accuracy will increase by 256 times.

Modern converters typically use 20-bit signal encoding, which allows for high-quality audio digitization.

Let's remember the formula K = 2 a. Here K is the number of all possible sounds (the number of different signal levels or states) that can be obtained by encoding sound with bits

We got acquainted with number systems - ways of encoding numbers. Numbers give information about the number of items. This information must be encoded and presented in some kind of number system. Which of the known methods to choose depends on the problem being solved.
Until recently, computers mainly processed numerical and textual information. But a person receives most of the information about the outside world in the form of images and sound. In this case, the image turns out to be more important. Remember the proverb: “It is better to see once than to hear a hundred times.” Therefore, today computers are beginning to work more and more actively with images and sound. We will definitely consider ways to encode such information.

Binary coding of numeric and text information.

Any information is encoded in a computer using sequences of two digits - 0 and 1. The computer stores and processes information in the form of a combination of electrical signals: voltage 0.4V-0.6V corresponds to logical zero, and voltage 2.4V-2.7V corresponds to logical one. Sequences of 0 and 1 are called binary codes , and the numbers 0 and 1 are bits (binary digits). This encoding of information on a computer is called binary coding . Thus, binary encoding is encoding with the minimum possible number of elementary symbols, encoding by the simplest means. This is why it is remarkable from a theoretical point of view.
Engineers are attracted to binary coding of information because it is easy to implement technically. Electronic circuits for processing binary codes must be in only one of two states: there is a signal / no signal or high voltage/low voltage .
In their work, computers operate with real and integer numbers, presented in the form of two, four, eight and even ten bytes. To represent the sign of a number when counting, an additional sign digit , which is usually located before the numeric digits. For positive numbers, the value of the sign bit is 0, and for negative numbers - 1. To write the internal representation of a negative integer number (-N), you must:
1) get the additional code of the number N by replacing 0 with 1 and 1 with 0;
2) add 1 to the resulting number.

Since one byte is not enough to represent this number, it is represented as 2 bytes or 16 bits, its complement code is 1111101111000101, therefore -1082=1111101111000110.
If a PC could only handle single bytes, it would be of little use. In reality, a PC works with numbers that are written in two, four, eight and even ten bytes.
Since the late 60s, computers have increasingly been used to process text information. To represent text information, 256 different characters are usually used, for example, capital and small letters of the Latin alphabet, numbers, punctuation marks, etc. In most modern computers, each character corresponds to a sequence of eight zeros and ones, called byte .
A byte is an eight-bit combination of zeros and ones.
When encoding information in these electronic computers, 256 different sequences of 8 zeros and ones are used, which allows 256 characters to be encoded. For example, the large Russian letter “M” has the code 11101101, the letter “I” has the code 11101001, the letter “P” has the code 11110010. Thus, the word “WORLD” is encoded with a sequence of 24 bits or 3 bytes: 111011011110100111110010.
The number of bits in a message is called the message information volume. This is interesting!

Initially, only the Latin alphabet was used in computers. It has 26 letters. So, five pulses (bits) would be enough to designate each one. But the text contains punctuation marks, decimal numbers, etc. Therefore, in the first English-language computers, a byte - a machine syllable - included six bits. Then seven - not only to distinguish large letters from small ones, but also to increase the number of control codes for printers, signal lights and other equipment. In 1964, the powerful IBM-360 appeared, in which the byte finally became equal to eight bits. The last eighth bit was needed for pseudographics characters.
Assigning a particular binary code to a symbol is a matter of convention, which is recorded in the code table. Unfortunately, there are five different encodings of Russian letters, so texts created in one encoding will not be reflected correctly in another.
Chronologically, one of the first standards for encoding Russian letters on computers was KOI8 (“Information Exchange Code, 8-bit”). The most common encoding is the standard Microsoft Windows Cyrillic encoding, denoted by the abbreviation SR1251 (“SR” stands for “Code Page” or “code page”). Apple has developed its own encoding of Russian letters (Mac) for Macintosh computers. The International Standards Organization (ISO) has approved the ISO 8859-5 encoding as a standard for the Russian language. Finally, a new international standard, Unicode, has appeared, which allocates not one byte for each character, but two, and therefore with its help you can encode not 256 characters, but as many as 65536.
All of these encodings continue the ASCII (American Standard Code for Information Interchange) code table, which encodes 128 characters.
ASCII character table:

Binary coding of text occurs as follows: when you press a key, a certain sequence of electrical impulses is transmitted to the computer, and each character corresponds to its own sequence of electrical impulses (zeros and ones in machine language). The keyboard and screen driver program determines the character using the code table and creates its image on the screen. Thus, texts and numbers are stored in the computer's memory in binary code and converted programmatically into images on the screen.

Since the 80s, the technology of processing graphic information on a computer has been rapidly developing. Computer graphics are widely used in computer simulation in scientific research, computer simulation, computer animation, business graphics, games, etc.
Graphic information on the display screen is presented in the form of an image, which is formed from dots (pixels). Look closely at a newspaper photograph and you will see that it also consists of tiny dots. If these are only black and white dots, then each of them can be encoded with 1 bit. But if there are shades in the photo, then two bits allows you to encode 4 shades of dots: 00 - white, 01 - light gray, 10 - dark gray, 11 - black. Three bits allow you to encode 8 shades, etc.
The number of bits required to encode one shade of color is called color depth.

In modern computers resolution (number of dots on the screen), as well as the number of colors depends on the video adapter and can be changed by software.
Color images can have different modes: 16 colors, 256 colors, 65536 colors ( high color), 16777216 colors ( true color). Per point for mode high color 16 bits or 2 bytes are needed.
The most common screen resolution is 800 by 600 pixels, i.e. 480000 points. Let's calculate the amount of video memory required for high color mode: 2 bytes *480000=960000 bytes.
Larger units are also used to measure the amount of information:

Therefore, 960000 bytes is approximately equal to 937.5 KB. If a person speaks for eight hours a day without a break, then over the course of 70 years of life he will speak about 10 gigabytes of information (that’s 5 million pages - a stack of paper 500 meters high).
Information transfer rate is the number of bits transmitted per second. The transmission rate of 1 bit per second is called 1 baud.

A bitmap, which is a binary image code, is stored in the computer's video memory, from where it is read by the processor (at least 50 times per second) and displayed on the screen.

Binary coding of audio information.

Since the early 90s, personal computers have been able to work with audio information. Every computer with a sound card can save as files ( a file is a certain amount of information stored on disk and has a name ) and play audio information. Using special software (audio file editors) opens up wide possibilities for creating, editing and listening to sound files. Speech recognition programs are being created, and it becomes possible to control the computer with your voice.
It is the sound card (card) that converts the analog signal into a discrete phonogram and vice versa, the “digitized” sound into an analog (continuous) signal that goes to the speaker input.

When binary coding an analog audio signal, the continuous signal is sampled, i.e. is replaced by a series of its individual samples - readings. The quality of binary encoding depends on two parameters: the number of discrete signal levels and the number of samples per second. The number of samples or sampling frequency in audio adapters can be different: 11 kHz, 22 kHz, 44.1 kHz, etc. If the number of levels is 65536, then 16 bits (216) are designed for one audio signal. A 16-bit audio adapter encodes and reproduces audio more accurately than an 8-bit audio adapter.
The number of bits required to encode one audio level is called audio depth.
The volume of a mono audio file (in bytes) is determined by the formula:

With stereophonic sound, the volume of the audio file doubles, with quadraphonic sound it quadruples.
As programs become more complex and their functions increase, as well as the emergence of multimedia applications, the functional volume of programs and data increases. If in the mid-80s the usual volume of programs and data was tens and only sometimes hundreds of kilobytes, then in the mid-90s it began to amount to tens of megabytes. The amount of RAM increases accordingly.