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76-412: A computer museum is devoted to the study of historic computer hardware and software , where a "museum" is a "permanent institution in the service of society and of its development, open to the public, which acquires, conserves, researches, communicates, and exhibits the tangible and intangible heritage of humanity and its environment, for the purposes of education, study, and enjoyment", as defined by

152-432: A monitor , mouse , keyboard , and speakers . By contrast, software is a set of written instructions that can be stored and run by hardware. Hardware derived its name from the fact it is hard or rigid with respect to changes, whereas software is soft because it is easy to change. Hardware is typically directed by the software to execute any command or instruction . A combination of hardware and software forms

228-526: A 0th symbol S 0 = "erase" or "blank", etc. However, he did not allow for non-printing, so every instruction-line includes "print symbol S k " or "erase" (cf. footnote 12 in Post (1947), The Undecidable , p. 300). The abbreviations are Turing's ( The Undecidable , p. 119). Subsequent to Turing's original paper in 1936–1937, machine-models have allowed all nine possible types of five-tuples: Any Turing table (list of instructions) can be constructed from

304-458: A GPU integrated into the motherboard. Most computers also have an external data bus to connect peripheral devices to the motherboard. Most commonly, Universal Serial Bus (USB) is used. Unlike the internal bus, the external bus is connected using a bus controller that allows the peripheral system to operate at a different speed from the CPU. Input and output devices are used to receive data from

380-429: A Turing machine, programming languages themselves do not necessarily have this limitation. Kirner et al., 2009 have shown that among the general-purpose programming languages some are Turing complete while others are not. For example, ANSI C is not Turing complete, as all instantiations of ANSI C (different instantiations are possible as the standard deliberately leaves certain behaviour undefined for legacy reasons) imply

456-485: A centralized memory that stored both data and programs, a central processing unit (CPU) with priority of access to the memory, and input and output (I/O) units . Von Neumann used a single bus to transfer data, meaning that his solution to the storage problem by locating programs and data adjacent to each other created the Von Neumann bottleneck when the system tries to fetch both at the same time—often throttling

532-590: A commensurate increase in energy use and cooling demand. The personal computer is one of the most common types of computer due to its versatility and relatively low price. Virtual hardware is software that mimics the function of hardware; it is commonly used in infrastructure as a Service (IaaS) and platform as a Service (PaaS). Embedded systems have the most variation in their processing power and cost: from an 8-bit processor that could cost less than USD $ 0.10, to higher-end processors capable of billions of operations per second and costing over USD$ 100. Cost

608-432: A computer, with the canonical machine using sequential memory to store data. Typically, the sequential memory is represented as a tape of infinite length on which the machine can perform read and write operations. In the context of formal language theory, a Turing machine ( automaton ) is capable of enumerating some arbitrary subset of valid strings of an alphabet . A set of strings which can be enumerated in this manner

684-459: A cord, light or takes some kind of battery. Some companies, such as Dell and Apple , will recycle computers of their make or any other make. Otherwise, a computer can be donated to Computer Aid International which is an organization that recycles and refurbishes old computers for hospitals, schools, universities, etc. Turing machine The machine operates on an infinite memory tape divided into discrete cells, each of which can hold

760-415: A desultory manner"). More explicitly, a Turing machine consists of: In the 4-tuple models, erasing or writing a symbol (a j1 ) and moving the head left or right (d k ) are specified as separate instructions. The table tells the machine to (ia) erase or write a symbol or (ib) move the head left or right, and then (ii) assume the same or a new state as prescribed, but not both actions (ia) and (ib) in

836-535: A different convention, with new state q m listed immediately after the scanned symbol S j : For the remainder of this article "definition 1" (the Turing/Davis convention) will be used. In the following table, Turing's original model allowed only the first three lines that he called N1, N2, N3 (cf. Turing in The Undecidable , p. 126). He allowed for erasure of the "scanned square" by naming

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912-414: A drawing. Whether a drawing represents an improvement on its table must be decided by the reader for the particular context. The reader should again be cautioned that such diagrams represent a snapshot of their table frozen in time, not the course ("trajectory") of a computation through time and space. While every time the busy beaver machine "runs" it will always follow the same state-trajectory, this

988-479: A finite-space memory. This is because the size of memory reference data types, called pointers , is accessible inside the language. However, other programming languages like Pascal do not have this feature, which allows them to be Turing complete in principle. It is just Turing complete in principle, as memory allocation in a programming language is allowed to fail, which means the programming language can be Turing complete when ignoring failed memory allocations, but

1064-453: A model through which one can reason about an algorithm or "mechanical procedure" in a mathematically precise way without being tied to any particular formalism. Studying the abstract properties of Turing machines has yielded many insights into computer science , computability theory , and complexity theory . In his 1948 essay, "Intelligent Machinery", Turing wrote that his machine consists of: ...an unlimited memory capacity obtained in

1140-410: A single symbol drawn from a finite set of symbols called the alphabet of the machine. It has a "head" that, at any point in the machine's operation, is positioned over one of these cells, and a "state" selected from a finite set of states. At each step of its operation, the head reads the symbol in its cell. Then, based on the symbol and the machine's own present state, the machine writes a symbol into

1216-419: A source of confusion, as it can mean two things. Most commentators after Turing have used "state" to mean the name/designator of the current instruction to be performed—i.e. the contents of the state register. But Turing (1936) made a strong distinction between a record of what he called the machine's "m-configuration", and the machine's (or person's) "state of progress" through the computation—the current state of

1292-453: A third element of the set of directions { L , R } {\displaystyle \{L,R\}} . The 7-tuple for the 3-state busy beaver looks like this (see more about this busy beaver at Turing machine examples ): Initially all tape cells are marked with 0 {\displaystyle 0} . In the words of van Emde Boas (1990), p. 6: "The set-theoretical object [his formal seven-tuple description similar to

1368-497: A universal machine). Another mathematical formalism, lambda calculus , with a similar "universal" nature was introduced by Alonzo Church . Church's work intertwined with Turing's to form the basis for the Church–Turing thesis . This thesis states that Turing machines, lambda calculus, and other similar formalisms of computation do indeed capture the informal notion of effective methods in logic and mathematics and thus provide

1444-421: A usable computing system, although other systems exist with only hardware. Early computing devices were more complicated than the ancient abacus date to the seventeenth century. French mathematician Blaise Pascal designed a gear-based device that could add and subtract, selling around 50 models. The stepped reckoner was invented by Gottfried Leibniz by 1676, which could also divide and multiply. Due to

1520-400: A variety of plastics that are present in bulk in computers or other electronics can reduce the costs of constructing new systems. Components frequently contain copper , gold , tantalum , silver , platinum , palladium , and lead as well as other valuable materials suitable for reclamation. The central processing unit contains many toxic materials. It contains lead and chromium in

1596-444: A very similar commodity . Profit margins have also been reduced. Even when the performance is not increasing, the cost of components has been dropping over time due to improved manufacturing techniques that have fewer components rejected at quality assurance stage. The most common instruction set architecture (ISA)—the interface between a computer's hardware and software—is based on the one devised by von Neumann in 1945. Despite

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1672-495: Is a growing movement to recycle old and outdated parts. Computer hardware contain dangerous chemicals such as lead, mercury, nickel, and cadmium. According to the EPA these e-wastes have a harmful effect on the environment unless they are disposed of properly. Making hardware requires energy, and recycling parts will reduce air pollution , water pollution, as well as greenhouse gas emissions. Disposing unauthorized computer equipment

1748-427: Is a particular concern with these systems, with designers often choosing the cheapest option that satisfies the performance requirements. A computer case encloses most of the components of a desktop computer system. It provides mechanical support and protection for internal elements such as the motherboard, disk drives, and power supply, and controls and directs the flow of cooling air over internal components. The case

1824-464: Is also part of the system to control electromagnetic interference radiated by the computer and protects internal parts from electrostatic discharge. Large tower cases provide space for multiple disk drives or other peripherals and usually stand on the floor, while desktop cases provide less expansion room. All-in-one style designs include a video display built into the same case. Portable and laptop computers require cases that provide impact protection for

1900-418: Is called a recursively enumerable language . The Turing machine can equivalently be defined as a model that recognises valid input strings, rather than enumerating output strings. Given a Turing machine M and an arbitrary string s , it is generally not possible to decide whether M will eventually produce s . This is due to the fact that the halting problem is unsolvable, which has major implications for

1976-484: Is either true or false. Boolean algebra is now the basis of the circuits that model the transistors and other components of integrated circuits that make up modern computer hardware. In 1945, Turing finished the design for a computer (the Automatic Computing Engine ) that was never built. Around this time, technological advancement in relays and vacuum tubes enabled the construction of

2052-469: Is equivalent to a single-stack pushdown automaton (PDA) that has been made more flexible and concise by relaxing the last-in-first-out (LIFO) requirement of its stack. In addition, a Turing machine is also equivalent to a two-stack PDA with standard LIFO semantics, by using one stack to model the tape left of the head and the other stack for the tape to the right. At the other extreme, some very simple models turn out to be Turing-equivalent , i.e. to have

2128-527: Is in fact illegal. Legislation makes it mandatory to recycle computers through the government approved facilities. Recycling a computer can be made easier by taking out certain reusable parts. For example, the RAM , DVD drive, the graphics card , hard drive or SSD , and other similar removable parts can be reused. Many materials used in computer hardware can be recovered by recycling for use in future production. Reuse of tin , silicon , iron , aluminum , and

2204-495: Is not true for the "copy" machine that can be provided with variable input "parameters". The diagram "progress of the computation" shows the three-state busy beaver's "state" (instruction) progress through its computation from start to finish. On the far right is the Turing "complete configuration" (Kleene "situation", Hopcroft–Ullman "instantaneous description") at each step. If the machine were to be stopped and cleared to blank both

2280-474: Is supposed to not to appear elsewhere) and then by the note of instructions. This expression is called the "state formula". Earlier in his paper Turing carried this even further: he gives an example where he placed a symbol of the current "m-configuration"—the instruction's label—beneath the scanned square, together with all the symbols on the tape ( The Undecidable , p. 121); this he calls "the complete configuration " ( The Undecidable , p. 118). To print

2356-434: Is surrounded by cooling fluid) and direct-to-chip (where the cooling fluid is directed to each computer chip) can be more expensive but are also more efficient. Most computers are designed to be more powerful than their cooling system, but their sustained operations cannot exceed the capacity of the cooling system. While performance can be temporarily increased when the computer is not hot ( overclocking ), in order to protect

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2432-449: Is the ability for a computational model or a system of instructions to simulate a Turing machine. A programming language that is Turing complete is theoretically capable of expressing all tasks accomplishable by computers; nearly all programming languages are Turing complete if the limitations of finite memory are ignored. A Turing machine is an idealised model of a central processing unit (CPU) that controls all data manipulation done by

2508-537: Is the main component of a computer. It is a board with integrated circuitry that connects the other parts of the computer including the CPU , the RAM , the disk drives ( CD , DVD , hard disk , or any others) as well as any peripherals connected via the ports or the expansion slots . The integrated circuit (IC) chips in a computer typically contain billions of tiny metal–oxide–semiconductor field-effect transistors (MOSFETs). Components directly attached to or to part of

2584-499: Is the unlimited amount of tape and runtime that gives it an unbounded amount of storage space . Following Hopcroft & Ullman (1979 , p. 148), a (one-tape) Turing machine can be formally defined as a 7- tuple M = ⟨ Q , Γ , b , Σ , δ , q 0 , F ⟩ {\displaystyle M=\langle Q,\Gamma ,b,\Sigma ,\delta ,q_{0},F\rangle } where A variant allows "no shift", say N, as

2660-866: The International Council of Museums . Some computer museums exist within larger institutions , such as the Science Museum in London , United Kingdom; and the Deutsches Museum in Munich , Germany. Others are dedicated specifically to computing, such as: Some specialize in the early history of computing, others in the era that started with the first personal computers such as the Apple I and Altair 8800 , Apple II systems, older Mac models, Amiga , IBM PCs and rarer computers such as

2736-450: The NFA to DFA conversion algorithm). For practical and didactic intentions, the equivalent register machine can be used as a usual assembly programming language . A relevant question is whether or not the computation model represented by concrete programming languages is Turing equivalent. While the computation of a real computer is based on finite states and thus not capable to simulate

2812-546: The Osborne 1 . Some concentrate more on research and conservation, others more on education and entertainment. There are also private collections, most of which can be visited by appointment. Computer hardware Computer hardware includes the physical parts of a computer , such as the central processing unit (CPU), random access memory (RAM) , motherboard , computer data storage , graphics card , sound card , and computer case . It includes external devices such as

2888-401: The operating system to map virtual memory to different areas of the finite physical memory. Computer processors generate heat, and excessive heat impacts their performance and can harm the components. Many computer chips will automatically throttle their performance to avoid overheating. Computers also typically have mechanisms for dissipating excessive heat, such as air or liquid coolers for

2964-425: The right of the scanned square. But Kleene refers to "q 4 " itself as "the machine state" (Kleene, p. 374–375). Hopcroft and Ullman call this composite the "instantaneous description" and follow the Turing convention of putting the "current state" (instruction-label, m-configuration) to the left of the scanned symbol (p. 149), that is, the instantaneous description is the composite of non-blank symbols to

3040-508: The uncomputability of the Entscheidungsproblem ('decision problem'). Turing machines proved the existence of fundamental limitations on the power of mechanical computation. While they can express arbitrary computations, their minimalist design makes them too slow for computation in practice: real-world computers are based on different designs that, unlike Turing machines, use random-access memory . Turing completeness

3116-601: The "complete configuration" on one line, he places the state-label/m-configuration to the left of the scanned symbol. A variant of this is seen in Kleene (1952) where Kleene shows how to write the Gödel number of a machine's "situation": he places the "m-configuration" symbol q 4 over the scanned square in roughly the center of the 6 non-blank squares on the tape (see the Turing-tape figure in this article) and puts it to

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3192-742: The "state register" and entire tape, these "configurations" could be used to rekindle a computation anywhere in its progress (cf. Turing (1936) The Undecidable , pp. 139–140). Many machines that might be thought to have more computational capability than a simple universal Turing machine can be shown to have no more power (Hopcroft and Ullman p. 159, cf. Minsky (1967)). They might compute faster, perhaps, or use less memory, or their instruction set might be smaller, but they cannot compute more powerfully (i.e. more mathematical functions). (The Church–Turing thesis hypothesises this to be true for any kind of machine: that anything that can be "computed" can be computed by some Turing machine.) A Turing machine

3268-403: The CPU and GPU and heatsinks for other components, such as the RAM . Computer cases are also often ventilated to help dissipate heat from the computer. Data centers typically use more sophisticated cooling solutions to keep the operating temperature of the entire center safe. Air-cooled systems are more common in smaller or older data centers, while liquid-cooled immersion (where each computer

3344-478: The above nine 5-tuples. For technical reasons, the three non-printing or "N" instructions (4, 5, 6) can usually be dispensed with. For examples see Turing machine examples . Less frequently the use of 4-tuples are encountered: these represent a further atomization of the Turing instructions (cf. Post (1947), Boolos & Jeffrey (1974, 1999), Davis-Sigal-Weyuker (1994)); also see more at Post–Turing machine . The word "state" used in context of Turing machines can be

3420-587: The above] provides only partial information on how the machine will behave and what its computations will look like." For instance, Definitions in literature sometimes differ slightly, to make arguments or proofs easier or clearer, but this is always done in such a way that the resulting machine has the same computational power. For example, the set could be changed from { L , R } {\displaystyle \{L,R\}} to { L , R , N } {\displaystyle \{L,R,N\}} , where N ("None" or "No-operation") would allow

3496-548: The annual rate of improvement in hardware performance exceeded 50 percent, enabling the development of new computing devices such as tablets and mobiles. Alongside the density of transistors, DRAM memory as well as flash and magnetic disk storage also became exponentially more compact and cheaper. The rate of improvement slackened off in the twenty-first century. In the twenty-first century, increases in performance have been driven by increasing exploitation of parallelism . Applications are often parallelizable in two ways: either

3572-650: The atmosphere, landfill or waterways. While electronics consist a small fraction of total waste generated, they are far more dangerous. There is stringent legislation designed to enforce and encourage the sustainable disposal of appliances, the most notable being the Waste Electrical and Electronic Equipment Directive of the European Union and the United States National Computer Recycling Act. E-cycling ,

3648-443: The design of the CPU, memory, and memory interconnect . Memory hierarchy ensures that the memory quicker to access (and more expensive) is located closer to the CPU, while slower, cheaper memory for large-volume storage is located further away. Memory is typically segregated to separate programs from data and limit an attacker's ability to alter programs. Most computers use virtual memory to simplify addressing for programs, using

3724-440: The design was incorporated into the earliest computers: punch cards for input and output, memory , an arithmetic unit analogous to central processing units , and even a primitive programming language similar to assembly language . In 1936, Alan Turing developed the universal Turing machine to model any type of computer, proving that no computer would be able to solve the decision problem . The universal Turing machine

3800-631: The external world or write data respectively. Common examples include keyboards and mice (input) and displays and printers (output). Network interface controllers are used to access the Internet . USB ports also allow power to connected devices—a standard USB supplies power at 5 volts and up to 500 milliamps (2.5 watts ), while powered USB ports with additional pins may allow the delivery of more power—up to 6 amps at 24v. Global revenue from computer hardware in 2023 reached $ 705.17 billion. Because computer parts contain hazardous materials, there

3876-608: The first computers. Building on Babbage's design, relay computers were built by George Stibitz at Bell Laboratories and Harvard University 's Howard Aiken , who engineered the MARK I . Also in 1945, mathematician John von Neumann —working on the ENIAC project at the University of Pennsylvania —devised the underlying von Neumann architecture that has served as the template for most modern computers. Von Neumann's design featured

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3952-412: The form of an infinite tape marked out into squares, on each of which a symbol could be printed. At any moment there is one symbol in the machine; it is called the scanned symbol. The machine can alter the scanned symbol, and its behavior is in part determined by that symbol, but the symbols on the tape elsewhere do not affect the behavior of the machine. However, the tape can be moved back and forth through

4028-461: The hardware from excessive heat, the system will automatically reduce performance or shut down the processor if necessary. Processors also will shut off or enter a low power mode when inactive to reduce heat. Power delivery as well as heat dissipation are the most challenging aspects of hardware design, and have been the limiting factor to the development of smaller and faster chips since the early twenty-first century. Increases in performance require

4104-561: The left of the scanned symbol or to the right of the scanned symbol. Turing's biographer Andrew Hodges (1983: 107) has noted and discussed this confusion. To the right: the above table as expressed as a "state transition" diagram. Usually large tables are better left as tables (Booth, p. 74). They are more readily simulated by computer in tabular form (Booth, p. 74). However, certain concepts—e.g. machines with "reset" states and machines with repeating patterns (cf. Hill and Peterson p. 244ff)—can be more readily seen when viewed as

4180-420: The left, state of the machine, the current symbol scanned by the head, and the non-blank symbols to the right. Example: total state of 3-state 2-symbol busy beaver after 3 "moves" (taken from example "run" in the figure below): This means: after three moves the tape has ... 000110000 ... on it, the head is scanning the right-most 1, and the state is A . Blanks (in this case represented by "0"s) can be part of

4256-413: The limitations of contemporary fabrication and design flaws, Leibniz' reckoner was not very functional, but similar devices ( Leibniz wheel ) remained in use into the 1970s. In the 19th century, Englishman Charles Babbage invented the difference engine , a mechanical device to calculate polynomials for astronomical purposes. Babbage also designed a general-purpose computer that was never built. Much of

4332-525: The lungs, liver, and kidneys. Computer components contain many toxic substances, like dioxins , polychlorinated biphenyls (PCBs), cadmium , chromium , radioactive isotopes and mercury . Circuit boards contain considerable quantities of lead-tin solders that are more likely to leach into groundwater or create air pollution due to incineration. Recycling of computer hardware is considered environmentally friendly because it prevents hazardous waste , including heavy metals and carcinogens, from entering

4408-477: The machine to stay on the same tape cell instead of moving left or right. This would not increase the machine's computational power. The most common convention represents each "Turing instruction" in a "Turing table" by one of nine 5-tuples, per the convention of Turing/Davis (Turing (1936) in The Undecidable , p. 126–127 and Davis (2000) p. 152): Other authors (Minsky (1967) p. 119, Hopcroft and Ullman (1979) p. 158, Stone (1972) p. 9) adopt

4484-425: The machine, this being one of the elementary operations of the machine. Any symbol on the tape may therefore eventually have an innings. The Turing machine mathematically models a machine that mechanically operates on a tape. On this tape are symbols, which the machine can read and write, one at a time, using a tape head. Operation is fully determined by a finite set of elementary instructions such as "in state 42, if

4560-506: The metal plates. Resistors, semiconductors, infrared detectors, stabilizers, cables, and wires contain cadmium. The circuit boards in a computer contain mercury, and chromium. When these types of materials, and chemicals are disposed improperly will become hazardous for the environment. When e-waste byproducts leach into groundwater, are burned, or get mishandled during recycling, it causes harm. Health problems associated with such toxins include impaired mental development, cancer, and damage to

4636-443: The motherboard include: An expansion card in computing is a printed circuit board that can be inserted into an expansion slot of a computer motherboard or backplane to add functionality to a computer system via the expansion bus. Expansion cards can be used to obtain or expand on features not offered by the motherboard. Using expansion cards for a video processor used to be common, but modern computers are more likely to instead have

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4712-509: The number of instructions the machines need to use. Based on a recognition that only a few instructions are commonly used, RISC shrinks the instruction set for added simplicity, which also enables the inclusion of more registers . After the invention of RISC in the 1980s, RISC based architectures that used pipelining and caching to increase performance displaced CISC architectures, particularly in applications with restrictions on power usage or space (such as mobile phones ). From 1986 to 2003,

4788-552: The recycling of computer hardware, refers to the donation, reuse, shredding and general collection of used electronics. Generically, the term refers to the process of collecting, brokering, disassembling, repairing and recycling the components or metals contained in used or discarded electronic equipment, otherwise known as electronic waste (e-waste). E-cyclable items include, but are not limited to: televisions, computers, microwave ovens, vacuum cleaners, telephones and cellular phones, stereos, and VCRs and DVDs just about anything that has

4864-462: The same cell, and moves the head one step to the left or the right, or halts the computation. The choice of which replacement symbol to write, which direction to move the head, and whether to halt is based on a finite table that specifies what to do for each combination of the current state and the symbol that is read. Like a real computer program, it is possible for a Turing machine to go into an infinite loop which will never halt. The Turing machine

4940-489: The same computational power as the Turing machine model. Common equivalent models are the multi-tape Turing machine , multi-track Turing machine , machines with input and output, and the non-deterministic Turing machine (NDTM) as opposed to the deterministic Turing machine (DTM) for which the action table has at most one entry for each combination of symbol and state. Read-only, right-moving Turing machines are equivalent to DFAs (as well as NFAs by conversion using

5016-646: The same function is running across multiple areas of data ( data parallelism ) or different tasks can be performed simultaneously with limited interaction ( task parallelism ). These forms of parallelism are accommodated by various hardware strategies, including instruction-level parallelism (such as instruction pipelining ), vector architectures and graphical processing units (GPUs) that are able to implement data parallelism, thread-level parallelism and request-level parallelism (both implementing task-level parallelism). Microarchitecture , also known as computer organization, refers to high-level hardware questions such as

5092-403: The same instruction. In some models, if there is no entry in the table for the current combination of symbol and state, then the machine will halt; other models require all entries to be filled. Every part of the machine (i.e. its state, symbol-collections, and used tape at any given time) and its actions (such as printing, erasing and tape motion) is finite , discrete and distinguishable ; it

5168-454: The separation of the computing unit and the I/O system in many diagrams, typically the hardware is shared, with a bit in the computing unit indicating whether it is in computation or I/O mode. Common types of ISAs include CISC ( complex instruction set computer ), RISC ( reduced instruction set computer ), vector operations , and hybrid modes. CISC involves using a larger expression set to minimize

5244-522: The symbol seen is 0, write a 1; if the symbol seen is 1, change into state 17; in state 17, if the symbol seen is 0, write a 1 and change to state 6;" etc. In the original article (" On Computable Numbers, with an Application to the Entscheidungsproblem ", see also references below ), Turing imagines not a mechanism, but a person whom he calls the "computer", who executes these deterministic mechanical rules slavishly (or as Turing puts it, "in

5320-445: The system's performance. Computer architecture requires prioritizing between different goals, such as cost, speed, availability, and energy efficiency. The designer must have a good grasp of the hardware requirements and many different aspects of computing, from compilers to integrated circuit design. Cost has also become a significant constraint for manufacturers seeking to sell their products for less money than competitors offering

5396-405: The theoretical limits of computing. The Turing machine is capable of processing an unrestricted grammar , which further implies that it is capable of robustly evaluating first-order logic in an infinite number of ways. This is famously demonstrated through lambda calculus . A Turing machine that is able to simulate any other Turing machine is called a universal Turing machine (UTM, or simply

5472-423: The total state as shown here: B 01; the tape has a single 1 on it, but the head is scanning the 0 ("blank") to its left and the state is B . "State" in the context of Turing machines should be clarified as to which is being described: the current instruction, or the list of symbols on the tape together with the current instruction, or the list of symbols on the tape together with the current instruction placed to

5548-428: The total system. What Turing called "the state formula" includes both the current instruction and all the symbols on the tape: Thus the state of progress of the computation at any stage is completely determined by the note of instructions and the symbols on the tape. That is, the state of the system may be described by a single expression (sequence of symbols) consisting of the symbols on the tape followed by Δ (which

5624-449: The unit. Hobbyists may decorate the cases with colored lights, paint, or other features, in an activity called case modding . Most personal computer power supply units meet the ATX standard and convert from alternating current (AC) at between 120 and 277 volts provided from a power outlet to direct current (DC) at a much lower voltage: typically 12, 5, or 3.3 volts. The motherboard

5700-451: Was a type of stored-program computer capable of mimicking the operations of any Turing machine (computer model) based on the software instructions passed to it. The storage of computer programs is key to the operation of modern computers and is the connection between computer hardware and software. Even prior to this, in the mid-19th century mathematician George Boole invented Boolean algebra —a system of logic where each proposition

5776-457: Was invented in 1936 by Alan Turing , who called it an "a-machine" (automatic machine). It was Turing's doctoral advisor, Alonzo Church , who later coined the term "Turing machine" in a review. With this model, Turing was able to answer two questions in the negative: Thus by providing a mathematical description of a very simple device capable of arbitrary computations, he was able to prove properties of computation in general—and in particular,

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