363 research outputs found
TFI-FTS: An efficient transient fault injection and fault-tolerant system for asynchronous circuits on FPGA platform
Designing VLSI digital circuits is challenging tasks because of testing the circuits concerning design time. The reliability and productivity of digital integrated circuits are primarily affected by the defects in the manufacturing process or systems. If the defects are more in the systems, which leads the fault in the systems. The fault tolerant systems are necessary to overcome the faults in the VLSI digital circuits. In this research article, an asynchronous circuits based an effective transient fault injection (TFI) and fault tolerant system (FTS) are modelled. The TFI system generates the faults based on BMA based LFSR with faulty logic insertion and one hot encoded register. The BMA based LFSR reduces the hardware complexity with less power consumption on-chip than standard LFSR method. The FTS uses triple mode redundancy (TMR) based majority voter logic (MVL) to tolerant the faults for asynchronous circuits. The benchmarked 74X-series circuits are considered as an asynchronous circuit for TMR logic. The TFI-FTS module is modeled using Verilog-HDL on Xilinx-ISE and synthesized on hardware platform. The Performance parameters are tabulated for TFI-FTS based asynchronous circuits. The performance of TFI-FTS Module is analyzed with 100% fault coverage. The fault coverage is validated using functional simulation of each asynchronous circuit with fault injection in TFI-FTS Module
Investigations into the feasibility of an on-line test methodology
This thesis aims to understand how information coding and the protocol that it
supports can affect the characteristics of electronic circuits. More specifically, it
investigates an on-line test methodology called IFIS (If it Fails It Stops) and its
impact on the design, implementation and subsequent characteristics of circuits
intended for application specific lC (ASIC) technology.
The first study investigates the influences of information coding and protocol on the
characteristics of IFIS systems. The second study investigates methods of circuit
design applicable to IFIS cells and identifies theΒ· technique possessing the
characteristics most suitable for on-line testing. The third study investigates the
characteristics of a 'real-life' commercial UART re-engineered using the techniques
resulting from the previous two studies. The final study investigates the effects of the
halting properties endowed by the protocol on failure diagnosis within IFIS systems.
The outcome of this work is an identification and characterisation of the factors that
influence behaviour, implementation costs and the ability to test and diagnose IFIS
designs
ΠΠ΅ΡΠΎΠ΄ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΡΠ½ΠΊΡΠΈΠΎΠ½Π°Π»ΡΠ½ΠΎΠΉ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ ΡΠ°Π±ΠΎΡΠΈΡ Π²ΡΡ ΠΎΠ΄ΠΎΠ² Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ ΠΊΠΎΠΌΠ±ΠΈΠ½Π°ΡΠΈΠΎΠ½Π½ΡΡ ΡΡ Π΅ΠΌ ΠΎΡ ΠΏΡΠΎΡΠ²Π»Π΅Π½ΠΈΡ ΠΌΠΎΠ½ΠΎΡΠΎΠ½Π½ΡΡ ΠΎΡΠΈΠ±ΠΎΠΊ
Structural dependences of the working outputs of logical combinational circuits were studied with the aim of subsequent identification of the type of possible errors. The types of manifested errors and the classification of the working outputs of logical combinational circuits are given. It is shown that the presence of an internal structural connection of discrete devices leads to an increase in the multiplicity of possible errors. The condition for determining the functional dependence of outputs on the manifestation of errors of the studied multiplicity is given. It is noted that out of the many types of errors, unidirectional errors can appear at the outputs of the circuits. A well-known method for determining unidirectionally dependent operating outputs of discrete device circuits is presented, which has a drawback. It is only necessary to pairwise compare each output with the rest of the whole set. For the convenience of the process of searching for such outputs, the author of the article proposed a new method for identifying unidirectionally dependent working outputs. This method differs from known methods in that it is applicable for any number of outputs, which requires much less time to search for the above outputs. It is shown that logical combinational circuits can have functional features, in which only unidirectional errors can appear at the working outputs. Therefore, a new method for identifying any number of unidirectionally independent operating outputs of combinational circuits has been proposed. It is shown that the methods proposed in the article for finding unidirectionally dependent and unidirectionally independent outputs of logical combinational circuits require simple mathematical calculations. In the Multisim, internal faults of the diagnosable circuits are simulated and all possible errors at the working outputs are fixed. According to the results of the experiments, the validity of the theoretical results obtained was also confirmed.Π ΡΠ°Π±ΠΎΡΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½Ρ ΡΡΡΡΠΊΡΡΡΠ½ΡΠ΅ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ ΡΠ°Π±ΠΎΡΠΈΡ
Π²ΡΡ
ΠΎΠ΄ΠΎΠ² Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΊΠΎΠΌΠ±ΠΈΠ½Π°ΡΠΈΠΎΠ½Π½ΡΡ
ΡΡ
Π΅ΠΌ Ρ ΡΠ΅Π»ΡΡ ΠΏΠΎΡΠ»Π΅Π΄ΡΡΡΠ΅ΠΉ ΠΈΠ΄Π΅Π½ΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ Π²ΠΈΠ΄Π° Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΡΡ
ΠΎΡΠΈΠ±ΠΎΠΊ. ΠΡΠΈΠ²Π΅Π΄Π΅Π½Ρ Π²ΠΈΠ΄Ρ Π²ΠΎΠ·Π½ΠΈΠΊΠ°ΡΡΠΈΡ
ΠΎΡΠΈΠ±ΠΎΠΊ ΠΈ ΠΊΠ»Π°ΡΡΠΈΡΠΈΠΊΠ°ΡΠΈΡ ΡΠ°Π±ΠΎΡΠΈΡ
Π²ΡΡ
ΠΎΠ΄ΠΎΠ² Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΊΠΎΠΌΠ±ΠΈΠ½Π°ΡΠΈΠΎΠ½Π½ΡΡ
ΡΡ
Π΅ΠΌ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ Π½Π°Π»ΠΈΡΠΈΠ΅ Π²Π½ΡΡΡΠ΅Π½Π½Π΅ΠΉ ΡΡΡΡΠΊΡΡΡΠ½ΠΎΠΉ ΡΠ²ΡΠ·ΠΈ Π΄ΠΈΡΠΊΡΠ΅ΡΠ½ΡΡ
ΡΡΡΡΠΎΠΉΡΡΠ² ΠΏΡΠΈΠ²ΠΎΠ΄ΠΈΡ ΠΊ ΡΠ²Π΅Π»ΠΈΡΠ΅Π½ΠΈΡ ΠΊΡΠ°ΡΠ½ΠΎΡΡΠΈ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΡΡ
ΠΎΡΠΈΠ±ΠΎΠΊ. ΠΡΠΈΠ²ΠΎΠ΄ΠΈΡΡΡ ΡΡΠ»ΠΎΠ²ΠΈΠ΅ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΡΠ½ΠΊΡΠΈΠΎΠ½Π°Π»ΡΠ½ΠΎΠΉ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ Π²ΡΡ
ΠΎΠ΄ΠΎΠ² ΠΎΡ ΠΏΡΠΎΡΠ²Π»Π΅Π½ΠΈΡ ΠΎΡΠΈΠ±ΠΎΠΊ ΠΈΡΡΠ»Π΅Π΄ΡΠ΅ΠΌΠΎΠΉ ΠΊΡΠ°ΡΠ½ΠΎΡΡΠΈ. ΠΡΠΌΠ΅ΡΠ΅Π½ΠΎ, ΡΡΠΎ ΠΈΠ· ΠΌΠ½ΠΎΠΆΠ΅ΡΡΠ²Π° Π²ΠΈΠ΄ΠΎΠ² ΠΎΡΠΈΠ±ΠΎΠΊ, Π½Π° Π²ΡΡ
ΠΎΠ΄Π°Ρ
ΡΡ
Π΅ΠΌ ΠΌΠΎΠ³ΡΡ ΠΏΡΠΎΡΠ²Π»ΡΡΡΡΡ ΠΎΠ΄Π½ΠΎΠ½Π°ΠΏΡΠ°Π²Π»Π΅Π½Π½ΡΠ΅ (ΠΌΠΎΠ½ΠΎΡΠΎΠ½Π½ΡΠ΅) ΠΎΡΠΈΠ±ΠΊΠΈ. ΠΡΠΈΠ²Π΅Π΄Π΅Π½ ΠΈΠ·Π²Π΅ΡΡΠ½ΡΠΉ ΠΌΠ΅ΡΠΎΠ΄ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΠΌΠΎΠ½ΠΎΡΠΎΠ½Π½ΠΎ Π·Π°Π²ΠΈΡΠΈΠΌΡΡ
ΡΠ°Π±ΠΎΡΠΈΡ
Π²ΡΡ
ΠΎΠ΄ΠΎΠ² Π΄ΠΈΡΠΊΡΠ΅ΡΠ½ΡΡ
ΡΡΡΡΠΎΠΉΡΡΠ² ΠΈ ΡΠΊΠ°Π·Π°Π½ Π΅Π³ΠΎ Π½Π΅Π΄ΠΎΡΡΠ°ΡΠΎΠΊ, Π·Π°ΠΊΠ»ΡΡΠ°ΡΡΠΈΠΉΡΡ Π² Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎΡΡΠΈ ΡΠΎΠ»ΡΠΊΠΎ ΠΏΠΎΠΏΠ°ΡΠ½ΠΎΠ³ΠΎ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ ΠΊΠ°ΠΆΠ΄ΠΎΠ³ΠΎ Π²ΡΡ
ΠΎΠ΄Π° Ρ ΠΎΡΡΠ°Π»ΡΠ½ΡΠΌΠΈ ΠΈΠ· ΡΠ΅Π»ΠΎΠ³ΠΎ ΠΌΠ½ΠΎΠΆΠ΅ΡΡΠ²Π°. ΠΠ»Ρ ΡΠ΄ΠΎΠ±ΡΡΠ²Π° ΠΏΡΠΎΡΠ΅ΡΡΠ° ΠΏΠΎΠΈΡΠΊΠ° ΠΏΠΎΠ΄ΠΎΠ±Π½ΡΡ
Π²ΡΡ
ΠΎΠ΄ΠΎΠ² Π°Π²ΡΠΎΡΠΎΠΌ ΡΡΠ°ΡΡΠΈ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ Π½ΠΎΠ²ΡΠΉ ΠΌΠ΅ΡΠΎΠ΄ ΠΈΠ΄Π΅Π½ΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ ΠΌΠΎΠ½ΠΎΡΠΎΠ½Π½ΠΎ Π·Π°Π²ΠΈΡΠΈΠΌΡΡ
ΡΠ°Π±ΠΎΡΠΈΡ
Π²ΡΡ
ΠΎΠ΄ΠΎΠ², ΠΎΡΠ»ΠΈΡΠ°ΡΡΠΈΠΉΡΡ ΠΎΡ ΠΈΠ·Π²Π΅ΡΡΠ½ΡΡ
ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ² ΡΠ΅ΠΌ, ΡΡΠΎ Π΄Π°Π½Π½ΡΠΉ ΠΌΠ΅ΡΠΎΠ΄ ΠΏΡΠΈΠΌΠ΅Π½ΠΈΠΌ Π΄Π»Ρ Π»ΡΠ±ΠΎΠ³ΠΎ ΡΠΈΡΠ»Π° Π²ΡΡ
ΠΎΠ΄ΠΎΠ², ΡΡΠΎ ΡΡΠ΅Π±ΡΠ΅Ρ Π·Π½Π°ΡΠΈΡΠ΅Π»ΡΠ½ΠΎ ΠΌΠ΅Π½ΡΡΠ΅Π³ΠΎ Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ Π΄Π»Ρ ΠΏΠΎΠΈΡΠΊΠ° Π²ΡΡΠ΅ΠΏΡΠΈΠ²Π΅Π΄Π΅Π½Π½ΡΡ
Π²ΡΡ
ΠΎΠ΄ΠΎΠ². ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΊΠΎΠΌΠ±ΠΈΠ½Π°ΡΠΈΠΎΠ½Π½ΡΠ΅ ΡΡ
Π΅ΠΌΡ ΠΌΠΎΠ³ΡΡ ΠΎΠ±Π»Π°Π΄Π°ΡΡ ΡΡΠ½ΠΊΡΠΈΠΎΠ½Π°Π»ΡΠ½ΡΠΌΠΈ ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΡΠΌΠΈ, ΠΏΡΠΈ ΠΊΠΎΡΠΎΡΡΡ
Π½Π° ΡΠ°Π±ΠΎΡΠΈΡ
Π²ΡΡ
ΠΎΠ΄Π°Ρ
ΠΌΠΎΠ³ΡΡ ΠΏΡΠΎΡΠ²Π»ΡΡΡΡΡ ΡΠΎΠ»ΡΠΊΠΎ ΠΌΠΎΠ½ΠΎΡΠΎΠ½Π½ΡΠ΅ ΠΎΡΠΈΠ±ΠΊΠΈ. Π‘Π»Π΅Π΄ΠΎΠ²Π°ΡΠ΅Π»ΡΠ½ΠΎ, ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ Π½ΠΎΠ²ΡΠΉ ΠΌΠ΅ΡΠΎΠ΄ ΠΈΠ΄Π΅Π½ΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ Π»ΡΠ±ΠΎΠ³ΠΎ ΡΠΈΡΠ»Π° ΠΌΠΎΠ½ΠΎΡΠΎΠ½Π½ΠΎ Π½Π΅Π·Π°Π²ΠΈΡΠΈΠΌΡΡ
ΡΠ°Π±ΠΎΡΠΈΡ
Π²ΡΡ
ΠΎΠ΄ΠΎΠ² ΠΊΠΎΠΌΠ±ΠΈΠ½Π°ΡΠΈΠΎΠ½Π½ΡΡ
ΡΡ
Π΅ΠΌ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ ΠΏΡΠ΅Π΄Π»Π°Π³Π°Π΅ΠΌΡΠ΅ Π² ΡΡΠ°ΡΡΠ΅ ΠΌΠ΅ΡΠΎΠ΄Ρ ΠΏΠΎΠΈΡΠΊΠ° ΠΌΠΎΠ½ΠΎΡΠΎΠ½Π½ΠΎ Π·Π°Π²ΠΈΡΠΈΠΌΡΡ
ΠΈ ΠΌΠΎΠ½ΠΎΡΠΎΠ½Π½ΠΎ Π½Π΅Π·Π°Π²ΠΈΡΠΈΠΌΡΡ
Π²ΡΡ
ΠΎΠ΄ΠΎΠ² Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΊΠΎΠΌΠ±ΠΈΠ½Π°ΡΠΈΠΎΠ½Π½ΡΡ
ΡΡ
Π΅ΠΌ ΡΡΠ΅Π±ΡΡΡ Π²ΡΠΏΠΎΠ»Π½Π΅Π½ΠΈΡ Π½Π΅ΡΠ»ΠΎΠΆΠ½ΡΡ
ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΡ
Π²ΡΡΠΈΡΠ»Π΅Π½ΠΈΠΉ. Π ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ½ΠΎΠΉ ΡΡΠ΅Π΄Π΅ Multisim ΡΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½Ρ Π²Π½ΡΡΡΠ΅Π½Π½ΠΈΠ΅ Π½Π΅ΠΈΡΠΏΡΠ°Π²Π½ΠΎΡΡΠΈ Π΄ΠΈΠ°Π³Π½ΠΎΡΡΠΈΡΡΠ΅ΠΌΡΡ
ΡΡ
Π΅ΠΌ ΠΈ Π·Π°ΡΠΈΠΊΡΠΈΡΠΎΠ²Π°Π½Ρ Π²ΡΠ΅ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΡΠ΅ ΠΎΡΠΈΠ±ΠΊΠΈ Π½Π° ΡΠ°Π±ΠΎΡΠΈΡ
Π²ΡΡ
ΠΎΠ΄Π°Ρ
. ΠΠΎ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ°ΠΌ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠΎΠ² ΡΠ°ΠΊΠΆΠ΅ ΠΏΠΎΠ΄ΡΠ²Π΅ΡΠΆΠ΄Π΅Π½Π° ΡΠΏΡΠ°Π²Π΅Π΄Π»ΠΈΠ²ΠΎΡΡΡ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΡ
ΡΠ΅ΠΎΡΠ΅ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΎΠ²
ΠΠ΅ΡΠΎΠ΄ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΡΠ½ΠΊΡΠΈΠΎΠ½Π°Π»ΡΠ½ΠΎΠΉ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ ΡΠ°Π±ΠΎΡΠΈΡ Π²ΡΡ ΠΎΠ΄ΠΎΠ² Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ ΠΊΠΎΠΌΠ±ΠΈΠ½Π°ΡΠΈΠΎΠ½Π½ΡΡ ΡΡ Π΅ΠΌ ΠΎΡ ΠΏΡΠΎΡΠ²Π»Π΅Π½ΠΈΡ ΠΌΠΎΠ½ΠΎΡΠΎΠ½Π½ΡΡ ΠΎΡΠΈΠ±ΠΎΠΊ
Π ΡΠ°Π±ΠΎΡΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½Ρ ΡΡΡΡΠΊΡΡΡΠ½ΡΠ΅ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ ΡΠ°Π±ΠΎΡΠΈΡ
Π²ΡΡ
ΠΎΠ΄ΠΎΠ² Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΊΠΎΠΌΠ±ΠΈΠ½Π°ΡΠΈΠΎΠ½Π½ΡΡ
ΡΡ
Π΅ΠΌ Ρ ΡΠ΅Π»ΡΡ ΠΏΠΎΡΠ»Π΅Π΄ΡΡΡΠ΅ΠΉ ΠΈΠ΄Π΅Π½ΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ Π²ΠΈΠ΄Π° Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΡΡ
ΠΎΡΠΈΠ±ΠΎΠΊ. ΠΡΠΈΠ²Π΅Π΄Π΅Π½Ρ Π²ΠΈΠ΄Ρ Π²ΠΎΠ·Π½ΠΈΠΊΠ°ΡΡΠΈΡ
ΠΎΡΠΈΠ±ΠΎΠΊ ΠΈ ΠΊΠ»Π°ΡΡΠΈΡΠΈΠΊΠ°ΡΠΈΡ ΡΠ°Π±ΠΎΡΠΈΡ
Π²ΡΡ
ΠΎΠ΄ΠΎΠ² Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΊΠΎΠΌΠ±ΠΈΠ½Π°ΡΠΈΠΎΠ½Π½ΡΡ
ΡΡ
Π΅ΠΌ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ Π½Π°Π»ΠΈΡΠΈΠ΅ Π²Π½ΡΡΡΠ΅Π½Π½Π΅ΠΉ ΡΡΡΡΠΊΡΡΡΠ½ΠΎΠΉ ΡΠ²ΡΠ·ΠΈ Π΄ΠΈΡΠΊΡΠ΅ΡΠ½ΡΡ
ΡΡΡΡΠΎΠΉΡΡΠ² ΠΏΡΠΈΠ²ΠΎΠ΄ΠΈΡ ΠΊ ΡΠ²Π΅Π»ΠΈΡΠ΅Π½ΠΈΡ ΠΊΡΠ°ΡΠ½ΠΎΡΡΠΈ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΡΡ
ΠΎΡΠΈΠ±ΠΎΠΊ. ΠΡΠΈΠ²ΠΎΠ΄ΠΈΡΡΡ ΡΡΠ»ΠΎΠ²ΠΈΠ΅ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΡΠ½ΠΊΡΠΈΠΎΠ½Π°Π»ΡΠ½ΠΎΠΉ Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ Π²ΡΡ
ΠΎΠ΄ΠΎΠ² ΠΎΡ ΠΏΡΠΎΡΠ²Π»Π΅Π½ΠΈΡ ΠΎΡΠΈΠ±ΠΎΠΊ ΠΈΡΡΠ»Π΅Π΄ΡΠ΅ΠΌΠΎΠΉ ΠΊΡΠ°ΡΠ½ΠΎΡΡΠΈ. ΠΡΠΌΠ΅ΡΠ΅Π½ΠΎ, ΡΡΠΎ ΠΈΠ· ΠΌΠ½ΠΎΠΆΠ΅ΡΡΠ²Π° Π²ΠΈΠ΄ΠΎΠ² ΠΎΡΠΈΠ±ΠΎΠΊ, Π½Π° Π²ΡΡ
ΠΎΠ΄Π°Ρ
ΡΡ
Π΅ΠΌ ΠΌΠΎΠ³ΡΡ ΠΏΡΠΎΡΠ²Π»ΡΡΡΡΡ ΠΎΠ΄Π½ΠΎΠ½Π°ΠΏΡΠ°Π²Π»Π΅Π½Π½ΡΠ΅ (ΠΌΠΎΠ½ΠΎΡΠΎΠ½Π½ΡΠ΅) ΠΎΡΠΈΠ±ΠΊΠΈ. ΠΡΠΈΠ²Π΅Π΄Π΅Π½ ΠΈΠ·Π²Π΅ΡΡΠ½ΡΠΉ ΠΌΠ΅ΡΠΎΠ΄ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΠΌΠΎΠ½ΠΎΡΠΎΠ½Π½ΠΎ Π·Π°Π²ΠΈΡΠΈΠΌΡΡ
ΡΠ°Π±ΠΎΡΠΈΡ
Π²ΡΡ
ΠΎΠ΄ΠΎΠ² Π΄ΠΈΡΠΊΡΠ΅ΡΠ½ΡΡ
ΡΡΡΡΠΎΠΉΡΡΠ² ΠΈ ΡΠΊΠ°Π·Π°Π½ Π΅Π³ΠΎ Π½Π΅Π΄ΠΎΡΡΠ°ΡΠΎΠΊ, Π·Π°ΠΊΠ»ΡΡΠ°ΡΡΠΈΠΉΡΡ Π² Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎΡΡΠΈ ΡΠΎΠ»ΡΠΊΠΎ ΠΏΠΎΠΏΠ°ΡΠ½ΠΎΠ³ΠΎ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ ΠΊΠ°ΠΆΠ΄ΠΎΠ³ΠΎ Π²ΡΡ
ΠΎΠ΄Π° Ρ ΠΎΡΡΠ°Π»ΡΠ½ΡΠΌΠΈ ΠΈΠ· ΡΠ΅Π»ΠΎΠ³ΠΎ ΠΌΠ½ΠΎΠΆΠ΅ΡΡΠ²Π°. ΠΠ»Ρ ΡΠ΄ΠΎΠ±ΡΡΠ²Π° ΠΏΡΠΎΡΠ΅ΡΡΠ° ΠΏΠΎΠΈΡΠΊΠ° ΠΏΠΎΠ΄ΠΎΠ±Π½ΡΡ
Π²ΡΡ
ΠΎΠ΄ΠΎΠ² Π°Π²ΡΠΎΡΠΎΠΌ ΡΡΠ°ΡΡΠΈ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ Π½ΠΎΠ²ΡΠΉ ΠΌΠ΅ΡΠΎΠ΄ ΠΈΠ΄Π΅Π½ΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ ΠΌΠΎΠ½ΠΎΡΠΎΠ½Π½ΠΎ Π·Π°Π²ΠΈΡΠΈΠΌΡΡ
ΡΠ°Π±ΠΎΡΠΈΡ
Π²ΡΡ
ΠΎΠ΄ΠΎΠ², ΠΎΡΠ»ΠΈΡΠ°ΡΡΠΈΠΉΡΡ ΠΎΡ ΠΈΠ·Π²Π΅ΡΡΠ½ΡΡ
ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ² ΡΠ΅ΠΌ, ΡΡΠΎ Π΄Π°Π½Π½ΡΠΉ ΠΌΠ΅ΡΠΎΠ΄ ΠΏΡΠΈΠΌΠ΅Π½ΠΈΠΌ Π΄Π»Ρ Π»ΡΠ±ΠΎΠ³ΠΎ ΡΠΈΡΠ»Π° Π²ΡΡ
ΠΎΠ΄ΠΎΠ², ΡΡΠΎ ΡΡΠ΅Π±ΡΠ΅Ρ Π·Π½Π°ΡΠΈΡΠ΅Π»ΡΠ½ΠΎ ΠΌΠ΅Π½ΡΡΠ΅Π³ΠΎ Π²ΡΠ΅ΠΌΠ΅Π½ΠΈ Π΄Π»Ρ ΠΏΠΎΠΈΡΠΊΠ° Π²ΡΡΠ΅ΠΏΡΠΈΠ²Π΅Π΄Π΅Π½Π½ΡΡ
Π²ΡΡ
ΠΎΠ΄ΠΎΠ². ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΊΠΎΠΌΠ±ΠΈΠ½Π°ΡΠΈΠΎΠ½Π½ΡΠ΅ ΡΡ
Π΅ΠΌΡ ΠΌΠΎΠ³ΡΡ ΠΎΠ±Π»Π°Π΄Π°ΡΡ ΡΡΠ½ΠΊΡΠΈΠΎΠ½Π°Π»ΡΠ½ΡΠΌΠΈ ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΡΠΌΠΈ, ΠΏΡΠΈ ΠΊΠΎΡΠΎΡΡΡ
Π½Π° ΡΠ°Π±ΠΎΡΠΈΡ
Π²ΡΡ
ΠΎΠ΄Π°Ρ
ΠΌΠΎΠ³ΡΡ ΠΏΡΠΎΡΠ²Π»ΡΡΡΡΡ ΡΠΎΠ»ΡΠΊΠΎ ΠΌΠΎΠ½ΠΎΡΠΎΠ½Π½ΡΠ΅ ΠΎΡΠΈΠ±ΠΊΠΈ. Π‘Π»Π΅Π΄ΠΎΠ²Π°ΡΠ΅Π»ΡΠ½ΠΎ, ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ Π½ΠΎΠ²ΡΠΉ ΠΌΠ΅ΡΠΎΠ΄ ΠΈΠ΄Π΅Π½ΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ Π»ΡΠ±ΠΎΠ³ΠΎ ΡΠΈΡΠ»Π° ΠΌΠΎΠ½ΠΎΡΠΎΠ½Π½ΠΎ Π½Π΅Π·Π°Π²ΠΈΡΠΈΠΌΡΡ
ΡΠ°Π±ΠΎΡΠΈΡ
Π²ΡΡ
ΠΎΠ΄ΠΎΠ² ΠΊΠΎΠΌΠ±ΠΈΠ½Π°ΡΠΈΠΎΠ½Π½ΡΡ
ΡΡ
Π΅ΠΌ. ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ ΠΏΡΠ΅Π΄Π»Π°Π³Π°Π΅ΠΌΡΠ΅ Π² ΡΡΠ°ΡΡΠ΅ ΠΌΠ΅ΡΠΎΠ΄Ρ ΠΏΠΎΠΈΡΠΊΠ° ΠΌΠΎΠ½ΠΎΡΠΎΠ½Π½ΠΎ Π·Π°Π²ΠΈΡΠΈΠΌΡΡ
ΠΈ ΠΌΠΎΠ½ΠΎΡΠΎΠ½Π½ΠΎ Π½Π΅Π·Π°Π²ΠΈΡΠΈΠΌΡΡ
Π²ΡΡ
ΠΎΠ΄ΠΎΠ² Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΊΠΎΠΌΠ±ΠΈΠ½Π°ΡΠΈΠΎΠ½Π½ΡΡ
ΡΡ
Π΅ΠΌ ΡΡΠ΅Π±ΡΡΡ Π²ΡΠΏΠΎΠ»Π½Π΅Π½ΠΈΡ Π½Π΅ΡΠ»ΠΎΠΆΠ½ΡΡ
ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΡ
Π²ΡΡΠΈΡΠ»Π΅Π½ΠΈΠΉ. Π ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ½ΠΎΠΉ ΡΡΠ΅Π΄Π΅ Multisim ΡΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½Ρ Π²Π½ΡΡΡΠ΅Π½Π½ΠΈΠ΅ Π½Π΅ΠΈΡΠΏΡΠ°Π²Π½ΠΎΡΡΠΈ Π΄ΠΈΠ°Π³Π½ΠΎΡΡΠΈΡΡΠ΅ΠΌΡΡ
ΡΡ
Π΅ΠΌ ΠΈ Π·Π°ΡΠΈΠΊΡΠΈΡΠΎΠ²Π°Π½Ρ Π²ΡΠ΅ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΡΠ΅ ΠΎΡΠΈΠ±ΠΊΠΈ Π½Π° ΡΠ°Π±ΠΎΡΠΈΡ
Π²ΡΡ
ΠΎΠ΄Π°Ρ
. ΠΠΎ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ°ΠΌ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠΎΠ² ΡΠ°ΠΊΠΆΠ΅ ΠΏΠΎΠ΄ΡΠ²Π΅ΡΠΆΠ΄Π΅Π½Π° ΡΠΏΡΠ°Π²Π΅Π΄Π»ΠΈΠ²ΠΎΡΡΡ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΡ
ΡΠ΅ΠΎΡΠ΅ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΎΠ²
Π Π²ΠΎΠΏΡΠΎΡΡ ΡΠΈΠ½ΡΠ΅Π·Π° Π³Π΅Π½Π΅ΡΠ°ΡΠΎΡΠΎΠ² ΠΌΠΎΠ΄ΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ ΠΊΠΎΠ΄ΠΎΠ² Ρ ΡΡΠΌΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ Π²Π·Π²Π΅ΡΠ΅Π½Π½ΡΡ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΡΡ ΡΠ°Π·ΡΡΠ΄ΠΎΠ² Ρ ΠΏΠΎΡΠ»Π΅Π΄ΠΎΠ²Π°ΡΠ΅Π»ΡΠ½ΠΎΡΡΡΡ Π²Π΅ΡΠΎΠ²ΡΡ ΠΊΠΎΡΡΡΠΈΡΠΈΠ΅Π½ΡΠΎΠ², ΠΎΠ±ΡΠ°Π·ΡΡΡΠ΅ΠΉ Π½Π°ΡΡΡΠ°Π»ΡΠ½ΡΠΉ ΡΡΠ΄ ΡΠΈΡΠ΅Π»
ΠΠ·Π»Π°Π³Π°ΡΡΡΡ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ, ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ Π°Π²ΡΠΎΡΠΎΠΌ Π² ΠΎΠ±Π»Π°ΡΡΠΈ ΡΠΈΠ½ΡΠ΅Π·Π° Π³Π΅Π½Π΅ΡΠ°ΡΠΎΡΠΎΠ² ΠΊΠΎΠ½ΡΡΠΎΠ»ΡΠ½ΡΡ
Π²Π΅ΠΊΡΠΎΡΠΎΠ² ΠΌΠΎΠ΄ΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΠΊΠΎΠ΄ΠΎΠ² ΠΠ΅ΡΠ³Π΅ΡΠ°. ΠΠ°Π½Π½ΡΠ΅ ΠΊΠΎΠ΄Ρ ΠΏΡΠΈΠ½Π°Π΄Π»Π΅ΠΆΠ°Ρ ΠΊ ΠΊΠ»Π°ΡΡΡ ΠΌΠΎΠ΄ΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΠΌΠΎΠ΄ΡΠ»ΡΠ½ΠΎ Π²Π·Π²Π΅ΡΠ΅Π½Π½ΡΡ
ΠΊΠΎΠ΄ΠΎΠ² Ρ ΡΡΠΌΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΠΎΠ±ΡΠΈΠ΅ ΡΡΡΡΠΊΡΡΡΡ Π³Π΅Π½Π΅ΡΠ°ΡΠΎΡΠΎΠ² ΡΠ°ΠΊΠΈΡ
ΠΊΠΎΠ΄ΠΎΠ², Π° ΡΠ°ΠΊΠΆΠ΅ Π°Π»Π³ΠΎΡΠΈΡΠΌ ΠΏΠΎΡΡΡΠΎΠ΅Π½ΠΈΡ Π³Π΅Π½Π΅ΡΠ°ΡΠΎΡΠ°, ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡΠΈΠΉ ΠΎΠΏΡΠΈΠΌΠΈΠ·ΠΈΡΠΎΠ²Π°ΡΡ Π΅Π³ΠΎ ΡΡΡΡΠΊΡΡΡΡ, ΡΠΎΠΊΡΠ°ΡΠΈΠ² ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΠ΅ΠΌΡΡ
ΡΡΠ½ΠΊΡΠΈΠΎΠ½Π°Π»ΡΠ½ΡΡ
ΡΠ»Π΅ΠΌΠ΅Π½ΡΠΎΠ². ΠΡΠ²ΠΎΠ΄ΠΈΡΡΡ ΡΠΎΡΠΌΡΠ»Π° ΠΏΠΎΠ΄ΡΡΠ΅ΡΠ° ΠΎΠ±ΡΠ΅Π³ΠΎ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π° Π΄Π²ΡΡ
Π²Ρ
ΠΎΠ΄ΠΎΠ²ΡΡ
Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΠ»Π΅ΠΌΠ΅Π½ΡΠΎΠ², Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΡΡ
Π΄Π»Ρ ΡΠ΅Ρ
Π½ΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ΅Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ Π³Π΅Π½Π΅ΡΠ°ΡΠΎΡΠ°. ΠΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π½ΡΠΉ Π°Π»Π³ΠΎΡΠΈΡΠΌ ΡΠΈΠ½ΡΠ΅Π·Π° Π³Π΅Π½Π΅ΡΠ°ΡΠΎΡΠΎΠ² ΡΠ²Π»ΡΠ΅ΡΡΡ ΡΠ½ΠΈΠ²Π΅ΡΡΠ°Π»ΡΠ½ΡΠΌ ΠΈ ΠΌΠΎΠΆΠ΅Ρ Π±ΡΡΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ Π΄Π»Ρ ΠΏΠΎΡΡΡΠΎΠ΅Π½ΠΈΡ Π³Π΅Π½Π΅ΡΠ°ΡΠΎΡΠΎΠ² Π»ΡΠ±ΡΡ
ΠΌΠΎΠ΄ΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΠΌΠΎΠ΄ΡΠ»ΡΠ½ΠΎ Π²Π·Π²Π΅ΡΠ΅Π½Π½ΡΡ
ΠΊΠΎΠ΄ΠΎΠ² Ρ ΡΡΠΌΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ
A Survey on the Best Choice for Modulus of Residue Code
Nowadays, the development of technology and the growing need for dense and complex chips have led chip industries to increase their attention on the circuit testability. Also, using the electronic chips in certain industries, such as the space industry, makes the design of fault tolerant circuits a challenging issue. Coding is one of the most suitable methods for error detection and correction. The residue code, as one of the best choices for error detection aims, is wildly used in large arithmetic circuits such as multiplier and also finds a wide range of applications in processors and digital filters. The modulus value in this technique directly effect on the area overhead parameter. A large area overhead is one of the most important disadvantages especially for testing the small circuits. The purpose of this paper is to study and investigate the best choice for residue code check base that is used for simple and small circuits such as a simple ripple carry adder. The performances are evaluated by applying stuck-at-faults and transition-faults by simulators. The efficiency is defined based on fault coverage and normalized area overhead. The results show that the modulus 3 with 95% efficiency provided the best result. Residue code with this modulus for checking a ripple carry adder, in comparison with duplex circuit, 30% improves the efficiency
Π‘ΠΈΠ½ΡΠ΅Π· ΡΠ°ΠΌΠΎΠΏΡΠΎΠ²Π΅ΡΡΠ΅ΠΌΡΡ ΡΡ Π΅ΠΌ Π²ΡΡΡΠΎΠ΅Π½Π½ΠΎΠ³ΠΎ ΠΊΠΎΠ½ΡΡΠΎΠ»Ρ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΌΠ΅ΡΠΎΠ΄Π° Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ Π΄ΠΎΠΏΠΎΠ»Π½Π΅Π½ΠΈΡ Π΄ΠΎ ΡΠ°Π²Π½ΠΎΠ²Π΅ΡΠ½ΠΎΠ³ΠΎ ΠΊΠΎΠ΄Π° Β«2 ΠΈΠ· 4Β»
The article explores the peculiarities of self-checking integrated control circuits synthesis by the Boolean complement method based on the "2-out-of-4'' constant-weight code. The article describes the features of integrated control circuits implementation by the Boolean complement method. It is noted that it is possible to synthesize the structures of discrete devices, which have less structural redundancy than in situation of the control circuit implementation by the method of duplication. The effect in structural redundancy reducing is achieved by minimizing the complexity of the control logic block technical implementation and using checkers that are simpler in their structures than the comparator in the system of duplication. The article proposes a method of the integrated control circuit organization based on determining the values of control functions taking into account the maintenance of testability of elements of addition by modulo two in the Boolean complement block and the checker of the "2-out-of-4" code.ΠΡΡΠ»Π΅Π΄ΡΡΡΡΡ ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΠΈ ΡΠΈΠ½ΡΠ΅Π·Π° ΡΠ°ΠΌΠΎΠΏΡΠΎΠ²Π΅ΡΡΠ΅ΠΌΡΡ
ΡΡ
Π΅ΠΌ Π²ΡΡΡΠΎΠ΅Π½Π½ΠΎΠ³ΠΎ ΠΊΠΎΠ½ΡΡΠΎΠ»Ρ ΠΏΠΎ ΠΌΠ΅ΡΠΎΠ΄Ρ Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ Π΄ΠΎΠΏΠΎΠ»Π½Π΅Π½ΠΈΡ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ ΡΠ°Π²Π½ΠΎΠ²Π΅ΡΠ½ΠΎΠ³ΠΎ ΠΊΠΎΠ΄Π° Β«2 ΠΈΠ· 4Β». ΠΠΏΠΈΡΡΠ²Π°ΡΡΡΡ ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΠΈ ΡΠ΅Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΡΡ
Π΅ΠΌ Π²ΡΡΡΠΎΠ΅Π½Π½ΠΎΠ³ΠΎ ΠΊΠΎΠ½ΡΡΠΎΠ»Ρ ΠΏΠΎ ΠΌΠ΅ΡΠΎΠ΄Ρ Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ Π΄ΠΎΠΏΠΎΠ»Π½Π΅Π½ΠΈΡ. ΠΡΠΌΠ΅ΡΠ°Π΅ΡΡΡ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΡ ΡΠΈΠ½ΡΠ΅Π·Π° ΡΡΡΡΠΊΡΡΡ Π΄ΠΈΡΠΊΡΠ΅ΡΠ½ΡΡ
ΡΡΡΡΠΎΠΉΡΡΠ², ΠΈΠΌΠ΅ΡΡΠΈΡ
ΠΌΠ΅Π½ΡΡΡΡ ΡΡΡΡΠΊΡΡΡΠ½ΡΡ ΠΈΠ·Π±ΡΡΠΎΡΠ½ΠΎΡΡΡ, ΡΠ΅ΠΌ ΠΏΡΠΈ ΡΠ΅Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΡΡ
Π΅ΠΌΡ ΠΊΠΎΠ½ΡΡΠΎΠ»Ρ ΠΏΠΎ ΠΌΠ΅ΡΠΎΠ΄Ρ Π΄ΡΠ±Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ. ΠΡΡΠ΅ΠΊΡ Π² ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΠΈ ΡΡΡΡΠΊΡΡΡΠ½ΠΎΠΉ ΠΈΠ·Π±ΡΡΠΎΡΠ½ΠΎΡΡΠΈ Π΄ΠΎΡΡΠΈΠ³Π°Π΅ΡΡΡ Π·Π° ΡΡΠ΅Ρ ΠΌΠΈΠ½ΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ ΡΠ»ΠΎΠΆΠ½ΠΎΡΡΠΈ ΡΠ΅Ρ
Π½ΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ΅Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ Π±Π»ΠΎΠΊΠ° ΠΊΠΎΠ½ΡΡΠΎΠ»ΡΠ½ΠΎΠΉ Π»ΠΎΠ³ΠΈΠΊΠΈ ΠΈ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ Π±ΠΎΠ»Π΅Π΅ ΠΏΡΠΎΡΡΡΡ
ΠΏΠΎ ΡΠ²ΠΎΠΈΠΌ ΡΡΡΡΠΊΡΡΡΠ°ΠΌ ΡΠ΅ΡΡΠ΅ΡΠΎΠ², ΡΠ΅ΠΌ ΠΊΠΎΠΌΠΏΠ°ΡΠ°ΡΠΎΡ Π² ΡΠΈΡΡΠ΅ΠΌΠ΅ Π΄ΡΠ±Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ. ΠΡΠ΅Π΄Π»Π°Π³Π°Π΅ΡΡΡ ΡΠΏΠΎΡΠΎΠ± ΠΎΡΠ³Π°Π½ΠΈΠ·Π°ΡΠΈΠΈ ΡΡ
Π΅ΠΌΡ Π²ΡΡΡΠΎΠ΅Π½Π½ΠΎΠ³ΠΎ ΠΊΠΎΠ½ΡΡΠΎΠ»Ρ, ΠΎΡΠ½ΠΎΠ²Π°Π½Π½ΡΠΉ Π½Π° Π΄ΠΎΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠΈ Π·Π½Π°ΡΠ΅Π½ΠΈΠΉ ΠΊΠΎΠ½ΡΡΠΎΠ»ΡΠ½ΡΡ
ΡΡΠ½ΠΊΡΠΈΠΉ Ρ ΡΡΠ΅ΡΠΎΠΌ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠ΅Π½ΠΈΡ ΡΠ΅ΡΡΠΈΡΡΠ΅ΠΌΠΎΡΡΠΈ ΡΠ»Π΅ΠΌΠ΅Π½ΡΠΎΠ² ΡΠ»ΠΎΠΆΠ΅Π½ΠΈΡ ΠΏΠΎ ΠΌΠΎΠ΄ΡΠ»Ρ Π΄Π²Π° Π² Π±Π»ΠΎΠΊΠ΅ Π»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ Π΄ΠΎΠΏΠΎΠ»Π½Π΅Π½ΠΈΡ ΠΈ ΡΠ΅ΡΡΠ΅ΡΠ° ΠΊΠΎΠ΄Π° Β«2 ΠΈΠ· 4Β»
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