Remember how your first computer was and compare it with the current one. Why is each next smartphone or computer gets more powerful and compact than the previous one? The answer to this question will be found in the law of Moore, who says: "The number of transistors placed on the integrated circuit crystal is doubled every 24 months!". They are ready to argue that many hear about this law for the first time and besides, they do not understand at all what we are talking about. Meanwhile, he noted his 50th anniversary. And these consoles of electronics developed strictly according to it. But will it always be so?
Observation
Moore's law is known to anyone who relates to the production of microprocessors, disassembled in microelectronics and chips or well understands how the computer is arranged. The meaning of the Moore law has become clear to you, we will formulate it differently, using simple and understandable words: Computing power and computer performance doubles every 24 months.
Indeed, personal, laptops, smartphones are very quickly stolen. You probably noticed: I did not have time to buy a new model, after some time more powerful, faster, with a large memory volume appear. At the same time, their price remains the same, and if rising, then not a lot. And all this thanks to the development of technology.
Gordon Moore is one of those in 1968 founded Intel. During the first seven years, he was the executive vice president of the corporation. Then by the president and the main managers intel. Until 1997, he served as Chairman of the Board of Directors. Now 87-year-old Gordon Moore is the Honorary Chairman of the Board of Directors of Intel Corporation and lives in Hawaii.
Gordon Moore puts his law on the basis of observations, but he announced him in 1965. He noticed that annually the cost of one transistor decreases, and their amount on one crystal doubles. This was explained by the rapid development of microelectronics and growing needs in more powerful computers. But after ten years, Gordon Moore has made small changes in his law: the number of transistors doubles every two years.
This was due to the fact that the development of new products costs additional money and they need to be recharged. Therefore, too frequent release of new products does not give a company enough time to earn on them, and too rare release of new products would open the way to competitors. So that the company does not go in losses, the Golden Middle is needed, which Russed Moore.
The fact that was initially interesting observation, subsequently became the rule and law for the entire industry, which lived and developed on them all 50 years. However, now many experts declare that the days of the Moore law are considered. To understand, if it, it is necessary to become a little specialist. Let's try?
How the transistor works
So, the integrated circuit (synonyms: microcircuit, chip) is, as it were, the brain of any electronic device. We did not use the word brain in vain, because the chip also has its own memory and logic. The human brain receives information, processes, and then transmits it with other human agencies. Rather, it makes neurons of the brain with the help of chemical and electrical signals. Chip, like the brain, also processes, stores and transmits information using electrical signals. But only the role of neurons is played by transistors. Thanks to the transistors, the chip can perform our teams. For example, bank cards, identity cards, SIM cards have built-in chips that store different information, processed it, and also perform different operations.
Thus, transistors determine the operation of the entire integrated circuit, because they enhance, generate and convert electrical signals. In other words, the transistor is an amplifying element. It allows you to control much stronger with a weak signal.
To be clear, we give an analogy. When you press the pedal accelerator (gas pedals), the vehicle speed increases. At the same time, it is not very strong to press the pedal. Pressing the pedal is negligible compared to the power that the engine develops. The greater the angle of pressing the pedal, the more special valves open (dampers in the carburetor), which regulate the amount of fuel-air mixture into the engine, where it burns, increasing the pressure inside the engine. As a result, the frequency of rotation of the engine shaft and the speed of the car increases.
That is, the accelerator can be called an amplifying element, which, with a weak energy spent by a person when pressed on the pedal, controls and converts more powerful energy, the source of which is gasoline.
In transistor, everything is happening. Only through it is not gasoline, but an electric current.
Physical limit
As you remember, the Moore's law is the result of the observation of Mr. Mura, who in his wording did not think about the laws of mathematics and physics. Therefore, so that it worked and then, it is necessary that manufacturers will manage to "push out" in the chip twice the transistors every two years.
Unfortunately, this process cannot be infinite, and the decrease in the size of the transistors has its limit. This is primarily due to physical restrictions: it is impossible to make items infinitely small. When the transistor becomes a size of several atoms, quantum interactions will come into force. This means that the movement of the electron will be simply impossible to predict, and this will make the transistor useless.
But problems will not end this. The greater the number of transistors in the chip, the more heat dissipation. As you know, high temperatures strongly affect the conductivity of the current, which can again make the transistor unsuitable.
At the moment, the smallest size of transistors is 22 nanometer - in the Intel Haswell processor (1 nanometer is one billion meter, i.e. 10-9 meters). Intel has a potential to further reduce the size of the transistor. So, 10 nanometer chips should appear on the market in the second half of 2017.
Every year the doubling of transistors on the crystal no longer makes them cheaper. In other words, follow the Moore law is already unprofitable for manufacturers. After all, with each new step to overcome physical barriers, more funds starts: complex materials, super-modern equipment, a huge staff of researchers and at the same time - a large number of chip rejected, because when creating a superthon of crystalline silicon record with microscopic transistors embedded in it, even To a small, imperceptible person, changes, such as the oscillations of the earth's crust.
So, sooner or later, the laws of nature will put an end to the domination of the Moore law. The end of the era of the rapid development of silicon transistors is predicted at 2020-2025. What awaits computers on? Experts predict that 3D and molecular transistors will appear, and in a longer perspective - quantum.
In the previous weekly issue.
The middle class's fictional personal computer contains from 50 to 70 integrated circuits. This is, first of all, the microprocessor is the most complex of the schemes that perform the sequences of commands for working with data. Over 40 years of the existence of integrated circuits, the engineering thought, naturally, did not stand in place, and the development of semiconductor technologies made it possible to reduce the size of the transistors, accordingly, increasing their number on the microprocessor. Several pieces, then several dozen, several tens of thousands, and finally, a million elements on an integrated circuit. Not once, researchers and analysts predicted that the miniaturization process will reach some of the physical limits that can no longer be overcome. However, until now, none of the predictions come true. The highest degree of integration allows you to increase the power of microprocessors from the year and on the outcome of the millennium makes it possible to issue RAM chips capable of keeping billions of data bits.
Nevertheless, increase the speed of the processor, reducing the size of the transistors placed on several square centimeters of silicon, is really becoming more complicated. It is now that the transistor on the processor has the size of the order of two microns (this is about a hundred times smaller than the width of the human hair) and may contain elements of several tenths of the micron, the problem of reaching the limit in further miniaturization is so acute that the laboratories of the largest scientific centers and companies - Manufacturers seriously work on the means of improving the modern technology of the production of integrated circuits, and in scientific circles, the question of possible alternatives to the transistor is generally more actively discussed as the basis of computing technology.
Again about physics
A further decrease in the size of the transistor is able to generate a number of physical conditions that will prevent the process of miniaturization. In particular, it may be extremely difficult, if it is possible to connect to each other of the smallest elements. Approaching the conductivity areas to each other for a distance of about 100 angstroms can generate quantum effects that will threaten the normal operation of transistors. In laboratories, the limit has already been achieved, and scientists explore possible consequences, however, for commercial production in the next decade, this problem will not be relevant yet.
Miniaturization of the field transistor is inevitably accompanied by the reinforcement of electric fields, which can affect the movement of electrons in different ways. In particular, the electrons passing through such a strong electric field can purchase very large energy, and ultimately an avalanche-like electric current will arise capable of destroying the scheme. Modern processors in pursuit of an increasingly high processing rate are already approaching the drawing, behind which such an increase in electric fields is quite possible. Engineers resort to various tricks in order to avoid unwanted consequences. Developed field transistors in which the field can move to the place where it does not destructive effect on other electronic functions. However, such tricks inevitably require a compromise with respect to other characteristics of the device, complicating the development and production or reducing the reliability and life cycle of the transistor and the scheme as a whole.
The smaller the size of the transistors, the higher the density of their placement on the processor, and the consumption of thermal energy increases. Now each square centimeter of the circuit allocates 30 watts of thermal energy - radiation, which is characteristic of the material heated to a temperature of about 1200 degrees Celsius. Naturally, such temperatures are not allowed in the production of microprocessors, therefore various cooling systems are used to remove excess heat as it occurs. The cost of using these sufficiently powerful systems increases with an increase in the intensity of the heated thermal energy.
Problems of production
In addition to purely physical problems, the process of reducing the size of transistors and increasing their degree of integration on the microprocessor can come across limitations associated with the features of the production of integrated circuits. Generally speaking, the properties of devices that are created on one silicon plate, as well as on different plates, are not identical. Deviations may occur at each of the steps. The nature of the probable differences between the processors produced and the frequency of the appearance of simply defective devices can become a real obstacle on the path of further miniaturization of the elements of the integrated circuit.
Miniaturization concerns not only the length and width of the diagram element, but also the thickness of the processor itself. Transistors and connections on it are implemented using a series of levels, in modern processors there may be five or six. Reducing the size of the transistor and an increase in the density of their placement on the processor entails an increase in the number of levels. However, the more layers in the scheme, the more carefully there must be control over them in the production process, since each of the levels will have the effect of underlying. The cost of improving controls and the cost of creating compounds between multiple levels may be a factor restraining an increase in the number of layers.
Among other things, the complication of the integrated circuit will require the improvement of the conditions of production to which the unprecedented high demands are presented. It will take more accurate mechanical control over the positioning of the original silicon plate. The "sterile" room where microprocessors are created, should be more sterile, in order to exclude the falling of the smallest dust particles capable of destroying the most complex scheme. With the complication of the processor, an increase in the degree of integration of the elements on it will increase the number of potential defects, and, therefore, ultra-slip-quality test procedures will be required. All this will make even more expensive already the most expensive production in the world. But, according to one of the inventors of the microprocessor of Gordon Moore, the process of miniaturization of transistors will stop if the costs of increasing the number of elements on the processor will exceed possible profits from the use of such complex chips.
Finally, the most important scientific and engineering developments are carried out towards improving the key stage of production of the integrated circuit - lithography, since it is here that it is really possible to achieve a certain limit in the foreseeable future.
Lithograph - what was that will
The development of lithographic technology since its invention at the beginning of the 70s went in the direction of reducing the length of the light wave. This allowed to reduce the size of the elements of the integrated circuit. From the mid-80s in photolithography uses ultraviolet radiation, obtained by a laser. Now the most powerful commercial processors are made using ultraviolet rays with a wavelength of 0.248 MK. To create crystals of gigabit memory, that is, integrated circuits with billions of transistors, a terrorist technology with a pulsating laser has been developed, which provides a wavelength of 0.193 MK. However, when the photolithography has crossed the border of 0.2 MK, there were serious problems that for the first time for the history of this technology questioned the possibility of its further use. For example, with a wavelength, less than 0.2 MK, too much light is absorbed by the photosensitive layer, therefore it is complicated and slows down the process of transmitting a pattern of the scheme for the processor.
On the other hand, for gigabit memory, transistors with elements of 0.18 MK elements are required, and the use of even radiation with a wavelength of 0.193 MK is not enough, since it is very difficult to build a scheme structure, the size of which is less than the length of the light wave in lithography. As one of the manufacturers of steppers (machines for photolithography) noted, it is like drawing a thin line a much thicker brush - the way you can find, but it is very difficult to keep it under control.
All these problems encourage researchers and manufacturers to look for alternatives to traditional lithographic technology. In fact, they are now three - x-rays, electronic rays and the so-called soft x-ray (Soft X-Ray).
The possibility of replacing ultraviolet rays X-rays is investigated in the US scientific laboratories for more than two decades. IBM company showed special activity in this regard. A few years ago, uniting with several firms, including Motorola, the company set a goal to bring lithography based on X-ray from the laboratory in production.
Very short, order of one nanometer, X-ray wavelength is only four hundredths of light waves, which are now used to produce the most perfect commercial processors. Therefore, it seems quite natural to apply this technology to create, say, integrated rates of robust gigabit volume. However, when it comes to an analysis of real production based on X-ray lithography, there are problems that have not yet been found adequate solution. The technology of obtaining X-ray rays is fundamentally different from radiation methods that are used in the modern production of integrated circuits. In optical lithography, laser installations are used, and the required X-ray radiation can be obtained only with a special device - synchrotron. And although the cost of such an X-ray generator is no more than 3% of the total value of the most modern semiconductor industries, the use of X-ray lithography will require reflashing production as a whole. And this is completely different amounts.
Nevertheless, the activity of X-ray technology opponents is increasingly investigated in the search for the improvement of traditional lithography methods; Search and other ways to specify the pattern of the integrated circuit on the silicon plate are underway.
Interestingly, in the process of production of integrated circuits, a technology is used daily, with which in principle the creation of the smallest elements of the semiconductor processor is possible. Electron beam (Electron Beams) Lithography allows a focused beam ("pencil") of charged particles "draw" lines directly on the lighting layer. This method is now used to draw pattern templates on a photolithographic mask. And during the same 20 years, scientists cherish hope to transfer the technology of electronic rays into the process of creating the diagram itself. However, the electronic rays are too slow a method for this task: an electronic "pencil" draws each element of the processor separately, therefore, it may take several hours to process one scheme, which is unacceptable for mass production. From the mid-80s in Bell Labs, a study is underway to scan a wide electron beam according to the scheme. As in photolithography, this method uses the design of the rays through the mask and reducing the image on the mask using the lenses. According to the estimates of a number of researchers, in the long run, it is the technology of scanning electron rays that can become the most real substitute for traditional lithography.
Search Alternative to transistors
In the end, the computer is a physical device, and its basic operations are described by the laws of physics. And from a physical point of view, the type of transistor, which is the basis of a modern integrated circuit, can be reduced by about 10 times, up to size in 0.03 MK. Behind this facet, the process of turning on / off microscopic switches will be almost impossible. The behavior of transistors will be similar to the current cranes - the movement of the electron from one end to the other will be out of control.
As already mentioned, the miniaturization limit of the elements of the processor may occur earlier due to various physical and production problems. Therefore, some scientists formulate the task unequivocally - to find physical replacement based basics. Not a transistor transmitting and enhancing an electrical signal under the action of the field, but something else. But what? Physicists claim, for example, that at a certain stage of miniaturization, the elements of the scheme will be so small that their behavior will need to be described by the laws of quantum mechanics. In the early 80s, the researchers of one of the US scientific laboratories showed that the computer in principle could function on quantum-mechanical laws. In such a quantum computer for storing information, for example, hydrogen atoms, various energy states of which will correspond to 0 and 1. Scientists are looking for ways to implement quantum logic. In the current decade in a number of US scientific centers, quite active work were conducted on the creation of the architectural principles of quantum computers. It is still unclear whether (and how efficiently) can be used by completely different physical principles of work, solve traditional mathematical tasks and the more to get out of their classical competitors in this. However, ideas are advancing about the usefulness of quantum computers when modeling precisely quantum physical systems.
Other alternatives to the transistor are also offered, for example, nonlinear optical devices in which electrical currents and voltages replace the intensity of optical rays. The implementation of this idea is associated with a number of problems. It is especially important that, in contrast to electricity, the light interacts poorly with light, and the interaction of the signals is a necessary condition for implementing logical functions.
Do not have to talk about the prospects for mass production of quantum or optical computers. Therefore, the future (at least foreseeable) computer equipment will still be associated with transistors. It is possible that those actual problems that fall on their further reduction and which we tried to give a submission to our reader will lead to a slowdown in the process of the emergence of new generations of memory and microprocessor schemes, which are now arising from the frequency of about once every three years. Developers will look for other ways to improve processor performance, not directly related to the decrease in integrated circuit components. For example, an increase in the size of the processor will allow you to place a greater number of transistors on it. The crystal can be "thicker" - by increasing the number of horizontal schema levels, it is possible to increase the density of the placement of memory elements or logic devices without changing their size. Or maybe barriers on the way of creating even more powerful and smart cars will be overcome using an unusually intelligent and powerful software, which is already subject to completely different, by no means physical laws.
How it's done
The process of production of my microshem can be divided into several stages.
1. Development of microprocessor. On a square silicon plate with the size of a nail child, it is necessary to build a scheme of millions of transistors, while their location and connections between them should be developed in advance and with extreme care. Each transistor in the diagram performs a specific function, the transistor group is combined in such a way as to implement a specific element of the circuit. The developer should also take into account the purpose of this crystal. The processor structure that executes the command will differ from the integrated memory scheme that stores data. Since modern microprocessors have a very complex structure, their development is carried out using a computer.
2. Creating a silicon plate. The basic material for constructing an integrated circuit is chosen silicon crystal, one of the most common elements on Earth with the natural properties of the semiconductor. For the production of microprocessor dedicated from Quartz silicon is subjected to chemical processing. From the resulting 100% silicon, a cylindrical ingot is formed by mirroring, which is then cut on the plate with a thickness of less than a millimeter. The plate is polished until the absolutely smooth, mirror surface is obtained. Silicon plates, as a rule, have a diameter of 200 mm, but in the near future it is planned to switch to a standard of diameter of 300 mm. Since hundreds of microprocessors are placed on one plate, the increase in diameter will increase the number of schemes that are produced at a time and, therefore, reduce the cost of one processor.
3. Creating initial levels. After the silicon plate is prepared, the process of creating an integrated circuit begins. Transistors and connections between them are implemented for several basic stages, the sequence of which is repeated many times. The most complex microprocessors may include more than 20 levels, and several hundred production steps are required to create them.
First of all, the level of the insulator is created over the silicon base of the chip - silicon dioxide. For this plate is placed in a special furnace, in which it
the thin layer of the insulator is increasing. The plate is then prepared to the first imposition of the scheme template. With the help of a special machine, the surface of the plate is uniformly covered with a photosensitive polymeric substance, which under the action of ultraviolet rays acquires the ability to dissolve.
4. Photolithography (masking). In order to apply the pattern of the circuit on the plate, a photolithography is performed using a computer-driven computer - the process of passing ultraviolet rays through a mask. A complex lenses system reduces the template specified on the mask to microscopic diagram sizes. The silicon plate is fixed in the position table under the lenses system and moves with it in such a way that all microprocessors placed on the plate are sequentially processed. Ultraviolet rays from a arc lamp or laser pass through free spaces on the mask. Under their action, the photosensitive layer in the appropriate places the plate acquires the ability to dissolve and is then removed by organic solvents.
5. etching. At this stage, the remaining photosensitive layer protects the underlying level of the insulator from removal when processing with acid (or reactive gas), with which the pattern of the circuit is rushing on the surface of the plate. Then this protective photosensitive level is removed.
6. Creating additional levels. Further disguise and etching processes determine the placement of additional materials on the surface of the plate, such as conducting polycrystalline silicon, as well as various oxides and metals. As a result, a necessary combination of conductive and non-conductive areas is created on the silicon plate, which in the next step will allow to implement transistors in the integrated circuit.
7. Deposition of impurities. At this stage, impurities such as boron or arsenic are added to silicon on the plate in certain places that allow you to change the method of transmitting the electrical current by a semiconductor. The base material of the microprocessor is silicon with P conductivity. During etching in the right places, the conductor (polycrystalline silica) layers (polycrystalline silicon) and an insulator (silicon dioxide) are removed on the basic silicon (silicon), so as to leave two p-region bands, separated by a lane with a unintended insulator and conductor (the shutter of the future transistor). Adding impurities converts the upper level of P-regions in the N-region, forming the source and flow of the transistor. Completed many times, these operations allow you to create a huge amount of transistors necessary for the implementation of the microprocessor. The following task is to connect them between themselves, in order for the integrated circuit to perform its functions.
8. Connections. The next masking and etching operations open areas of electrical contacts between different chip levels. Then, the layer of aluminum is precipitated on the plate and the diagram between all transistors on the microprocessor is being precipitated using photolithography.
This processing the original silicon plate is completed. Then, each processor on the plate is thoroughly verified for the correct functioning of its electrical connections, after which the special machine cuts the plate into separate integrated circuits. Quality processors are separated from defective and can be used for their intended purpose.
From the editorial Our regular readers know that occasionally in our newspaper there are reprints of the most famous, classical articles and works in the field of computer science. "Physical calculation limits" we wanted to print a long time ... Fifteen years old. But this wonderful article, everything was somehow there was no place from the point of view of the composition of other materials, it would be too strange to look at the newspaper, being printed "just so." And then such luck! The article was mentioned (absolutely deserved) in the last lecture of our advanced training course, as one of the few sources of information on this topic in Russian. Of course, we could not not take advantage of the opportunity. We hope you enjoy acquaintance with this beautiful popular material. After all, even 24 (!) The year, who have passed since his publication, did not make it "outdated", although, of course, technology went ahead to parses! But fundamental laws are not even technologies for teeth!
What physical factors limit the calculation process? Is there an extreme energy required, for example, to perform one logical step? Apparently, this minimum does not exist, but there are other issues that remain open.
Calculation, regardless of whether it is performed by electronic devices, on ordinary accounts or biological system, such as brain, is a physical process. They apply the same concepts as other physical processes. What amount of energy is needed to perform this or that calculation? How long will it take for it? What sizes should be a computing device? In other words, what are the physical limitations imposed on the calculation process?
Of course, ask these questions is much easier than answering them. The restrictions we are interested in, one way or another are very far from the real restrictions with which the business has a modern technique. Therefore, we cannot argue that our research help the engineer or technologist. These studies are more theoretical. Our goal is to identify general laws that are subject to all types of information processing, regardless of the means and methods of this processing. Any limitations we found should be based exclusively on fundamental physical principles, and not on the technologies currently used.
Such a search for fundamental restrictions already had precedents. In the 40s, K. Shennon, at the time, a Bell Telephone Laboratories company established that there are restrictions on the amount of information that can be transmitted via the communication channel in the presence of noise. These restrictions act regardless of how the message is encoded. Shannon's work marked the birth of modern information theory. Even earlier, in the middle and end of the last century, physics, trying to determine the fundamental restrictions on the effectiveness of the steam engine, created the science, the name "Thermodynamics". Approximately in 1960 Landauer (one of the authors of this article) together with J. Swanson, working in IBM, tried to apply the analysis of this kind to the calculation process. Starting from the mid-1970s, increasingly numerous groups of scientists from other organizations began to connect to these studies.
In our analysis of physical restrictions on calculations, we apply the term "information" in the sense in which it is defined in the theory of information. According to this definition, the information disappears whenever two previously distinguished situations become indistinguishable. In physical systems that differ in the absence of friction forces, information cannot be destroyed, because when the information is destroyed, a certain amount of energy should go into heat. As an example, consider two easily imaging physical situations. In one of them, the rubber ball is supported at an altitude of 1 m from the floor, in another - at an altitude of 2 m. If the ball is released, it will fall and bounce out from the floor up. In the absence of friction and, provided that the ball is absolutely elastic, the observer will always be able to say what was the initial state of the ball (in this case - at what height it was in the initial moment of time), since the ball, fallen from a height of 2 m, will bounce above, than in the case when it falls from a height of 1 m.
However, in the presence of friction forces, with each ball rebound from the floor, some energy will dissipate, and in the end the ball will stop bounce and remains to lie on the floor. Then it will be impossible to determine what was the initial state of the ball: the ball, fallen from a height of 2 m, will be completely identical to the ball, dropped from a height of 1 m. Information is lost as a result of dissipation of energy.
Conventional computing devices, scores and microprocessor during operation dispel energy. The scattering of energy by logical valves of the microprocessor is due to the disappearance of information. There are other reasons: electronic microprocessor circuits consume energy even when they simply store information without processing it. Scientists dissipative due to friction forces that cannot be eliminated: in the absence of static friction of the "bone", the situation would be changed under the action of a random thermal motion of molecules. Static friction is some minimum force that does not depend on the speed of moving the "bones", and therefore the scores require some minimal energy, no matter how slowly they did not work.
We give another example of the disappearance of information. The expression "2 + 2" contains more information than the expression "\u003d 4". If we only know that the number 4 was obtained as a result of the addition of two numbers, then we will not be able to determine which numbers it was: 1 + 3, 2 + 2, 0 + 4 or some other pair of numbers. Since the output information is implicitly contained in the input, we can assume that no computation generates information.
Ordinary logic valves dispel energy because they discard unnecessary information. For example, if at the exit of the valve and there is 0, then we cannot determine what was at the inputs.
In fact, the calculations performed on modern computing machines are carried out using many operations that destroy information. The so-called "valve AND "- This is a device with two input lines, on each of which a signal can be set equal to 1 or 0 and one output line - the value of its signal is determined by the input values. If on both inputs 1, then at the output will also be 1. if on one or on both inputs 0, then the output will be 0. Whenever at the output of the valve 0, we lose the information because we are unknown, in which of Three possible states were input lines (0 and 1; 1 and 0 or 0 and 0). In fact, in any logical valve in which the number of inputs exceeds the number of outputs, information loss inevitably occurs, since we cannot determine the status of the inputs by outputs. Therefore, whenever we use a similar "logically irreversible" valve, we dissipate energy into the environment. Erasing one bit of data in the memory of the computer is another commonly used when calculating the operation, which is also dissipative by its nature. When erasing one bit of data, we lose all the information about the preceding state of this bit.
However, it is right to ask whether the use of irreversible logical valves and erase operations in calculations is inevitable? If so, if any minimum amount of energy should be scattered with any calculation.
As Benno showed (one of the authors of this article) in 1973, when calculating, it is possible to do without irreversible logical elements, and without erasing information. Since then, the justice of this provision has been demonstrated on several models. The easiest way to describe the models based on the so-called "reversible logical elements", such as Fredkin's valve, named by Eduard Fredkina from the Massachusetts Institute of Technology. The valve has three entrance and three outlet lines. The signal on one input line, called the "control channel", does not change when passing through the valve. If the signal on the control channel is set to 0, then the input signals on the other two lines also pass unchanged. But if on the control line 1, then switching on two other output lines: the input signal of the same line becomes the output of the other, and vice versa. The Fredkina valve does not lose information, since the input status can always be determined by outputs.
Fredkin showed that any logical device necessary for the operation of the computer can be built in the form of an appropriate combination of Fredkina's valves. To calculate, certain values \u200b\u200bmust be previously installed on certain input lines (see the bottom drawing on the left).
The reversible logic valve of Fredkina may not disperse energy - the state at its inputs can be determined by outputs. The valve has a "control" line, the state of which does not change the valve. If on the control line 0, then the values \u200b\u200bof the signal on two other lines are also not changed, if the control line 1, then the input of the line A becomes the output of the line S, and vice versa. Using reversible valves, connected accordingly, you can implement any function performed by the usual irreversible device. To implement the operation and (right), one input is set to 0 and two output bits called "trash can" are temporarily ignored. When the calculation is complete, these bits are used when the valve is running in the opposite direction to return the computer to the initial state.
Fredkina's valves have more output lines than those that they simulate. Therefore, in the process of calculations, they would seem to be "trash bits", i.e. Information bits not required to obtain the result. Before you start another calculation, you need to somehow clean the computer from these bits. But if we will eat them, then there will be the most dissipation of the energy we wanted to avoid.
In fact, these bits play a very important role. After we obtained the result of the calculation and copied it from the machine from the usual output lines, the process should be launched in the opposite direction. In other words, we use "garbage bits" and output bits obtained by a computer during calculations, as an "input" entered from the "reverse side" of the machine. This turns out to be possible because each computer's logic valve is reversible. In the process of calculating in the opposite direction, there is no loss of information, and therefore there is no need to disperse energy. In the end, the computer will come to the state in which he was before the start of the calculation. Therefore, you can complete the "Cooling Cycle" - to drive a computer forward and then return to its original state, without any scattering of energy.
Until now, we talked about abstract logical operations, without touching physical devices that carry out these operations. However, it is not difficult to imagine a physical device working on the principle of Fredkina. In such a device, the channels for information transfer are represented in the form of tubes. In turn, the bit of information is presence or absence of a ball in a specific section of the tube. The presence of the ball is interpreted as 1, and the absence is like 0.
The control line is represented by a narrow section of the tube split in the middle in the longitudinal direction. When the ball enters into the split section of the tube, it spreads its side walls, thus leading the switching device. This switching device sends input balls that can be in two other tubes. When there is a ball in the control tube, any ball coming through the input line is automatically translated into another tube. To ensure that the switching device is turned off in the absence of a ball in the control tube, the split halves of the latter are pressed to each other with the springs. When the ball enters the control tube and compresses the springs, it should spend on it some amount of energy. However, this energy is not lost: it is given back when the control ball leaves the split tube and the springs are squeezed.
All the balls are related to each other and pushed forward with one mechanism, so they are moving synchronously; Otherwise, we could not provide the simultaneous arrival of various input and control balls to the logical valve. In some sense, the process of calculation occurs like a movement with one degree of freedom, as, for example, the movement of two wheels, rigidly sitting on the same axis. When the calculation is completed, we push all the balls in the opposite direction, eliminating all the operations carried out on the way and return the computer to the original state.
If the device is completely immersed in the perfect viscous liquid, then the friction forces acting on the balls will be proportional to their speed, the static friction will be absent. Therefore, if we are satisfied with the slow motion of the balls, the friction force will be very small. In any mechanical system, work to overcome the friction force is equal to the product of friction force for the distance traveled by the body. (Consequently, the faster the swimmer saves a certain distance, the more energy it costs, despite the fact that the distance remains one and the same regardless of the speed of the swimmer.) If the balls pass through the Fredkin's valves at low speed, then the work performed during the work (work of force The distance) will be very small, as the friction force is directly proportional to the ball speed. In fact, we can spend how little energy can be used, simply due to the corresponding slowing down the calculation process. Thus, we come to the conclusion that there is no minimum required amount of energy that you want to spend to perform any specified calculation.
Idealized physical model of Fredkin's valve: tubes play the role of conductors, and the presence or absence of a ball is interpreted as 1 or 0. A narrow split portion of the tube is a control channel. When the ball falls into it, the pipe walls are diverged on the parties, leading to the switching mechanism. The latter, in turn, transfers any arrived ball from the line A in line in and vice versa. Two springs support the control channel turned off when there is no ball. Such a valve does not require static friction to perform operations. It can be immersed in a viscous liquid, and then the friction force will depend only on the speed of the balls. In this case, the scattered energy can be arbitrarily small: to reduce the amount of scattered energy, you only need to reduce the speed of the balls through the valve.
In the considered model of the computing device, the energy lost for friction will be very small if this device acts quite slowly. Is it possible to build a model of an even more idealized machine that could calculate without friction? Or is the friction is the necessary attribute of the computing process? Fredkin, together with T.Taffoli and other specialists from MTI showed that friction is not necessary.
They demonstrated this on the model of a computing device, in which the calculations are conducted by shooting towards each other perfect billiard balls in the absence of friction forces. In the billiard model, ideally reflective "mirrors" - surfaces changing the direction of the movement of the balls, are located in such a way that the movement of the balls on the table models the passage of information bits through logic valves (see Figure). As before, the presence of a ball in a certain part of the "computer" is interpreted as 1, and the absence is like 0. If two balls simultaneously reach a logical valve, they are faced, and their trajectories are changed; New trajectories are the valve output. Fredkin, Tuffoli and others have developed mirrors arrangement schemes corresponding to different types of logical valves, and proved that you can build a billiard model of any logic element required for calculations.
Billiard model of a computer: The movement of the billiard balls over the table surface simulates the passage of information bits through a logic valve. In the billiard logical valves (left) the trajectories of the balls change during their collisions with each other or with "mirrors". In addition to the functions performed by them in the valves, the mirrors can change the angle of the trajectory of the ball (a), shift it to the side (b), delay the ball, without changing its final direction or speed (C), or force the trajectories to intersect (D). Mirrors can be placed in such a way that the resulting "computer" performed the functions of any logical device. For example, you can build a billiard computer to recognize prime numbers. Such a computer (right) at the input accepts an arbitrary five-digit binary number (in this case 01101, or 13) and a fixed input sequence 01. As well as the Fredkina valve, the billiard computer returns more bits at the output than the user needs. In the case under consideration, it returns the initial number itself (representing the "Excess" output) and the "response": sequence 10, if the number at the input is simple, and 01, if it is composite.
To start the calculation process, we shoot a billiard ball around the computer input if you need to enter a unit. Balls must enter the car at the same time. Since the balls are absolutely elastic, they do not lose energy when colliding with each other. They will come out of the car, possessing the same number of kinetic energy with which they entered it.
In the process of work, the billiard computer generates "trash bits", like a computer built on Fredkina's valves. After the computer completed the task, we reflect the billiard balls in the opposite direction, referring to reverse the calculation process. The balls will come out of the car exactly there, from where we sent them to the car, and at the same time will move at the same speed. Thus, the mechanism that runs the balls into the car can now get their kinetic energy back. And in this case, by performing a calculation, we can return the computer to the original state, without dispelning the energy.
The billiard computer has one significant disadvantage: it is extremely sensitive to the slightest inaccuracies. If the ball is sent with a slight deviation from the right direction or the mirror turned at an angle, slightly different from the calculated one, the balls will come from the desired trajectories. One or more balls will be deviated from the settlement path, and after some time the joint effect of these errors will violate the entire calculation process. Even if it was possible to make absolutely elastic, devoid of friction balls, a random heat movement of molecules, of which there are balls, it may be sufficient to make errors after several tens of collisions.
Of course, it would be possible to establish a corrective equipment that would return an incorrectly moving ball on the desired trajectory, but in this case it would have to destroy the information about the previous states of the ball. For example, it would be necessary to destroy the information relating to the magnitude of the mirror deviation from the correct position. However, to get rid of the information even in order to correct the error, it is possible only in the system in which the friction forces exist and the energy loss is possible. Therefore, the corrective equipment should dispel a certain amount of energy.
Many difficulties with which you have to face when using a billiard model of a computer, could be avoided or, in any case, to reduce them if instead of billiard balls, use submicroscopic particles, such as electrons. As the National Laboratory in Los Alamos pointed out, thanks to the laws of quantum mechanics, imposing restrictions on the state of elementary particles, the possibility of small deviations in the particle movement can be eliminated.
Although so far our reasoning was based mainly on classical dynamics, several researchers proposed other models of reversible computing machines based on the principles of quantum mechanics. Such machines, first proposed by P. Benioff from the National Laboratory in Argonne (France) and improved by others, especially R. Feinman from the California Institute of Technology, have so far been described only in the most general expressions. Essentially, particles in these models of computers must be arranged in such a way that the rules of quantum mechanics that control them interact are exactly similar to the rules predicting the values \u200b\u200bof the signals at the outputs of reversible logic valves. Suppose, for example, that the spin particles can have only two possible values: the upward direction (corresponding to binary 1) and down (corresponding 0). The interaction between the spin values \u200b\u200bof the particles should be underway so that the value of the spin of this particle varies depending on the spin of the particles nearby. In this case, the spin of the particle will correspond to one of the outputs of the logical valve.
Above we talked mainly about processing information. But the computer should not only process the data, but also to memorize them. The interaction between storage and processing of information is probably the best possible to describe the example of a device called "Machine of Turing" (named Alan M. Tyurring, the first one who suggested such a car in 1936). Turing machine can produce any computation performed by modern computer. Sh. Benne (one of the authors of this article) has proven to build a Turing machine, i.e. Such that does not lose information and, therefore, in the process of work can spend any predetermined small amount of energy.
The Turing Machine is capable of performing any calculation that can execute computers. The infinitely long tape is divided into discrete segments, each of which is recorded 0 or 1. "Head for reading and writing", which can be in any of several internal states (here only two states: and B) moves along the tape. Each cycle begins with the fact that the head reads one bit from the ribbon segment. Then, in accordance with the fixed set of transition rules, it records the data bits in the tape segment, changes its internal state and moves to one position to the left or right. Since this Turing machine has only two internal states, its ability is limited only by trivial calculations. More complex machines with a large number of states are able to simulate the behavior of any computer, including much more complicated than themselves. This turns out to be possible due to the fact that they store the complete representation of the logical state of a larger car on an endless ribbon and break each computing cycle for a large number of simple steps. The machine shown here is logically reversible: we can always determine the preceding states of the machine. Turing machines with other transition rules may not be logically reversible.
The Turing machine consists of several components. One of them is a tape divided into separate areas or segments, in each of which are recorded 0 or 1, which are input data. "Head for reading and writing" moves along the tape. The head can perform several functions - count one bit of data from the tape, write one bit on the tape and move to one segment to the left or right. In order for the next cycle to maintain information on what was done on the previous one, the head of the head has a number of so-called "states". Each state is its, somewhat different from other configuration of the inner parts of the head.
On each cycle, the head reads a bit from that tape segment, opposite which it is currently located. Then it writes a new bit value to the tape, changes its internal state and moves to one segment to the left or right. The value of the bit that it writes, the state to which it passes, and the direction in which it moves is determined by the fixed set of transition rules. Each rule describes certain actions. What rule the machine is currently determined by the state of the head and the value of the bit, just read from the tape. For example, a rule may be as follows: "If the head is in a state A and is located opposite the segment in which it is recorded 0, then it must change the value of this bit to 1, go to the state to and move to one segment to the right." According to some other rule, the machine should not change its state or not write a new bit on the tape, or must stop. Not all Turing machines are reversible, but you can build such a reversible Turing machine, which is capable of performing any calculation.
Models based on a reversible Turing machine have an advantage over machines such as a billiard computer in which there is no friction. In the billiard computer, the random thermal movement of molecules leads to inevitable errors. Reversible machines of Turing actually use random heat movement: they are constructed in such a way that it is a thermal movement with the assistance of a weak forceful force translates the machine from one state to another. The development of the computational process resembles the movement of the ion (charged particle) in the solution in a weak electric field. If you observe the behavior of the ion for a short period of time, it will seem random: the probability of movement in one direction is almost the same as in the other. However, the forcing force due to the action of the electric field gives the movement preferred direction. The probability that the ion will move in this direction are somewhat larger. At first glance, it may seem incredible that a targeted sequence of operations inherent in the calculation process can be implemented by the device, the direction of movement of which at any time can be considered almost random. However, this nature of actions is very common in nature. Its, in particular, can be observed in the microscopic world of chemical reactions. The Brownian movement occurring according to the method and error method, or a random heat movement, is quite effective that the reacting molecules come into contact are properly relative to each other, as this reaction requires, and new molecules have been formed, which are reaction products. In principle, all chemical reactions are reversible: the same Brownian movement, which ensures the reaction in the forward direction, sometimes causes the reaction products through the reverse transition. In a state of equilibrium, the opposite direction of the reaction is as probably as direct. To force the reaction to go directly, you need to constantly add molecules that react and remove molecules - reaction products. In other words, we must attach a small amount of force. When this force is very small, the reaction will occur in direct and reverse directions, but on average it will go directly. To ensure the presence of forgoing power, we need to spend energy, however, as in the Fredkin valve model from tubes and balls, the amount of energy can be arbitrarily small. If we are satisfied with the very slow operation of operations, then there is no minimum required amount of energy that you need to spend on these operations. The explanation lies in the fact that the total amount of energy dissipated depends on the number of steps in the forward direction divided by the number of steps in the opposite. (In fact, it is proportional to the logarithm of this relationship; when the attitude itself increases or decreases, its logarithm varies into the same direction.) The slower the reaction passes in the forward direction, the less the relationship is. (Here again is appropriate an analogy with fast and slow swimmers: if the reaction is slower, the total amount of energy spent will be less, despite the fact that the number of intermediate decays and connections remains the same.)
RNA polymerase is an enzyme acting as a reversible ribbon copying machine. It is a catalyst for the reaction of RNA synthesis, which is a copy of DNA. Moved along the DNA chain, the enzyme chooses from the surrounding solution with a nucleosidthththththrifhosphate molecule (each nucleosidththrifosphate consists of any base of RNA, sugar molecules and three phosphate groups), the base of which is complementary to the reason for the DNA, which is currently copied. It attaches a new base by the end of the RNA circuit under construction and releases the pyrophosphate ion. The reaction is reversible: sometimes the enzyme attaches to the last link of RNA pyrophosphate (the resulting nucleosidetriphosphate returns to the solution) and moves one position back along the DNA chain. When the reaction is close to the state of the chemical equilibrium, the enzyme makes almost as many steps back as forward, and the total energy required to copy one DNA segment is very small. The dissipation of energy is the less, the slower the reaction proceeds. Therefore, there is no minimum of the energy required in order to copy the DNA segment.
Let's see how the Brownian Turing Machine works on the example of the Brownian car to copy the tape. Such a car already exists in nature. This RNA polymerase is an enzyme involved in the RNA synthesis process that is a copy of DNA from which genes consist. Single-stranded DNA largely resembles a tension of the Turing machine. In each item, i.e. In each position along the chain, one of four nucleotides is located, or bases: adenine, guanine, cytosine or thymine (abbreviated A, G, C, T). The structure of RNA is very similar to DNA. It is also a long chain-like molecule consisting of the bases of four types - adenine, guanin, cytosine and uracil (respectively, A, G, C and U). RNA bases are able to communicate with their complementary DNA bases.
RNA polymerase catalyzes the formation process on the DNA of its complementary copy - RNA. Typically twisted in the helix double chain of DNA is surrounded by a solution containing a large number of ribonucleosidetriphosphate molecules, each of which consists of a connected ribonucleotide (RNA base), sugar and tail of three phosphate groups. RNA polymerase chooses from a solution one of the RNA bases, complementary to the base, which is currently copied from the DNA circuit, and attaches it to the end of the growing RNA chain, releaseing two phosphate into the surrounding solution in the form of a pyrophosphate ion. Next, the enzyme moves forward to one position along the DNA circuit, preparing to attach the following base to the RNA circuit. As a result, the RNA chain is formed, complementary to the matrix - DNA chain. Without RNA polymerase, these reactions would flow very slowly and there would be no guarantee that the resulting RNA exactly complementary DNA.
The reactions described are reversible: Sometimes the enzyme attaches to the last base of the RNA's growing chain, the free ion of pyrophosphate is released and the ribonucleoside approxpate molecule is released, and the enzyme itself is returned to one position back along the DNA chain. In a state of equilibrium, the steps in the forward and reverse directions occur with the same frequency, but in a living cell, other metabolic processes shift the equilibrium towards the direct reaction by removing the pyrophosphate and creating an excess of ribonucleoside triumphosphates. In the laboratory conditions, the rate of RNA polymerase reaction can be adjusted, varying the concentration of starting reagents (this was proved by J. Levin and M. Cheberlane from California University in Berkeley). As the concentrations are approaching the equilibrium, the enzyme works more slowly, and when copying this section of DNA, less and less energy is scattered, since the ratio of the number of steps in the forward and reverse directions becomes less.
RNA polymerase simply copies information without treating it, it is not difficult to imagine how a hypothetical chemical machine of Turing could work. The tape is one long skeletal molecule to which the bases of two types are attached at an equal gaps, interpreted as bits 0 and 1. Another small molecule is attached to one of the positions in the zeros circuit and units. The position to which this molecule is attached is not that other than the ribbon segment on which the head of the Turing machine is located. There are several different types of "head molecules". Each type represents one of the possible internal states of the machine.
Machine transition rules are represented by enzymes. Each enzyme is a catalyst for a certain reaction. To better understand how these enzymes work, consider an example.
Suppose that the head molecule refers to the type BUT (This means that the car is in a state BUT ) And attached to zero base. Suppose also that the following transition rule acts: "When the head is in a state BUT and read 0, replace 0 to 1, go to state IN And move to the right. " The enzyme molecule representing this rule takes place suitable for attaching a type molecule BUT Based 1. It also has a place suitable for attaching the base 0, and the place suitable for the type head IN (See Figure).
To carry out the required transition, the enzyme molecule first approaches the position on the tape located directly to the right of the base to which the type head is attached at the moment. BUT . Then it separates from the tape and the head molecule, and the base 0 to which the head is attached, and places the base on their place 1. Then it attaches the type head IN To the base located to the right of a single base, just attached to the tape. This transition terminates. On the source segment of the tape 0 was replaced by 1, the head molecule is now related to the type IN And attached to the base located on one position to the right of the original.
The hypothetical enzyme machine of Turing can perform calculation with arbitrarily low energy. Molecules representing bits 0 and 1 are attached to the skeletal molecule. A molecule representing the head of the Turing machine is attached to one of the positions in the chain (7). Different types of head molecules represent different states of the machine. Transition rules are represented by enzymes. On each cycle, the enzyme is connected to the head and a bit molecule associated with the head (2), separates them from the chain, places the desired molecule-bit (3) in their place. By doing this, it rotates, attaching the corresponding molecule head to the next bit on the right or left of the only changed. Now the cycle is completed (4): the bit value is changed, the head has changed the state and moved. Reactions similar to RNA synthesis can disperse an arbitrarily small amount of energy.
Brownian car Turing - a clock mechanism consisting of rigid smooth details that are loosely adjacent to each other and supported in the desired position without friction, but a system of grooves and teeth. Despite the free connection of parts, they can only make such a large-scale movement that corresponds to the number of computing in direct or opposite direction, in other words, they can follow only one "computing path". The mechanism is slightly pushed by very weak external force, so the probability of movement forward is almost the same as back. However, on average, the car will move forward and the calculation will eventually be completed. You can get the car to spend an arbitrarily small amount of energy due to the corresponding reduction of the forcing force.
Ribbon segments are represented by discs with grooves, and bits - e-shaped blocks, which are attached to the disk or in the upper (7) or in the lower (0) position. The head consists of rigid parts connected into a complex mechanism (most of which is not shown here). It is suspended with a reading element, a manipulator and a rod having a screwdriver. The machine is controlled by a roller with a grooves applied to its surface like a roller to play records on the phonograph (on the left at the top, right in depth). Various grooves correspond to different states of the head.
At the beginning of the cycle, the head is located above one of the disks, and the "needle" is located in the "reading" segment of the groove of the control roller corresponding to the current state of the machine head. During the reading phase of the cycle (7), the reading element determines how the block represents the bit, up or down, performing the procedure for reading the obstacle (in the center of the right). The reading item passes along the block over the upper or lower path. On one of these paths, he must meet an obstacle in the form of a protrusion at the end of the block, so only one way remains possible. At the point of the control roller corresponding to this "solution", the grooves are branched, and the needle is sent to the groove corresponding to the bit value (2). Then the control roller turns until the needle reaches the recording segment (3). Here, each groove contains a set of "instructions", which are transmitted by the machine using an intricate connection between the needle and the rest of the mechanism.
If the instruction requires a change to change the value of the bit, the manipulator is driven and engages for the protrusion of the block, then the screwdriver turns the disk until the block is free, the manipulator turns the block up or down, and the screwdrum turns the disk again, so the block takes its place. Having passed the segment of the "recording" of the control roller, the needle is included in the shear segment (4). Each groove of this segment contains instructions for moving the head to one position to the left or right. Next, the needle enters the "state change" segment (5), where the grooves merge in such a way that the needle falls into the groove representing the following state of the head. Now the cycle is completed (6). Discs, adjacent to the currently read, are held in the desired position of the head. Discs that are further locked on a special "castle". The lock of each disk is associated with a special bit called the Q-bit, the adjacent disk. The device of this connection is such that the disc readable at the moment is released and can move it, while the discs removed from it both on the left and right are maintained in a fixed state.
In order for the Brownian Turing Machine to work, the tape must be immersed in a solution containing many enzyme molecules, as well as sufficient reserves of "zerule", "units" and "heads" BUT and IN . In order for the reaction to take place in the forward direction, some other reaction is necessary, which would purify the enzyme molecules from the heads and the bases separated from the tape. The concentrations of substances that purify the enzyme molecules are forcing force that causes the Turing machine to work in the forward direction. And again we can spend an arbitrarily small amount of energy if the machine will perform the operations quite slowly.
The machine of Turing on the basis of enzymes will not be free from errors. From time to time, reactions occur without catalysis enzymes. For example, the base 0 can spontaneously separate from the skeletal molecule, and the base 1 is to take its place. In fact, such mistakes really occur in the RNA synthesis process.
In principle, it would be possible to get rid of these mistakes, building a brown car of Turing on the basis of a hard, absolutely smooth hour mechanism. This Turing Machine is a less idealized model than a billiard computer, but more idealized than an enzyme machine. On the one hand, its parts do not require absolutely accurate processing, as needed for billiard balls, the details of the hourly mechanism may have some tolerances and the machine can work even in the presence of significant heat noise. And yet the car must be absolutely tough and free from static friction, and no macroscopic body has these qualities.
Because the parts of the machine fit to each other, they are held in the desired position without friction, but with the help of a system of grooves - grooves and teeth (see Figure). Although each piece of the machine has a small free course, like a fairly rubbed chucks of a wooden puzzle, in general, the mechanism can follow only one "computing path". In other words, the details are connected to each other in such a way that at any time the car can perform only two types of large-scale movement: the movement corresponding to the step of calculations in the forward direction and movement in the opposite direction.
The computer performs transitions between these two types of movement only as a result of a random heat movement of their parts, due to the influence of weak external force. The probability of movement in the opposite direction eliminating the results of the last operation is almost the same as the probability of movement in the forward direction. A small force attached from the outside, pushes the calculations forward. And again this force can be made arbitrarily small; And, therefore, there is no minimum of energy that must be spent to ensure the functioning of the Turing machine based on the hourly mechanism.
Thus, for reasons of classical thermodynamics, the required minimum of energy for calculations does not exist. Does not enter the thermodynamic analysis in a contradiction with quantum mechanics? Indeed, according to the quantum-mechanical principle of uncertainty, there should be an inverse relationship between the degree of uncertainty about how much time the process lasts, and the degree of uncertainty relative to the amount of energy spent. Some researchers are considered therefore that in any process with switching occurring in a very short period of time, some minimum energy should be spent.
In fact, the principle of uncertainty does not require any final energy minimum for a quick switchal event. The principle of uncertainty would be applied only if we tried to measure the accurate moment of time when an event occurred. Even under the laws of quantum mechanics, extremely fast events can occur without any energy loss. Our confidence is that quantum mechanics allows calculations with an arbitrarily lowest considerable energy, finds confirmation in models of reversible quantum mechanical computing machines developed by Benioff with colleagues. These models do not disperse energy and obey the laws of quantum mechanics.
Thus, the principle of uncertainty, apparently, does not impose fundamental restrictions on the calculation process. The classic thermodynamics also imposes them. Does this mean that the calculations do not have any physical restrictions at all? No, it's far wrong. Real restrictions are associated with questions that are much more difficult to respond than those that we set and reviewed in this article. For example, do elementary logic operations require some minimum final time? What are the minimum dimensions of the device capable of performing such operations? Since the scale of size and time is associated with the final speed of light, then, apparently, the answers to these questions are somehow interrelated. However, we will not be able to find these answers, in any case, until the question of whether there is some kind of elementary discreteness in the universal scale of length and time.
On another pole, the problem is the question of how big we can make computer memory. How many particles in the universe can we collect and connect for these purposes? The fact is that the maximum possible size of the computer's memory imposes a limit on the accuracy with which the calculations can be carried out. For example, the amount of decimal signs in the calculated value of the number P will be limited. Another, possibly associated with the latter, the question concerns the inevitable processes of destruction flowing in real computing machines as they become agitated. Is it possible to reduce the rate of the process of destruction and accumulation of errors to arbitrarily small values, or this speed imposes a limit on the maximum calculation duration? In other words, are there any computational tasks that can not be completed before the material part of the computer will be unusable?
In fact, such issues relate to restrictions on the physical implementation of mathematical operations. Physical laws that should ultimately be based on answers themselves are expressed with such mathematical operations. Thus, we are asked about in which physical laws under restrictions imposed by the properties of the Universe, which themselves, in turn, are described by these laws.
Many enthusiasts of computer technologies with experience remember times when processor frequencies were measured in megaherts, and manufacturers (i.e. Intel and AMD) tried to get ahead of each other in this indicator. Then the level of power consumption and processor heat transfer rose so much that it was impossible to continue this race. In recent years, the number of processor nuclei has begun to increase, but as a result, the limit was achieved when this growth became unprofitable. Now getting the highest power on Watt has become the main productivity factor.
All these changes have occurred not because the developers faced the physical limits for the further development of existing processors. Rather, the performance turned out to be limited to the fact that progress in some areas - primarily energy efficiency - was slower than progress in other areas, such as expanding the functionality and sets of commands. However, can it be so that now the physical limit of processors and their computing power is already close? Igor Markov from the University of Michigan considered this question in the article in the Nature magazine.
We consider barriers
Markov notes that, based on purely physical restrictions, some scientists calculated that the Moore law is enough for another hundreds of years. On the other hand, the International Technology Roadmap for Semiconductors (ITRS) gives him a couple of decades of life. However, ITRS predictions can be questioned: earlier, this group predicted processors with a frequency of 10 GHz during Core2 chips. The reason for this discrepancy is that many hard physical constraints never entered the game.
For example, the extreme limit of the size of the function block is one atom, which is a finite physical limit. But long before it is possible to achieve this limit, physics limits the ability to accurately control the flow of electrons. In other words, the schemes can potentially reach the thickness of one atom, but their behavior will become significantly earlier. Most of the current work of Intel in transition to more subtle technological processes (smaller transistors) is to find out how to structure individual components so that they can continue to function as it should be.
The essence of the Markov argument can be understood something like this: although there are hard physical limits, they often have no relation to problems that restrain modern semiconductor progress. Instead, we face softer restrictions that often can be circumvented. "When the moment of a certain restriction impeding the progress comes, the understanding of its nature is the key to overcoming it," he writes. "Some restrictions can be simply ignored, while others remain hypothetical and are based only on empirical data; They are difficult to establish with a high degree of certainty. "
As a result, what seems of development barriers is often overcome by a combination of creative thinking and improved technology. An example of Markov is a diffraction limit. Initially, he had to keep the lasers based on argon-fluorine from etching of any structures thinner than 65 nanometers. But with the help of sub-wave diffraction, we currently work on 14 nm structures using the same laser.
Where are the modern limits?
Markov pays attention to two issues that considers the largest limits: energy and communication. The issue of energy consumption occurs from the fact that the amount of energy used by modern chains is not reduced in proportion to the decrease in their physical dimensions. The main result of this: the efforts made in order to block parts of the chip in those moments when they are not involved. But with the current rate of development of this approach at each specific point in time, most of the chip is inactive - from here there is a term "dark silicon".
The use of energy is proportional to the operating voltage of the chip, and the transistors simply cannot work below 200 mV. Now their voltage is 5 times higher, so there is a space for reducing. But progress in reducing the working voltage slowed down, so we can again come to technological restrictions earlier than to physical.
The problem of using energy is associated with the issue of communication: most of the physical volume of the chip and most of its power consumption is spent on the interaction between different blocks or the rest of the computer. Here we really get to the physical limits. Even if the signals in the chip were moving at the speed of light, the chip at frequency above 5 GHz will not be able to transfer information on one side of the chip to another. The best thing we can do with the account of modern technologies is to try to develop chips in which the blocks often exchanging with each other would be physically closely located. The inclusion in the third dimension equation (that is, three-dimensional chains) could help, but only slightly.
What's next?
Markov is not particularly optimistic about the coming changes. In the near future, it expects the use of carbon nanotubes for wiring and optical interconnects to communicate a tendency that helps us avoid collisions with physical limits. However, he notes that both of these technologies have their own limitations. Carbon nanotubes can be small, to a nanometer in diameter, but they have the limit of size. And photons, if they are used for communication, require hardware and energy.
Many have hopes for quantum computers, but brands are not one of their fans. "Quantum computers, both digital and analog, instill hope only in niche applications and do not offer significant productivity in the field of general purpose computing, since they cannot quickly perform sorting and other specific tasks," it afflates. The problem is also that this equipment works best when the temperature is close to the absolute zero, with the room the same performance is extremely low.
However, all calculations in one extent rely on quantum effects, and Markov believes that it is possible to extract something useful from quantum systems. "Separate quantum devices are approaching the energy limits for switching, while the non-target devices remain an order of magnitude." Obviously, obtaining even a small degree of efficiency of quantum systems can make a large ground at energy consumption within the entire chip.
Another physical limit on Markov: Erasing the bit of information has a thermodynamic value that cannot be avoided - the calculations always consume energy. One of the ideas in order to avoid this limit - "reversible calculations", when the components are returned to the initial state after the calculation. This method can, at least in theory, allow to obtain the opposite of the energy used.
This idea is not completely theoretical. Markov quotes work using superconducting chains (which it calls "very exotic"), providing reversible behavior and dispersion of energy below the thermodynamic limit. Of course, only 4 microelvin applies here, so more energy is spent on checking the performance of chains than on their work itself.
Outside of physics
While physics and materials are put in many restrictions on the hardware component, mathematics imposes restrictions on what we can do with them. And despite its reputation as accurate science, mathematical limitations are much more vague than physical. For example, there is still no answer to the equality of the complexity classes P and NP, despite the years of effort. And although we can prove that some algorithms are the most effective for general cases, it is easy to find also the ranges of problems where alternative computing approaches work better.
The biggest problem that Markov sees here is the struggle for extracting greater parallelism from the code. Even cheap smartphones are now working on multi-core processors, but so far their use is not optimal.
In general, it seems that the main limitation is the human mind. Although Markov does not see the approach of new fantastic technologies on the approach, it optimically hopes to eliminate current obstacles or their bypass due to progress in other areas.
To address operands in the physical address space of the program, use logical addressing. The processor automatically broadcasts logical addresses into the physical, then issued to the system bus.
The computer architecture distinguishes the physical address space (FAP) and logical address space (lap). Physical address spaceit is a simple one-dimensional array of bytes, access to which is implemented by memory equipment at the address present on the tire of the microprocessor address. Logical address space It is organized by the Programmer itself based on specific needs. The broadcast of logical addresses to the physical is performed by the MMU memory control unit.
In the architecture of modern microprocessors, the paws is presented in the form of a set of elementary structures: bytes, segments and pages. The following options for organizing are used in microprocessors. logical address space:
- flat (linear) paw: consists of an array of bytes that does not have a certain structure; The translation of the address is not required, since the logical address coincides with the physical;
- segmented paws: consists of segments - continuous areas of memory containing in the general case a variable number of bytes; The logical address contains 2 parts: segment identifier and displacement inside the segment; The translation of the address is performed by the MMU segmentation unit;
- pastal paw: Consists of pages - continuous areas of memory, each of which contains a fixed number of bytes. The logical address consists of the number (identifier) \u200b\u200bof the page and offset inside the page; The broadcast of the logical address to the physical is carried out by the MMU page conversion unit;
- segment-page lap: comprises segments which, in turn, consist of pages; The logical address consists of a segment identifier and displacement inside the segment. The MMU segment conversion unit translates the logical address to the page number and the offset in it, which are then broadcast to the physical address of the MMU page conversion unit.
The microprocessor is capable of working in two modes: real and protected.
When working in real modethe capabilities of the processor are limited: the capacity of the addressable memory is 1 MB, there is no page organization of memory, segments Have a fixed length of 216 bytes.
This mode is usually used at the initial stage of the computer loading to go to protected mode.
IN real modeprocessor segment registers contain older 16 bits of the physical address segment. Shifted on 4 categories left selectorgives a 20-bit basic address of the segment. The physical address is obtained by adding this address with a 16-bit displacement value in the segment formed by the specified addressing mode for the operand or the EIP extracted from the register (Fig. 3.1). The address received is a sample of information from memory.
Fig. 3.1. Diagram of obtaining a physical address
The most fully features of the microprocessor to address memory are implemented when working in secure mode. The amount of the addressable memory increases to 4 GB, the possibility of addressing page mode appears. Segments May have a variable length from 1 byte to 4 GB.
General scheme for the formation of the physical address microprocessor operating in protected mode, presented in Fig. 3.2.
As already noted, the basis of the formation of the physical address is the logical address. It consists of two parts: selectorand offset in segment.
Selector It is contained in the microprocessor segment register and allows you to find a description of the segment. (descriptor) In a special table of descriptors. Descriptors Segments are stored in special system objects of global (GDT) and local (LDT) tables of descriptors. Descriptorit plays a very important role in the functioning of the microprocessor, from the formation of a physical address at various organization of address space and to the organization of multiprogram mode. Therefore, we consider its structure in more detail.
Segments microprocessor operating in protected modecharacterized by a large number of parameters. Therefore, in universal 32-bit microprocessors, information about the segment is stored in
Fig. 3.2. Formation of the physical address in the segment-page organization of memory
special 8-byte data structure called descriptorThe main function is fixed for segment registers - determining the location of the descriptor.
Structure segment descriptor Presented in Fig. 3.3.
Fig. 3.3. Structure of the segment descriptor
We will consider the structure, and not the format of the descriptor, since when moving from the I286 microprocessor to 32-bit MP, the location of the individual fields of the descriptor lost its slightness and partially began to have the appearance of "patches" delivered to mechanically increase the bit of these fields.
The 32-bit base address field allows you to determine the initial address of the segment at any point of the address space in 2 32 bytes (4 GB).
Field of limit(Limit) Indicates the length of the segment (more precisely, the length of the minus 1 segment is: if the field is recorded 0, this means that the segment has a length 1) in the additive units, that is, the maximum size of the segment is 2 20 elements.
The element value is determined by one of the attributes of the bit descriptor G (Granularity - granularity, or fragility):
Thus, the segment may have a size with an accuracy of 1 byte in the range from 1 byte to 1 MB (with G \u003d 0). At the volume of the page at 2 12 \u003d 4 KB, you can set the volume of the segment to 4 GB (PR \u003d L):
Since the IA-32 architecture segment can begin in an arbitrary point of the address space and have an arbitrary length, the segments in memory can be partially or completely overlap.
Bit dimension (Default Size) Determines the length of addresses and operands used in the default command:
his discretion. Of course, this bit is designed not for a regular user, but for a system programmer using it, for example, for marking segments to collect "garbage" or segments, the basic addresses of which cannot be modified. This bit is available only to privilege programs. The microprocessor in his work does not change it and does not use.
Byte access Determines the basic rules for handling the segment.
Bit presence P (Present) shows the ability to access the segment. The operating system (OS) notes a segment transmitted from operational to the outer memory, as temporarily missing, stiring in its descriptor P \u003d 0. At p \u003d 1, the segment is in physical memory. When the descriptor is selected with P \u003d 0 (the segment is missing in RAM), the fields of the base address and limit are ignored. This is natural: for example, how can we talk about the basic address of the segment, if the segment itself is generally not in RAM? In this situation, the processor rejects all subsequent attempts to use descriptor in teams and defined descriptor The address space seems to "disappear."
There is a special case of the untested segment. In this case, the operating system copies the requested segment from the disk to the memory (at the same time, possibly by removing another segment), loads into descriptor The basic address of the segment sets P \u003d 1 and performs the restart of the team that appealed to the segment absent in RAM.
The DPL two-sided field (Descriptor Privilege LEVEL) indicates one of four possible (from 0 to 3) levels of privilege descriptor, determining the possibility of accessing the segment by certain programs (level 0 corresponds to the highest level of privileges).
Bit appeals A (Accessed) is installed in "1" with any appeal to the segment. Used by the operating system in order to track the segments to which there were no appeals longer.
Let, for example, 1 times a second, the operating system in the descriptors of all segments resets the BIT A. If after some time it is necessary to upload a new segment to the RAM, the places for which is not enough, the operating system determines the "candidates" to clear part of the RAM , among those segments, in descriptors which bits and before that moment was not installed in "1", that is, there was no appeal in recent times.
Field type In the access of access determines the appointment and features of the use of the segment. If the bit S (System - Bit 4 of the Access Byte) is 1, then this descriptor Describes the real memory segment. If S \u003d 0, then this descriptor describes a special system object that may not be a memory segment, for example, a call gateway used when switching tasks, or a LAN descriptor descriptor LDT descriptors. Purpose of bits<3...0> Access byte is determined by the type of segment (Fig. 3.4).
Fig. 3.4. Access byte field format
In the code segment: The subordination bit, or matching, C (conforming) defines additional rules of treatment that protect program segments. With C \u003d 1, this segment is a subordinate code segment. In this case, he intentionally deprives protection for privileges. Such a means is convenient for an organization, for example, subroutines that must be accessible to all tasks performed in the system. At c \u003d 0 is a conventional code segment; The read bit R (Readable) sets whether it is possible to access the segment only to execute or read and read, for example, constants as data using a segment replacement prefix. When R \u003d 0, only a sample from the command segment is allowed for their execution. When R \u003d 1 also allowed reading data from the segment.
Recording to the code segment is prohibited. If any recording attempts, a software interruption occurs.
In the data segment:
- ED (EXPAND DOWN) - bits of expansion directions. With ED \u003d 1, this segment is a stack segment and the offset in the segment must be greater than the size of the segment. With ED \u003d 0 - this is the segment of the data itself (the offset should be less than or equal to the size of the segment);
- writeable write permission bit (Writeable). When W \u003d 1, a change in the segment is allowed. When w \u003d 0, the entry into the segment is prohibited, when trying to write to the segment, a software interrupt occurs.
In the event of an appeal for operand offset in segment Formed by a microprocessor according to the operand addressing mode specified in the command. The shift in the code segment is extracted from register signs EIP.
The amount of the segment of the segment learned from the descriptor of the segment and formed displacement in the segment gives linear address (La).
If only the segment view of the address space is used in the microprocessor, the resulting linear address is also physical.
If in addition to the segment and the page mechanism of memory organization is used, then linear address It seems in the form of two fields: the older discharges contain a virtual page number, and the younger offset in the page. Converting a virtual page number to the physical number is carried out using special system tables: page tables directory (KTS) and tables pages (TC). The position of the directory of tables of pages in memory is determined by the CR3 system register. The physical address is calculated as the sum of the address received from the page of the page of the physical page and the offset in the page obtained from the linear address.
Consider now all the stages of the transformation of the logical address in physical in more detail.
