Characteristics of Microprocessors
Characteristics of Microprocessors
Microprocessors may be characterized in more than one way. The basic particulars used to set up or pick a microprocessor are as follows.
- Type of microprocessor (general-purpose or special purpose, single-chip or bit-slice).
- Technology: p-channel MOS, n-channel MOS, CMOS, silicon-on-sapphire, bipolar TTL, Schottky TTL, I2L, ECL. (Knowledge of the technology used gives an idea about the power requirements and speed of the microprocessor.)
Data word size (4, 8, 16, or 32 bits). It defines the smallest block of data that can be handled by a microprocessor as an entity. It may be fixed or expandable (in the case of bit-slice microprocessors).
- Addressable memory size. It characterizes the capability of a microprocessor in accessing its memory.
- Form of control: by wired-in programs or by stored programs (microprogramming).
- Speed (or throughput). Most often, this parameter is stated as the time required for the microprocessor to execute one operation (or as the number of "register-to-register" transfers per second), in terms of the clock rate, or the access time.
- Power consumption.
- Supply voltages (number and values of logic levels).
- Package dimensions and number of pins.
- Service conditions (operating temperature range, relative humidity, level of vibration, etc.).
- Reliability.
- Cost.
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Architecture of the Microprocessor
General. Dictionaries define βarchitectureβ (from the Greek architekton for βbuilderβ) as the art and science of building.
The term βarchitectureβ as applied to computers is a bit arbitrary, it has become part and parcel of computer usage. This can be proved by a reference to dictionaries on computers and the titles of many books.
Still, what is the architecture of a microprocessor? Most often it is defined as the general philosophy of microprocessor organization, its overall structure, the specific logic design of the various units, repertoire, and the specification of the relationships between its hardware (that is, its physical equipment) and its software (that is, its programs, procedures).
In many respects, microprocessor architectures are similar to those of large computers, but they also have distinctions of their own.
Obviously, an in-depth study of microprocessor architecture would call for the coverage of a wide range of things. This could hardly be done in a small book like this, nor is it necessary in view of the objective formulated in the title of this chapter - an introduction to microprocessors.
One way to classify the multitude of microprocessors available on the market is to group them into single-chip types and bit-slice types. Single-chip microprocessors have a fixed word length and a fixed repertoire. Bit-slice microprocessors use a word length that can be expanded at will. A bit-slice microprocessor uses LSI components called bit slices usually designed to handle 4 bits of the computer word and arranged so that any number of them can be used together to form words of any size. Recently, single-chip microprocessors using microprograms have also been developed.
The logic design of single-chip microprocessors is to a large extent similar to that of general-purpose computers.
Owing to their structure and the use of microprogramming, bit-slice microprocessors show an extreme flexibility in applications and a far better performance. Using relatively simple means, we can arrange for a parallel execution of machine operations, thus enhancing the capacity of the computers built around such microprocessors.
Despite the superior capabilities of bit-slice microprocessors, however, many applied tasks, notably automatic measuring instruments, can well be achieved using single-chip microprocessors. Therefore, we will limit ourselves to a look at the structure of a single-chip processor.
Structure of the microprocessor. To be more specific, we will examine the structure of an 8-bit single-chip general-purpose microprocessor. As is seen from the block diagram of Fig. 1.3, it consists of an arithmetic logic unit, a control unit, and several internal registers.
The arithmetic logic unit (ALU), which is the core of the microprocessor, usually consists of a binary adder complete with fast carry
circuits, a shift register, and registers for temporary storage of operands. As a rule, the ALU executes several simple operations in response to specific instructions. These operations are addition, subtraction, shifting, transfer, logic OR, logic AND. We have named two more things which are new to the readerβregisters and operands. Let us define them before we go on discussing the other component units of the microprocessor.
A register is an electronic circuit which serves to receive, temporarily store, and deliver a computer word as a string of 1s and 0s. A register is made from flip-flops, each flip-flop being capable of handling one bit of information at a time (a 1 or a 0). The length (or width) of a register is the same as the size of the word it stores. Thus, an 8-bit register consists of eight flip-flops (suitably interconnected) and can handle an 8-bit word.
An operand is the number or the character which is to be the subject of an arithmetic operation. For example, in the expression
y = a + b
or
w = 2k - 1
the operands are a, b, 2, k, and 1. A typical example of operands involved in data processing by microprocessors is the byte.
The control unit (CU) βcoordinatesβ the operation of the ALU and of the internal registers during the execution of an instruction. Each instruction word consists of two parts, an operation code (op code) and an operand. The op code βtellsβ the control unit what signals it should generate for control of the microprocessor units. The operand supplies a coded indication (that is, an address) that tells where any data to be operated or should be retrieved from or written into memory.
The internal registers, which expand the capabilities of the ALU, serve as the microprocessor's internal memoryβ they are used for temporary storage of data and instructions. They may also perform some data processing operations. As a rule, the internal register section includes general-purpose registers and special-purpose registers such as an accumulator register, a memory address register, a memory data register, an instruction counter, stack registers, and a status register.
The general-purpose registers, GPR, of which there may be from 4 to 64, determine to a certain extent the computational capabilities of the microprocessors. They are primarily used for the manipulation and temporary storage of data.
The accumulator similarly serves as a scratch pad for arithmetic, logical and input/output operations. In most microprocessors the accumulator also stores the results of the mathematical operations which replace the operand that was originally stored there. Normally, data words fetched from memory and words to be written into memory are first loaded into the accumulator. The size (or width) of the accumulator is the same as the data word size (in our example the accumulator is 8 bits wide). Some microprocessors may have two or more accumulatorsβthis enhances their flexibility and efficiency in problem solving.
The memory address register is a specialized register used to store the address of the word to be fetched from, or loaded into, the microprocessor memory or some other register before it goes to the address bus. The maximum number of directly addressable data words in the memory depends on the size of the memory address register. For example, by rearranging the 0s and 1s in the various bits of a two-byte word we can store 216 = 65 536 addresses of memory locations (words) in a 16-bit memory address register (of course, one at time).
The memory data register is used to store the word. The width of this register is the same as the data word size (an 8-bit memory data register is needed to store a one-byte word, and a 16-bit memory data register for a two-byte word).
The instruction counter is a register that contains the memory address of the next instruction word to be executed. As a rule, the instructions of a particular program are stored in consecutive memory locations: for a one-byte instruction the number giving the address of every next memory location is by one greater than that of the current location. Each time the microprocessor accesses memory, the instruction counter is incremented by one to point to the memory location from which the next instruction is to be fetched.
Π₯Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠΈ ΠΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠΎΠ²
ΠΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΡ ΠΌΠΎΠ³ΡΡ Π±ΡΡΡ Ρ Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΠ·ΠΎΠ²Π°Π½Ρ Π±ΠΎΠ»ΡΡΠ΅ ΡΠ΅ΠΌ ΠΎΠ΄Π½ΠΈΠΌ ΡΠΏΠΎΡΠΎΠ±ΠΎΠΌ. ΠΡΠ½ΠΎΠ²Π½ΡΠ΅ ΠΏΠΎΠ΄ΡΠΎΠ±Π½ΡΠ΅ ΡΠ²Π΅Π΄Π΅Π½ΠΈΡ ΠΈΠΌΠ΅Π»ΠΈ ΠΎΠ±ΡΠΊΠ½ΠΎΠ²Π΅Π½ΠΈΠ΅ ΡΡΡΠ°Π½Π°Π²Π»ΠΈΠ²Π°ΡΡ, ΠΈΠ»ΠΈ Π²ΡΠ±ΠΈΡΠ°ΡΡ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡ ΡΠ»Π΅Π΄ΡΡΡΠΈΠ΅.
- Π’ΠΈΠΏ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠ° (ΡΠ½ΠΈΠ²Π΅ΡΡΠ°Π»ΡΠ½ΡΠΉ ΠΈΠ»ΠΈ ΡΠ΅Π»ΠΈ ΡΠΏΠ΅ΡΠΈΠ°Π»ΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠΉ ΠΠ‘, ΠΎΠ΄Π½ΠΎΡΠΈΠΏΠ½ΠΎΠΉ ΠΈΠ»ΠΈ ΡΠ΅ΠΊΡΠΈΠΎΠ½ΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠΉ).
- Π’Π΅Ρ Π½ΠΎΠ»ΠΎΠ³ΠΈΡ: ΠΠΠ-ΡΡΡΡΠΊΡΡΡΠ° Ρ ΠΊΠ°Π½Π°Π»ΠΎΠΌ Ρ-ΡΠΈΠΏΠ°, n-ΠΊΠ°Π½Π°Π»ΡΠ½Π°Ρ ΠΠΠ-ΡΡΡΡΠΊΡΡΡΠ°, ΠΊΠΎΠΌΠΏΠ»Π΅ΠΌΠ΅Π½ΡΠ°ΡΠ½Π°Ρ ΠΠΠ-ΡΡΡΡΠΊΡΡΡΠ°, ΠΠΠ‘-ΡΡΡΡΠΊΡΡΡΠ°, Π±ΠΈΠΏΠΎΠ»ΡΡΠ½Π°Ρ Π’Π’Π-Π‘Π₯ΠΠΠ, Π΄ΠΈΠΎΠ΄ Π¨ΠΎΡΠΊΠΈ Π’Π’Π-Π‘Π₯ΠΠΠ, I2L, ΡΠ·ΡΠΊ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ Π²ΡΡΠΈΡΠ»ΠΈΡΠ΅Π»ΡΠ½ΡΠΌ ΠΏΡΠΎΡΠ΅ΡΡΠΎΠΌ. (ΠΠ½Π°Π½ΠΈΠ΅ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΠ΅ΠΌΠΎΠΉ ΡΠ΅Ρ Π½ΠΎΠ»ΠΎΠ³ΠΈΠΈ Π΄Π°Π΅Ρ ΠΈΠ΄Π΅Ρ ΠΎ ΡΡΠ΅Π±ΠΎΠ²Π°Π½ΠΈΡΡ Π²Π»Π°ΡΡΠΈ{ΠΌΠΎΡΠ½ΠΎΡΡΠΈ} ΠΈ Π±ΡΡΡΡΠΎΠ΄Π΅ΠΉΡΡΠ²ΠΈΠΈ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠ°.)
Π Π°Π·ΠΌΠ΅Ρ{ΠΠΌΠΊΠΎΡΡΡ} ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ ΡΠ»ΠΎΠ²Π° (4, 8, 16, ΠΈΠ»ΠΈ 32 Π±ΠΈΡΠ°). ΠΡΠΎ ΠΎΠΏΡΠ΅Π΄Π΅Π»ΡΠ΅Ρ Π½Π°ΠΈΠΌΠ΅Π½ΡΡΠΈΠΉ Π±Π»ΠΎΠΊ Π΄Π°Π½Π½ΡΡ , ΠΊΠΎΡΠΎΡΡΠ΅ ΠΌΠΎΠ³ΡΡ Π±ΡΡΡ ΠΌΠ°Π½ΠΈΠΏΡΠ»ΠΈΡΠΎΠ²Π°Π½Ρ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠΎΠΌ ΠΊΠ°ΠΊ ΠΎΠ±ΡΠ΅ΠΊΡ. ΠΡΠΎ ΠΌΠΎΠΆΠ΅Ρ Π±ΡΡΡ ΡΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΎ ΠΈΠ»ΠΈ ΡΠ°ΡΡΠΈΡΡΠ΅ΠΌΡΠΌ (Π² ΡΠ»ΡΡΠ°Π΅ ΡΠ΅ΠΊΡΠΈΠΎΠ½Π½ΡΡ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠΎΠ²).
- ΠΠ΄ΡΠ΅ΡΡΠ΅ΠΌΠ°Ρ Π΅ΠΌΠΊΠΎΡΡΡ ΠΏΠ°ΠΌΡΡΠΈ. ΠΡΠΎ Ρ Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΠ·ΡΠ΅Ρ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΡ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠ° Π² Π΄ΠΎΡΡΡΠΏΠ΅ ΠΊ Π΅Π³ΠΎ Π·Π°ΠΏΠΎΠΌΠΈΠ½Π°ΡΡΠ΅ΠΌΡ ΡΡΡΡΠΎΠΉΡΡΠ²Ρ.
- ΠΠΈΠ΄ ΠΏΡΠΎΠ²Π΅ΡΠΊΠΈ: Π·Π°ΡΠΈΡΡΠΌ - Π² ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ°Ρ ΠΈΠ»ΠΈ Π·Π°ΠΏΠΈΡΠ°Π½Π½ΡΠΌΠΈ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ°ΠΌΠΈ (ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅).
- ΠΡΡΡΡΠΎΠ΄Π΅ΠΉΡΡΠ²ΠΈΠ΅ (ΠΈΠ»ΠΈ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΠΈΡΠ΅Π»ΡΠ½ΠΎΡΡΡ). ΠΠ°ΠΈΠ±ΠΎΠ»Π΅Π΅ ΡΠ°ΡΡΠΎ, ΡΡΠΎΡ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡ Π·Π°ΡΠ²Π»Π΅Π½ ΠΊΠ°ΠΊ Π²ΡΠ΅ΠΌΡ, ΡΡΠ΅Π±ΡΠ΅ΠΌΠΎΠ΅ Π΄Π»Ρ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠ° Π²ΡΠΏΠΎΠ»Π½ΠΈΡΡ ΠΎΠ΄Π½Ρ ΠΎΠΏΠ΅ΡΠ°ΡΠΈΡ (ΠΈΠ»ΠΈ ΠΊΠ°ΠΊ Π½ΠΎΠΌΠ΅Ρ ΠΏΠ΅ΡΠ΅Π΄Π°Ρ{ΠΏΠ΅ΡΠ΅ΠΌΠ΅ΡΠ΅Π½ΠΈΡ} "ΠΌΠ΅ΠΆΠ΄Ρ ΡΠ΅Π³ΠΈΡΡΡΠ°ΠΌΠΈ" Π² ΡΠ΅ΠΊΡΠ½Π΄Ρ), Π² ΡΠ΅ΡΠΌΠΈΠ½Π°Ρ ΡΠ°ΠΊΡΠΎΠ²ΠΎΠΉ ΡΠ°ΡΡΠΎΡΡ, ΠΈΠ»ΠΈ Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ Π΄ΠΎΡΡΡΠΏΠ°.
- ΠΠΎΡΡΠ΅Π±Π»ΡΠ΅ΠΌΠ°Ρ ΠΌΠΎΡΠ½ΠΎΡΡΡ.
- ΠΠ°ΠΏΡΡΠΆΠ΅Π½ΠΈΡ ΠΏΠΈΡΠ°Π½ΠΈΡ (Π½ΠΎΠΌΠ΅Ρ ΠΈ Π·Π½Π°ΡΠ΅Π½ΠΈΡ Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ ΡΡΠΎΠ²Π½Π΅ΠΉ).
- Π Π°Π·ΠΌΠ΅ΡΡ ΠΏΠ°ΠΊΠ΅ΡΠ° ΠΈ Π½ΠΎΠΌΠ΅Ρ ΡΡΡΡΡΠΊΠΎΠ².
- Π£ΡΠ»ΠΎΠ²ΠΈΡ ΡΠΊΡΠΏΠ»ΡΠ°ΡΠ°ΡΠΈΠΈ (Π½ΠΎΠΌΠ΅Π½ΠΊΠ»Π°ΡΡΡΠ° ΡΠ°Π±ΠΎΡΠ΅ΠΉ ΡΠ΅ΠΌΠΏΠ΅ΡΠ°ΡΡΡΡ, ΠΎΡΠ½ΠΎΡΠΈΡΠ΅Π»ΡΠ½Π°Ρ Π²Π»Π°ΠΆΠ½ΠΎΡΡΡ, ΡΡΠΎΠ²Π΅Π½Ρ{ΡΡΠ΅ΠΏΠ΅Π½Ρ} ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΠΉ, ΠΈ Ρ.Π΄.).
- ΠΠ°Π΄Π΅ΠΆΠ½ΠΎΡΡΡ.
12.Π‘ΡΠΎΠΈΠΌΠΎΡΡΡ.
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ΠΠΎΠ½ΡΡΡΡΠΊΡΠΈΡ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠ°
ΠΠ±ΡΠ΅Π΅. Π‘Π»ΠΎΠ²Π°ΡΠΈ Π΄Π°ΡΡ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠ΅ 'ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠΈ' (ΠΎΡ Π³ΡΠ΅ΡΠ΅ΡΠΊΠΎΠ³ΠΎ architekton 'ΡΡΡΠΎΠΈΡΠ΅Π»Ρ') ΠΊΠ°ΠΊ ΠΈΡΠΊΡΡΡΡΠ²ΠΎ ΠΈ Π½Π°ΡΠΊΠ° ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ.
Π’Π΅ΡΠΌΠΈΠ½ 'ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΡ' Π² ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΠΈ ΠΊ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ°ΠΌ Π½Π΅ΠΌΠ½ΠΎΠ³ΠΎ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ»Π΅Π½, ΠΎΠ½ ΡΡΠ°Π» Π½Π΅ΠΎΡΡΠ΅ΠΌΠ»Π΅ΠΌΠΎΠΉ ΡΠ°ΡΡΡΡ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΠΎΠ³ΠΎ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ. ΠΡΠΎ ΠΌΠΎΠΆΠ΅Ρ Π±ΡΡΡ Π΄ΠΎΠΊΠ°Π·Π°Π½ΠΎ ΡΡΡΠ»ΠΊΠΎΠΉ Π½Π° ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΡΠ΅ ΡΠ»ΠΎΠ²Π°ΡΠΈ ΠΈ Π·Π°Π³ΠΎΠ»ΠΎΠ²ΠΊΠ°Ρ ΠΌΠ½ΠΎΠ³ΠΈΡ ΠΊΠ½ΠΈΠ³.
ΠΠ΄Π½Π°ΠΊΠΎ, ΡΡΠΎ ΠΆΠ΅ ΡΠ²Π»ΡΠ΅ΡΡΡ ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΠ΅ΠΉ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠ°? ΠΠ°ΠΈΠ±ΠΎΠ»Π΅Π΅ ΡΠ°ΡΡΠΎ ΠΎΠ½Π° ΠΎΠΏΡΠ΅Π΄Π΅Π»ΡΠ΅ΡΡΡ ΠΊΠ°ΠΊ ΠΎΠ±ΡΠ°Ρ ΡΠΈΠ»ΠΎΡΠΎΡΠΈΡ Π°ΡΡ ΠΈΡΠ΅ΠΊΡΡΡΡ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠ°, Π΅Ρ ΠΏΠΎΠ»Π½ΠΎΠΉ ΡΡΡΡΠΊΡΡΡΡ, ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΠ΅ Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠ΅ ΠΏΡΠΎΠ΅ΠΊΡΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΡΠ°Π·Π»ΠΈΡΠ½ΡΡ ΠΌΠΎΠ΄ΡΠ»Π΅ΠΉ, Π½Π°Π±ΠΎΡΠ°, ΠΈ ΡΠΏΠ΅ΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ ΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΠΉ ΠΌΠ΅ΠΆΠ΄Ρ Π΅Ρ Π°ΠΏΠΏΠ°ΡΠ°ΡΠ½ΡΠΌΠΈ ΡΡΠ΅Π΄ΡΡΠ²Π°ΠΌΠΈ (ΡΠΎ Π΅ΡΡΡ Π΅Ρ ΡΠΈΠ·ΠΈΡΠ΅ΡΠΊΠΎΠ΅ ΠΎΠ±ΠΎΡΡΠ΄ΠΎΠ²Π°Π½ΠΈΠ΅) ΠΈ Π΅Π΅ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ½ΠΎΠ΅ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠ΅Π½ΠΈΠ΅ (ΡΠΎ Π΅ΡΡΡ Π΅Π΅ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΡ, ΠΏΡΠΎΡΠ΅Π΄ΡΡΡ).
ΠΠΎ ΠΌΠ½ΠΎΠ³ΠΈΡ ΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΡΡ , Π°ΡΡ ΠΈΡΠ΅ΠΊΡΡΡΠ° ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠ° ΠΎΠ΄ΠΈΠ½Π°ΠΊΠΎΠ²Π° Π΄Π»Ρ Π±ΠΎΠ»ΡΡΠΈΠ½ΡΡΠ²Π° ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠΎΠ², Π½ΠΎ ΠΎΠ½Π° ΡΠ°ΠΊΠΆΠ΅ ΠΈΠΌΠ΅Π΅Ρ ΡΠΎΠ±ΡΡΠ²Π΅Π½Π½ΡΠ΅ ΡΠ°Π·Π»ΠΈΡΠΈΡ.
ΠΡΠ΅Π²ΠΈΠ΄Π½ΠΎ, ΠΎΡΠ΅Π²ΠΈΠ΄Π½ΠΎ Π²ΡΠ΅ΡΡΠΎΡΠΎΠ½Π½Π΅Π΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅ Π°ΡΡ ΠΈΡΠ΅ΠΊΡΡΡΡ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠ° Π·Π°ΠΏΡΠΎΡΠΈΠ»ΠΎ Π±Ρ ΠΎΡ Π²Π°Ρ ΡΠΈΡΠΎΠΊΠΎΠ³ΠΎ Π΄ΠΈΠ°ΠΏΠ°Π·ΠΎΠ½Π° Π²Π΅ΡΠ΅ΠΉ. ΠΡΠΎ ΠΌΠΎΠ³Π»ΠΎ Π΅Π΄Π²Π° Π±ΡΡΡ ΡΠ΄Π΅Π»Π°Π½ΠΎ Π² ΠΌΠ°Π»Π΅Π½ΡΠΊΠΎΠΉ ΠΊΠ½ΠΈΠ³Π΅ ΠΏΠΎΠ΄ΠΎΠ±Π½ΠΎ ΡΡΠΎΠΉ, ΠΈ ΠΏΡΠΈ ΡΡΠΎΠΌ ΡΡΠΎ Π½Π΅ Π½Π΅ΠΎΠ±Ρ ΠΎΠ΄ΠΈΠΌΠΎ Π²Π²ΠΈΠ΄Ρ ΡΠ΅Π»ΠΈ, ΡΡΠΎΡΠΌΡΠ»ΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠΉ Π² Π·Π°Π³ΠΎΠ»ΠΎΠ²ΠΊΠ΅ ΡΡΠΎΠΉ Π³Π»Π°Π²Ρ - Π²Π²Π΅Π΄Π΅Π½ΠΈΠ΅ Π² ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΡ.
ΠΠ΄ΠΈΠ½ ΡΠΏΠΎΡΠΎΠ± ΠΊΠ»Π°ΡΡΠΈΡΠΈΡΠΈΡΠΎΠ²Π°ΡΡ ΠΌΠ½ΠΎΠΆΠ΅ΡΡΠ²ΠΎ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠΎΠ², Π΄ΠΎΡΡΡΠΏΠ½ΡΡ Π½Π° ΡΡΠ½ΠΊΠ΅ ΡΠΎΡΡΠΎΠΈΡ Π² ΡΠΎΠΌ, ΡΡΠΎΠ±Ρ Π³ΡΡΠΏΠΏΠΈΡΠΎΠ²Π°ΡΡ ΠΈΡ Π² ΠΎΠ΄Π½ΠΎΡΠΈΠΏΠ½ΡΠ΅ ΡΠΈΠΏΡ ΠΈ ΡΠ΅ΠΊΡΠΈΠΎΠ½ΠΈΡΠΎΠ²Π°Π½Π½ΡΠ΅ ΡΠΈΠΏΡ. ΠΠ΄Π½ΠΎΡΠΈΠΏΠ½ΡΠ΅ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΡ ΠΈΠΌΠ΅ΡΡ ΡΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½Π½ΡΡ Π΄Π»ΠΈΠ½Ρ ΡΠ»ΠΎΠ²Π° ΠΈ ΡΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½Π½ΡΠΉ Π½Π°Π±ΠΎΡ. Π‘Π΅ΠΊΡΠΈΠΎΠ½Π½ΡΠ΅ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΡΡ Π΄Π»ΠΈΠ½Ρ ΡΠ»ΠΎΠ²Π°, ΠΊΠΎΡΠΎΡΠ°Ρ ΠΌΠΎΠΆΠ΅Ρ Π±ΡΡΡ ΡΠ°ΡΡΠΈΡΠ΅Π½Π° ΠΏΠΎ ΠΆΠ΅Π»Π°Π½ΠΈΡ. Π‘Π΅ΠΊΡΠΈΠΎΠ½Π½ΡΠΉ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΠ΅Ρ ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½ΡΡ Π±ΠΎΠ»ΡΡΠΎΠΉ ΠΈΠ½ΡΠ΅Π³ΡΠ°Π»ΡΠ½ΠΎΠΉ ΡΡ Π΅ΠΌΡ, Π½Π°Π·Π²Π°Π½Π½ΠΎΠΉ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠ½ΠΎΠΉ ΡΠ΅ΠΊΡΠΈΠ΅ΠΉ, ΠΎΠ±ΡΡΠ½ΠΎ ΠΎΠ±ΡΠ°Π±Π°ΡΡΠ²Π°ΡΡ 4 Π±ΠΈΡΠ° ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΠΎΠ³ΠΎ ΡΠ»ΠΎΠ²Π° ΠΈ ΡΠ°Π·ΠΌΠ΅ΡΠ°ΡΡ ΡΠ°ΠΊ, ΡΡΠΎΠ±Ρ Π»ΡΠ±ΠΎΠΉ Π½ΠΎΠΌΠ΅Ρ ΠΈΡ ΠΌΠΎΠ³ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°ΡΡΡΡ ΠΎΠ΄Π½ΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎ, ΡΡΠΎΠ±Ρ ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°ΡΡ ΡΠ»ΠΎΠ²Π° Π»ΡΠ±ΠΎΠ³ΠΎ ΡΠ°Π·ΠΌΠ΅ΡΠ°. Π’Π°ΠΊΠΆΠ΅ Π½Π΅Π΄Π°Π²Π½ΠΎ, ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΡ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΡ, Π±ΡΠ»ΠΈ ΡΠ°Π·ΡΠ°Π±ΠΎΡΠ°Π½Ρ ΠΎΠ΄Π½ΠΎΡΠΈΠΏΠ½ΡΠ΅ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΡ
ΠΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠ΅ ΠΏΡΠΎΠ΅ΠΊΡΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΎΠ΄Π½ΠΎΡΠΈΠΏΠ½ΡΡ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠΎΠ² Π² Π±ΠΎΠ»ΡΡΠ΅ΠΉ ΡΡΠ΅ΠΏΠ΅Π½ΠΈ, ΠΏΠΎΠ΄ΠΎΠ±Π΅Π½ Π΄Π»Ρ ΡΠ½ΠΈΠ²Π΅ΡΡΠ°Π»ΡΠ½ΡΡ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠΎΠ².
ΠΡΠ»Π΅Π΄ΡΡΠ²ΠΈΠ΅ ΠΈΡ ΡΡΡΡΠΊΡΡΡΡ ΠΈ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ, ΡΠ΅ΠΊΡΠΈΠΎΠ½Π½ΡΠ΅ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΡ ΠΏΡΠΎΡΠ²Π»ΡΡΡ ΠΊΡΠΈΡΠΈΡΠ΅ΡΠΊΡΡ Π³ΠΈΠ±ΠΊΠΎΡΡΡ Π² ΠΏΡΠΈΠ»ΠΎΠΆΠ΅Π½ΠΈΡΡ ΠΈ Π½Π°ΠΌΠ½ΠΎΠ³ΠΎ Π»ΡΡΡΠ΅ Π² ΡΠ°Π±ΠΎΡΠΈΡ Ρ Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠ°Ρ . ΠΡΠΏΠΎΠ»ΡΠ·ΡΡ ΠΎΡΠ½ΠΎΡΠΈΡΠ΅Π»ΡΠ½ΠΎ ΠΏΡΠΎΡΡΡΠ΅ ΡΡΠ΅Π΄ΡΡΠ²Π°, ΠΌΡ ΠΌΠΎΠΆΠ΅ΠΌ ΡΡΡΡΠΎΠΈΡΡ ΠΎΠ΄Π½ΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠ΅ Π²ΡΠΏΠΎΠ»Π½Π΅Π½ΠΈΠ΅ ΠΌΠ°ΡΠΈΠ½Π½ΡΡ ΠΎΠΏΠ΅ΡΠ°ΡΠΈΠΉ, ΡΠ°ΠΊΠΈΠΌ ΠΎΠ±ΡΠ°Π·ΠΎΠΌ ΡΠ°ΡΡΠΈΡΡΡ ΡΠΏΠΎΡΠΎΠ±Π½ΠΎΡΡΡ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠΎΠ², ΡΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½Π½ΡΡ Π½Π° ΡΠ°ΠΊΠΈΡ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠ°Ρ .
ΠΠ΄Π½Π°ΠΊΠΎ, Π½Π΅ΡΠΌΠΎΡΡΡ Π½Π° ΠΏΡΠ΅Π²ΠΎΡΡ ΠΎΠ΄ΡΡΠΈΠ΅ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΠΈ ΡΠ΅ΠΊΡΠΈΠΎΠ½Π½ΡΡ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠΎΠ², ΠΌΠ½ΠΎΠ³ΠΎ ΠΏΡΠΈΠΊΠ»Π°Π΄Π½ΡΡ Π·Π°Π΄Π°Ρ, ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎ Π°Π²ΡΠΎΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΈΠ·ΠΌΠ΅ΡΠΈΡΠ΅Π»ΡΠ½ΡΠ΅ ΠΏΡΠΈΠ±ΠΎΡΡ, ΠΌΠΎΠ³ΡΡ ΠΊΠ°ΡΠΌΠ°Π½ Π±ΡΡΡ Π΄ΠΎΡΡΠΈΠ³Π½ΡΡΡΠΌΠΈ, ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΡ ΠΎΠ΄Π½ΠΎΡΠΈΠΏΠ½ΡΠ΅ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΡ. ΠΠΎΡΡΠΎΠΌΡ, ΠΌΡ ΠΎΠ³ΡΠ°Π½ΠΈΡΠΈΠΌ Π½Π°Ρ Π²Π·Π³Π»ΡΠ΄ΠΎΠΌ Π½Π° ΡΡΡΡΠΊΡΡΡΡ ΠΎΠ΄Π½ΠΎΡΠΈΠΏΠ½ΠΎΠ³ΠΎ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠ°.
Π‘ΡΡΡΠΊΡΡΡΠ° ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠ°. Π§ΡΠΎΠ±Ρ Π±ΡΡΡ Π±ΠΎΠ»Π΅Π΅ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΡΠΌΠΈ, ΠΌΡ ΠΈΡΡΠ»Π΅Π΄ΡΠ΅ΠΌ ΡΡΡΡΠΊΡΡΡΡ 8-Π±ΠΈΡΠΎΠ²ΠΎΠ³ΠΎ ΠΎΠ΄Π½ΠΎΡΠΈΠΏΠ½ΠΎΠ³ΠΎ ΡΠ½ΠΈΠ²Π΅ΡΡΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠ°. ΠΠ°ΠΊ ΠΏΠΎΠΊΠ°Π·Π°Π½ΠΎ Π½Π° Π±Π»ΠΎΠΊ-ΡΡ Π΅ΠΌΡ ΡΠΈΡ. 1.3, ΠΎΠ½ ΡΠΎΡΡΠΎΠΈΡ ΠΈΠ· Π°ΡΠΈΡΠΌΠ΅ΡΠΈΠΊΠΎ-Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΡΡΡΠΎΠΉΡΡΠ²Π°, Π±Π»ΠΎΠΊΠ° ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ, ΠΈ Π½Π΅ΡΠΊΠΎΠ»ΡΠΊΠΈΡ Π²Π½ΡΡΡΠ΅Π½Π½ΠΈΡ ΡΠ΅Π³ΠΈΡΡΡΠΎΠ².
ΠΡΠΈΡΠΌΠ΅ΡΠΈΠΊΠΎ-Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠ΅ ΡΡΡΡΠΎΠΉΡΡΠ²ΠΎ, ΠΊΠΎΡΠΎΡΠΎΠ΅ ΡΠ²Π»ΡΠ΅ΡΡΡ Π³Π»Π°Π²Π½ΠΎΠΉ ΡΠ°ΡΡΡΡ ΠΠ£ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠ°, ΠΎΠ±ΡΡΠ½ΠΎ ΡΠΎΡΡΠΎΠΈΡ ΠΈΠ· Π·Π°ΠΊΠΎΠ½ΡΠ΅Π½Π½ΠΎΠ³ΠΎ Π΄Π²ΠΎΠΈΡΠ½ΠΎΠ³ΠΎ ΡΡΠΌΠΌΠ°ΡΠΎΡΠ° ΡΡΡΡΡΠΎΠ΄Π΅ΠΉΡΡΠ²ΡΡΡΠΈΠΌΠΈ ΡΡ Π΅ΠΌΠ°ΠΌΠΈ ΠΏΠ΅ΡΠ΅Π½ΠΎΡΠ°, ΡΠ΄Π²ΠΈΠ³ΠΎΠ²ΡΠΌ ΡΠ΅Π³ΠΈΡΡΡΠΎΠΌ, ΠΈ ΡΠ΅Π³ΠΈΡΡΡΠ°ΠΌΠΈ Π΄Π»Ρ Π²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠ³ΠΎ Ρ ΡΠ°Π½Π΅Π½ΠΈΡ ΠΎΠΏΠ΅ΡΠ°Π½Π΄ΠΎΠ². ΠΠ°ΠΊ ΠΏΡΠ°Π²ΠΈΠ»ΠΎ, Π°ΡΠΈΡΠΌΠ΅ΡΠΈΠΊΠΎ-Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠ΅ ΡΡΡΡΠΎΠΉΡΡΠ²ΠΎ Π²ΡΠΏΠΎΠ»Π½ΡΠ΅Ρ Π½Π΅ΡΠΊΠΎΠ»ΡΠΊΠΎ ΠΏΡΠΎΡΡΡΡ ΠΎΠΏΠ΅ΡΠ°ΡΠΈΠΉ Π² ΠΎΡΠ²Π΅Ρ Π½Π° ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΡΠ΅ ΠΊΠΎΠΌΠ°Π½Π΄Ρ. ΠΡΠΈ ΠΎΠΏΠ΅ΡΠ°ΡΠΈΠΈ - Π΄ΠΎΠ±Π°Π²Π»Π΅Π½ΠΈΠ΅, Π²ΡΡΠΈΡΠ°Π½ΠΈΠ΅, ΡΠΌΠ΅ΡΠ΅Π½ΠΈΠ΅, ΠΏΠ΅ΡΠ΅Π΄Π°ΡΠ°, Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠ°Ρ ΡΡΠ½ΠΊΡΠΈΡ ΠΠΠ, Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠ°Ρ ΡΡΠ½ΠΊΡΠΈΡΒ Π. ΠΡ Π½Π°Π·Π²Π°Π»ΠΈ Π΅ΡΠ΅ Π΄Π²Π΅ Π²Π΅ΡΠΈ, ΠΊΠΎΡΠΎΡΡΠ΅ ΡΠ²Π»ΡΡΡΡΡ ΠΏΠ»ΠΎΡ ΠΎ Π·Π½Π°ΠΊΠΎΠΌΡΠΌΠΈ Ρ ΡΠ΅Π³ΠΈΡΡΡΠ°ΡΠΎΡΠ°ΠΌΠΈ ΡΡΠΈΡΡΠ²Π°ΡΡΠ΅Π³ΠΎ ΡΡΡΡΠΎΠΉΡΡΠ²Π° ΠΈ ΠΎΠΏΠ΅ΡΠ°Π½Π΄Π°ΠΌΠΈ. ΠΠΎΠ·Π²ΠΎΠ»ΡΡΠ΅ Π½Π°ΠΌ ΠΎΠΏΡΠ΅Π΄Π΅Π»ΠΈΡΡ ΠΈΡ ΠΏΡΠ΅ΠΆΠ΄Π΅, ΡΠ΅ΠΌ ΠΌΡ ΠΏΡΠΎΠ΄ΠΎΠ»ΠΆΠΈΠΌ ΠΎΠ±ΡΡΠΆΠ΄Π°ΡΡ Π΄ΡΡΠ³ΠΈΠ΅ ΡΠΎΡΡΠ°Π²Π»ΡΡΡΠΈΠ΅ ΠΌΠΎΠ΄ΡΠ»ΠΈ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠ°.
Π Π΅Π³ΠΈΡΡΡ - ΡΠ»Π΅ΠΊΡΡΠΎΠ½Π½Π°Ρ ΡΡ Π΅ΠΌΠ°, ΠΊΠΎΡΠΎΡΠ°Ρ ΡΠ»ΡΠΆΠΈΡ, ΡΡΠΎΠ±Ρ ΠΏΠΎΠ»ΡΡΠ°ΡΡ, Π²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎ Ρ ΡΠ°Π½ΠΈΡΡ, ΠΈ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»ΡΡΡ ΠΊΠΎΠΌΠΏΡΡΡΠ΅ΡΠ½ΠΎΠ΅ ΡΠ»ΠΎΠ²ΠΎ ΠΊΠ°ΠΊ ΡΡΡΠΎΠΊΡ ΠΈΠ· 1 ΠΈ 0. Π Π΅Π³ΠΈΡΡΡ ΡΠ΄Π΅Π»Π°Π½ ΠΈΠ· ΡΡΠΈΠ³Π³Π΅ΡΠ°, ΠΊΠ°ΠΆΠ΄ΡΠΉ ΡΡΠΈΠ³Π³Π΅Ρ ΡΠΏΠΎΡΠΎΠ±Π΅Π½ ΠΎΠ±ΡΠ°Π±Π°ΡΡΠ²Π°ΡΡ ΠΎΠ΄ΠΈΠ½ Π±ΠΈΡ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΈ ΠΎΠ΄Π½ΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎ (1 ΠΈΠ»ΠΈ 0). ΠΠ»ΠΈΠ½Π° (ΠΈΠ»ΠΈ ΡΠΈΡΠΈΠ½Π°) ΡΠ΅Π³ΠΈΡΡΡΠ° ΡΠ°ΠΊΠ°Ρ ΠΆΠ΅ ΠΊΠ°ΠΊ ΡΠ°Π·ΠΌΠ΅Ρ ΡΠ»ΠΎΠ²Π°, ΠΊΠΎΡΠΎΡΠΎΠ΅ ΠΎΠ½ Ρ ΡΠ°Π½ΠΈΡ. Π’Π°ΠΊΠΈΠΌ ΠΎΠ±ΡΠ°Π·ΠΎΠΌ, 8-Π±ΠΈΡΠΎΠ²ΡΠΉ ΡΠ΅Π³ΠΈΡΡΡ ΡΠΎΡΡΠΎΠΈΡ ΠΈΠ· Π²ΠΎΡΡΠΌΠΈ ΡΡΠΈΠ³Π³Π΅ΡΠΎΠ² ΠΈ ΠΌΠΎΠΆΠ΅Ρ ΠΎΠ±ΡΠ°Π±Π°ΡΡΠ²Π°ΡΡ 8-Π±ΠΈΡΠΎΠ²ΠΎΠ΅ ΡΠ»ΠΎΠ²ΠΎ.
ΠΠΏΠ΅ΡΠ°Π½Π΄ - ΡΠΈΡΠ»ΠΎ ΠΈΠ»ΠΈ ΡΠΈΠΌΠ²ΠΎΠ», ΠΊΠΎΡΠΎΡΡΠΉ Π΄ΠΎΠ»ΠΆΠ΅Π½ Π±ΡΡΡ ΠΏΡΠ΅Π΄ΠΌΠ΅ΡΠΎΠΌ Π°ΡΠΈΡΠΌΠ΅ΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΎΠΏΠ΅ΡΠ°ΡΠΈΠΈ. ΠΠ°ΠΏΡΠΈΠΌΠ΅Ρ, Π² Π²ΡΡΠ°ΠΆΠ΅Π½ΠΈΠΈ
y = a+ b
ΠΈΠ»ΠΈ
w = 2k - 1
ΠΎΠΏΠ΅ΡΠ°Π½Π΄Ρ - a, b, 2, k, ΠΈ 1. Π’ΠΈΠΏΠΈΡΠ½ΡΠΉ ΠΏΡΠΈΠΌΠ΅Ρ ΠΎΠΏΠ΅ΡΠ°Π½Π΄ΠΎΠ², Π²ΠΎΠ²Π»Π΅ΡΠ΅Π½Π½ΡΡ Π² ΠΎΠ±ΡΠ°Π±ΠΎΡΠΊΡ Π΄Π°Π½Π½ΡΡ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠ°ΠΌΠΈ - Π±Π°ΠΉΡ.
ΠΠ»ΠΎΠΊ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ "ΠΊΠΎΠΎΡΠ΄ΠΈΠ½ΠΈΡΡΠ΅Ρ" ΠΎΠΏΠ΅ΡΠ°ΡΠΈΡ Π°ΡΠΈΡΠΌΠ΅ΡΠΈΡΠ΅ΡΠΊΠΈ-Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΡΡΡΠΎΠΉΡΡΠ²Π° ΠΈ Π²Π½ΡΡΡΠ΅Π½Π½ΠΈΡ ΡΠ΅Π³ΠΈΡΡΡΠ°ΡΠΎΡΠΎΠ² Π²ΠΎ Π²ΡΠ΅ΠΌΡ Π²ΡΠΏΠΎΠ»Π½Π΅Π½ΠΈΡ ΠΊΠΎΠΌΠ°Π½Π΄Ρ. ΠΠ°ΠΆΠ΄ΠΎΠ΅ ΡΠ»ΠΎΠ²ΠΎ ΠΊΠΎΠΌΠ°Π½Π΄Ρ ΡΠΎΡΡΠΎΠΈΡ ΠΈΠ· Π΄Π²ΡΡ ΡΠ°ΡΡΠ΅ΠΉ, ΠΊΠΎΠ΄ ΠΎΠΏΠ΅ΡΠ°ΡΠΈΠΈ (op ΠΊΠΎΠ΄) ΠΈ ΠΎΠΏΠ΅ΡΠ°Π½Π΄. ΠΠΎΠ΄ op "Π³ΠΎΠ²ΠΎΡΠΈΡ" Π±Π»ΠΎΠΊΡ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ, ΠΊΠ°ΠΊΠΈΠ΅ ΡΠΈΠ³Π½Π°Π»Ρ ΠΎΠ½ Π΄ΠΎΠ»ΠΆΠ΅Π½ Π³Π΅Π½Π΅ΡΠΈΡΠΎΠ²Π°ΡΡ Π΄Π»Ρ ΠΏΡΠΎΠ²Π΅ΡΠΊΠΈ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠΎΠ². ΠΠΏΠ΅ΡΠ°Π½Π΄ ΠΏΠΎΡΡΠ°Π²Π»ΡΠ΅Ρ Π·Π°ΠΊΠΎΠ΄ΠΈΡΠΎΠ²Π°Π½Π½ΡΡ ΠΈΠ½Π΄ΠΈΠΊΠ°ΡΠΈΡ (ΡΠΎ Π΅ΡΡΡ Π°Π΄ΡΠ΅Ρ), ΠΊΠΎΡΠΎΡΡΠΉ Π³ΠΎΠ²ΠΎΡΠΈΡ, Π³Π΄Π΅ Π»ΡΠ±ΡΠ΅ Π΄Π°Π½Π½ΡΠ΅, ΠΊΠΎΡΠΎΡΡΠ΅ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΡΡΡΡ ΠΈΠ»ΠΈ Π΄ΠΎΠ»ΠΆΠ½Ρ Π±ΡΡΡ Π½Π°ΠΉΠ΄Π΅Π½Ρ ΠΈ Π·Π°ΠΏΠΈΡΠ°Π½Ρ Π² ΠΏΠ°ΠΌΡΡΡ.
ΠΠ½ΡΡΡΠ΅Π½Π½ΠΈΠ΅ ΡΠ΅Π³ΠΈΡΡΡΠ°ΡΠΎΡΡ, ΠΊΠΎΡΠΎΡΡΠ΅ ΡΠ°Π·Π²ΠΎΡΠ°ΡΠΈΠ²Π°ΡΡ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΠΈ Π°ΡΠΈΡΠΌΠ΅ΡΠΈΠΊΠΎ-Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΡΡΡΠΎΠΉΡΡΠ²Π°, ΡΠ»ΡΠΆΠ°Ρ Π²Π½ΡΡΡΠ΅Π½Π½Π΅ΠΉ ΠΏΠ°ΠΌΡΡΡΡ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠ° - ΠΎΠ½ΠΈ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΡΡΡΡ Π΄Π»Ρ Π²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠΉ ΠΏΠ°ΠΌΡΡΠΈ Π΄Π°Π½Π½ΡΡ ΠΈ ΠΊΠΎΠΌΠ°Π½Π΄. ΠΠ½ΠΈ ΠΌΠΎΠ³ΡΡ ΡΠ°ΠΊΠΆΠ΅ Π²ΡΠΏΠΎΠ»Π½ΡΡΡ Π½Π΅ΠΊΠΎΡΠΎΡΡΠ΅ ΠΎΠΏΠ΅ΡΠ°ΡΠΈΠΈ ΠΎΠ±ΡΠ°Π±ΠΎΡΠΊΠΈ Π΄Π°Π½Π½ΡΡ . ΠΠ°ΠΊ ΠΏΡΠ°Π²ΠΈΠ»ΠΎ, Π²Π½ΡΡΡΠ΅Π½Π½ΠΈΠΉ ΡΠ°Π·Π΄Π΅Π» ΡΠ΅Π³ΠΈΡΡΡΠ°, Π²ΠΊΠ»ΡΡΠ°Π΅Ρ ΡΠ½ΠΈΠ²Π΅ΡΡΠ°Π»ΡΠ½ΡΠ΅ ΡΠ΅Π³ΠΈΡΡΡΡ ΠΈ ΡΠ΅Π³ΠΈΡΡΡΡ ΡΠΏΠ΅ΡΠΈΠ°Π»ΡΠ½ΠΎΠ³ΠΎ Π½Π°Π·Π½Π°ΡΠ΅Π½ΠΈΡ ΡΠΈΠΏΠ° ΡΡΠΌΠΌΠ°ΡΠΎΡΠ°, ΡΠ΅Π³ΠΈΡΡΡ Π°Π΄ΡΠ΅ΡΠ° ΠΏΠ°ΠΌΡΡΠΈ, ΡΠ΅Π³ΠΈΡΡΡ Π΄Π°Π½Π½ΡΡ Π·Π°ΠΏΠΎΠΌΠΈΠ½Π°ΡΡΠ΅Π³ΠΎ ΡΡΡΡΠΎΠΉΡΡΠ²Π°, ΡΡΠ΅ΡΡΠΈΠΊ ΠΊΠΎΠΌΠ°Π½Π΄, ΡΠ΅Π³ΠΈΡΡΡ Π² ΡΡΠ΅ΠΊΠ° ΠΈ ΡΠ΅Π³ΠΈΡΡΡ ΡΠΎΡΡΠΎΡΠ½ΠΈΡ.
Π£Π½ΠΈΠ²Π΅ΡΡΠ°Π»ΡΠ½ΡΠ΅ ΡΠ΅Π³ΠΈΡΡΡΡ, ΡΠ΅Π³ΠΈΡΡΡ ΠΎΠ±ΡΠ΅Π³ΠΎ Π½Π°Π·Π½Π°ΡΠ΅Π½ΠΈΡ, ΠΌΠΎΠΆΠ΅Ρ Π±ΡΡΡ ΠΎΡ 4 Π΄ΠΎ 64, ΠΎΠΏΡΠ΅Π΄Π΅Π»ΡΠ΅Ρ Π΄ΠΎ Π½Π΅ΠΊΠΎΡΠΎΡΠΎΠΉ ΡΡΠ΅ΠΏΠ΅Π½ΠΈ Π²ΡΡΠΈΡΠ»ΠΈΡΠ΅Π»ΡΠ½ΡΠ΅ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΠΈ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠΎΠ². ΠΠ½ΠΈ ΠΏΡΠ΅ΠΆΠ΄Π΅ Π²ΡΠ΅Π³ΠΎ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΡΡΡΡ Π΄Π»Ρ ΠΌΠ°Π½ΠΈΠΏΡΠ»ΡΡΠΈΠΈ ΠΈ Π²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠΉ ΠΏΠ°ΠΌΡΡΠΈ Π΄Π°Π½Π½ΡΡ . ΠΡ Π½Π°Π·ΡΠ²Π°ΡΡ "ΡΠ°Π±ΠΎΡΠΈΠΌΠΈ ΡΠ΅Π³ΠΈΡΡΡΠ°ΠΌΠΈ" ΠΏΠ°ΠΌΡΡΠΈ ΠΊΠ»Π°Π²ΠΈΠ°ΡΡΡΡ.
Π‘ΡΠΌΠΌΠ°ΡΠΎΡ ΠΏΠΎΠ΄ΠΎΠ±Π½ΠΎ ΠΊΠ»Π°Π²ΠΈΠ°ΡΡΡΠ΅ ΡΠ»ΡΠΆΠΈΡ Π΄Π»Ρ Π°ΡΠΈΡΠΌΠ΅ΡΠΈΡΠ΅ΡΠΊΠΈΡ , Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ ΠΎΠΏΠ΅ΡΠ°ΡΠΈΠΉ ΠΈ ΠΎΠΏΠ΅ΡΠ°ΡΠΈΠΉ Π²Π²ΠΎΠ΄Π°-Π²ΡΠ²ΠΎΠ΄Π°. Π Π±ΠΎΠ»ΡΡΠΈΠ½ΡΡΠ²Π΅ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠΎΠ² ΡΡΠΌΠΌΠ°ΡΠΎΡ ΡΠ°ΠΊΠΆΠ΅ ΡΠΎΡ ΡΠ°Π½ΡΠ΅Ρ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΡ ΠΎΠΏΠ΅ΡΠ°ΡΠΈΠΉ, ΠΊΠΎΡΠΎΡΡΠ΅ Π·Π°ΠΌΠ΅Π½ΡΡΡ ΠΎΠΏΠ΅ΡΠ°Π½Π΄, ΠΊΠΎΡΠΎΡΡΠΉ Π±ΡΠ» ΠΏΠ΅ΡΠ²ΠΎΠ½Π°ΡΠ°Π»ΡΠ½ΠΎ ΡΠΎΡ ΡΠ°Π½Π΅Π½ ΡΠ°ΠΌ. ΠΠ±ΡΡΠ½ΠΎ, ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΡΠ΅ ΡΠ»ΠΎΠ²Π°, Π²ΡΠ±ΡΠ°Π½Π½ΡΠ΅ ΠΈΠ· ΠΏΠ°ΠΌΡΡΠΈ ΠΈ ΡΠ»ΠΎΠ²Π°, ΠΊΠΎΡΠΎΡΡΠ΅ Π±ΡΠ΄ΡΡ Π·Π°ΠΏΠΈΡΠ°Π½Ρ Π² ΠΏΠ°ΠΌΡΡΡ, ΡΠ½Π°ΡΠ°Π»Π° Π·Π°Π³ΡΡΠΆΠ°ΡΡΡΡ Π² ΡΡΠΌΠΌΠ°ΡΠΎΡ. Π Π°Π·ΠΌΠ΅Ρ (ΠΈΠ»ΠΈ ΡΠΈΡΠΈΠ½Π°) ΡΡΠΌΠΌΠ°ΡΠΎΡΠ° ΡΠ° ΠΆΠ΅ ΡΠ°ΠΌΠ°Ρ ΠΊΠ°ΠΊ ΠΈ ΡΠ°Π·ΠΌΠ΅Ρ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ ΡΠ»ΠΎΠ²Π° (Π² Π½Π°ΡΠ΅ΠΌ ΠΏΡΠΈΠΌΠ΅ΡΠ΅, ΡΡΠΌΠΌΠ°ΡΠΎΡ 8 Π±ΠΈΡΠΎΠ² ΡΠΈΡΠΈΠ½ΠΎΠΉ). ΠΠ΅ΠΊΠΎΡΠΎΡΡΠ΅ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΡ ΠΌΠΎΠ³ΡΡ ΠΈΠΌΠ΅ΡΡ Π΄Π²Π° ΠΈΠ»ΠΈ Π±ΠΎΠ»ΡΡΠ΅ ΡΡΠΌΠΌΠ°ΡΠΎΡΠ° - ΡΡΠΎ ΡΠ°ΡΡΠΈΡΡΠ΅Ρ ΠΈΡ Π³ΠΈΠ±ΠΊΠΎΡΡΡ ΠΈ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΡ Π² ΡΠ΅ΡΠ΅Π½ΠΈΠΈ Π·Π°Π΄Π°Ρ.
Π Π΅Π³ΠΈΡΡΡ Π°Π΄ΡΠ΅ΡΠ° ΠΏΠ°ΠΌΡΡΠΈ, ΡΠΏΠ΅ΡΠΈΠ°Π»ΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Π½ΡΠΉ ΡΠ΅Π³ΠΈΡΡΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΠ΅ΠΌΡΠΉ Π΄Π»Ρ Ρ ΡΠ°Π½Π΅Π½ΠΈΡ Π°Π΄ΡΠ΅ΡΠ° ΡΠ»ΠΎΠ²Π°, ΠΊΠΎΡΠΎΡΠΎΠ΅ Π±ΡΠ΄Π΅Ρ Π²ΡΠ±ΡΠ°Π½ΠΎ ΠΈΠ»ΠΈ Π·Π°Π³ΡΡΠΆΠ΅Π½ΠΎ Π² ΠΏΠ°ΠΌΡΡΡ ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡΠ°, ΠΈΠ»ΠΈ Π½Π΅ΠΊΠΎΡΠΎΡΡΠΉ Π΄ΡΡΠ³ΠΎΠΉ ΡΠ΅Π³ΠΈΡΡΡ ΠΏΡΠ΅ΠΆΠ΄Π΅, ΡΠ΅ΠΌ ΠΎΠ½ΠΎ Π²ΠΎΠΉΠ΄ΡΡ Π² Π°Π΄ΡΠ΅ΡΠ½ΡΡ ΡΠΈΠ½Ρ. ΠΠ°ΠΊΡΠΈΠΌΠ°Π»ΡΠ½ΠΎΠ΅ ΡΠΈΡΠ»ΠΎ Π½Π΅ΠΏΠΎΡΡΠ΅Π΄ΡΡΠ²Π΅Π½Π½ΠΎ Π°Π΄ΡΠ΅ΡΡΠ΅ΠΌΡΡ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΡΡ ΡΠ»ΠΎΠ² Π² ΠΏΠ°ΠΌΡΡΡ Π·Π°Π²ΠΈΡΠΈΡ ΠΎΡ ΡΠ°Π·ΠΌΠ΅ΡΠ° ΡΠ΅Π³ΠΈΡΡΡΠ° Π°Π΄ΡΠ΅ΡΠ° ΠΏΠ°ΠΌΡΡΠΈ. ΠΠ°ΠΏΡΠΈΠΌΠ΅Ρ, ΠΏΠ΅ΡΠ΅ΡΡΡΠ°ΠΈΠ²Π°Ρ 0 ΠΈ 1 Π² ΡΠ°Π·Π»ΠΈΡΠ½ΡΡ Π±ΠΈΡΠ°Ρ Π΄Π²ΡΡ -Π±Π°ΠΉΡΠΎΠ²ΠΎΠ³ΠΎ ΡΠ»ΠΎΠ²Π° ΠΌΡ ΠΌΠΎΠΆΠ΅ΠΌ ΡΠΎΡ ΡΠ°Π½ΠΈΡΡ 216 = 65 536 Π°Π΄ΡΠ΅ΡΠΎΠ² ΡΠ°Π·ΠΌΠ΅ΡΠ΅Π½ΠΈΠΉ ΡΠ»ΠΎΠ²Π° Π² 16-ΡΠ°Π·ΡΡΠ΄Π½ΠΎΠΌ ΡΠ΅Π³ΠΈΡΡΡΠ΅ Π°Π΄ΡΠ΅ΡΠ° ΠΏΠ°ΠΌΡΡΠΈ.
Π Π΅Π³ΠΈΡΡΡ ΠΏΠ°ΠΌΡΡΠΈ Π΄Π°Π½Π½ΡΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΠ΅ΡΡΡ, ΡΡΠΎΠ±Ρ Ρ ΡΠ°Π½ΠΈΡΡ Π°Π΄ΡΠ΅Ρ ΡΠ»ΠΎΠ²Π°. Π¨ΠΈΡΠΈΠ½Π° ΡΡΠΎΠ³ΠΎ ΡΠ΅Π³ΠΈΡΡΡΠ° ΡΠ°ΠΊΠ°Ρ ΠΆΠ΅ ΠΊΠ°ΠΊ ΠΈ ΡΠ°Π·ΠΌΠ΅Ρ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ ΡΠ»ΠΎΠ²Π° ( 8-Π±ΠΈΡΠΎΠ²ΡΠΉ ΡΠ΅Π³ΠΈΡΡΡ Π΄Π°Π½Π½ΡΡ Π·Π°ΠΏΠΎΠΌΠΈΠ½Π°ΡΡΠ΅Π³ΠΎ ΡΡΡΡΠΎΠΉΡΡΠ²Π°, ΡΡΠΎΠ±Ρ ΡΠΎΡ ΡΠ°Π½ΠΈΡΡ ΠΎΠ΄Π½ΠΎΠ±Π°ΠΉΡΠΎΠ²ΠΎΠ΅ ΡΠ»ΠΎΠ²ΠΎ, ΠΈ 16-ΡΠ°Π·ΡΡΠ΄Π½ΡΠΉ ΡΠ΅Π³ΠΈΡΡΡ ΠΏΠ°ΠΌΡΡΠΈ Π΄Π°Π½Π½ΡΡ Π΄Π»Ρ Π΄Π²ΡΡ -Π±Π°ΠΉΡΠΎΠ²ΠΎΠ³ΠΎ ΡΠ»ΠΎΠ²Π°).
Π‘ΡΠ΅ΡΡΠΈΠΊ ΠΊΠΎΠΌΠ°Π½Π΄Ρ ΡΠ΅Π³ΠΈΡΡΡ, ΠΊΠΎΡΠΎΡΡΠΉ ΡΠΎΠ΄Π΅ΡΠΆΠΈΡ Π°Π΄ΡΠ΅Ρ ΠΏΠ°ΠΌΡΡΠΈ ΡΠ»Π΅Π΄ΡΡΡΠ΅Π³ΠΎ ΡΠ»ΠΎΠ²Π° ΠΊΠΎΠΌΠ°Π½Π΄Ρ, ΠΊΠΎΡΠΎΡΠ°Ρ Π±ΡΠ΄Π΅Ρ Π²ΡΠΏΠΎΠ»Π½Π΅Π½Π°. ΠΠ°ΠΊ ΠΏΡΠ°Π²ΠΈΠ»ΠΎ, ΠΊΠΎΠΌΠ°Π½Π΄Ρ ΡΠΏΠ΅ΡΠΈΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΡ ΡΠΎΡ ΡΠ°Π½Π΅Π½Ρ Π² ΠΏΠΎΡΠ»Π΅Π΄ΠΎΠ²Π°ΡΠ΅Π»ΡΠ½ΡΡ ΠΌΠ΅ΡΡΠΎΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΡ ΠΏΠ°ΠΌΡΡΠΈ: Π΄Π»Ρ ΠΎΠ΄Π½ΠΎΠ±Π°ΠΉΡΠΎΠ²ΠΎΠΉ ΠΊΠΎΠΌΠ°Π½Π΄Ρ ΡΠΈΡΠ»ΠΎ, Π΄Π°ΡΡΠ΅Π΅ Π°Π΄ΡΠ΅Ρ ΠΊΠ°ΠΆΠ΄ΠΎΠ³ΠΎ ΡΠ»Π΅Π΄ΡΡΡΠ΅Π³ΠΎ ΡΠ°Π·ΠΌΠ΅ΡΠ΅Π½ΠΈΡ Π·Π°ΠΏΠΎΠΌΠΈΠ½Π°ΡΡΠ΅Π³ΠΎ ΡΡΡΡΠΎΠΉΡΡΠ²Π° ΠΎΠ΄Π½ΠΈΠΌ Π±ΠΎΠ»ΡΡΠ΅ ΡΠ΅ΠΌ ΠΈΠ· ΡΠ΅ΠΊΡΡΠ΅Π³ΠΎ ΠΌΠ΅ΡΡΠΎΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΡ. ΠΠ°ΠΆΠ΄ΡΠΉ ΡΠ°Π·, ΠΊΠΎΠ³Π΄Π° ΠΌΠΈΠΊΡΠΎΠΏΡΠΎΡΠ΅ΡΡΠΎΡ ΠΎΠ±ΡΠ°ΡΠ°Π΅ΡΡΡ ΠΊ ΠΏΠ°ΠΌΡΡΠΈ, ΡΡΠ΅ΡΡΠΈΠΊ ΠΊΠΎΠΌΠ°Π½Π΄ ΡΠ²Π΅Π»ΠΈΡΠΈΠ²Π°Π΅ΡΡΡ Π½Π° ΠΎΠ΄ΠΈΠ½, ΡΡΠΎΠ±Ρ ΡΠΊΠ°Π·Π°ΡΡ Π½Π° ΠΌΠ΅ΡΡΠΎΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΠ΅ ΠΏΠ°ΠΌΡΡΠΈ, ΠΎΡ ΠΊΠΎΡΠΎΡΠΎΠ³ΠΎ Π΄ΠΎΠ»ΠΆΠ½Π° Π±ΡΡΡ Π²ΡΠ±ΡΠ°Π½Π° ΡΠ»Π΅Π΄ΡΡΡΠ°Ρ ΠΊΠΎΠΌΠ°Π½Π΄Π°.
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