Number
int64 1
7.61k
| Text
stringlengths 2
3.11k
|
|---|---|
4,701
|
Abel–Ruffini theorem states that, in general, the roots of a polynomial of degree five or higher cannot be expressed in terms of n-th roots.
|
4,702
|
If A is a positive-definite matrix or operator, then there exists precisely one positive definite matrix or operator B with B2 = A; we then define A1/2 = B. In general matrices may have multiple square roots or even an infinitude of them. For example, the 2 × 2 identity matrix has an infinity of square roots, though only one of them is positive definite.
|
4,703
|
Each element of an integral domain has no more than 2 square roots. The difference of two squares identity u2 − v2 = is proved using the commutativity of multiplication. If u and v are square roots of the same element, then u2 − v2 = 0. Because there are no zero divisors this implies u = v or u + v = 0, where the latter means that two roots are additive inverses of each other. In other words if an element a square root u of an element a exists, then the only square roots of a are u and −u. The only square root of 0 in an integral domain is 0 itself.
|
4,704
|
In a field of characteristic 2, an element either has one square root or does not have any at all, because each element is its own additive inverse, so that −u = u. If the field is finite of characteristic 2 then every element has a unique square root. In a field of any other characteristic, any non-zero element either has two square roots, as explained above, or does not have any.
|
4,705
|
Given an odd prime number p, let q = pe for some positive integer e. A non-zero element of the field Fq with q elements is a quadratic residue if it has a square root in Fq. Otherwise, it is a quadratic non-residue. There are /2 quadratic residues and /2 quadratic non-residues; zero is not counted in either class. The quadratic residues form a group under multiplication. The properties of quadratic residues are widely used in number theory.
|
4,706
|
The construction is also given by Descartes in his La Géométrie, see figure 2 on page 2. However, Descartes made no claim to originality and his audience would have been quite familiar with Euclid.
|
4,707
|
The MOSFET is a type of insulated-gate field-effect transistor that is fabricated by the controlled oxidation of a semiconductor, typically silicon. The voltage of the covered gate determines the electrical conductivity of the device; this ability to change conductivity with the amount of applied voltage can be used for amplifying or switching electronic signals.
|
4,708
|
The MOSFET is the basic building block of most modern electronics, and the most frequently manufactured device in history, with an estimated total of 13 sextillion MOSFETs manufactured between 1960 and 2018. It is the most common semiconductor device in digital and analog circuits, and the most common power device. It was the first truly compact transistor that could be miniaturized and mass-produced for a wide range of uses. MOSFET scaling and miniaturization has been driving the rapid exponential growth of electronic semiconductor technology since the 1960s, and enable high-density integrated circuits such as memory chips and microprocessors.
|
4,709
|
MOSFETs in integrated circuits are the primary elements of computer processors, semiconductor memory, image sensors, and most other types of integrated circuits. Discrete MOSFET devices are widely used in applications such as switch mode power supplies, variable-frequency drives, and other power electronics applications where each device may be switching thousands of watts. Radio-frequency amplifiers up to the UHF spectrum use MOSFET transistors as analog signal and power amplifiers. Radio systems also use MOSFETs as oscillators, or mixers to convert frequencies. MOSFET devices are also applied in audio-frequency power amplifiers for public address systems, sound reinforcement, and home and automobile sound systems.
|
4,710
|
The MOSFET is the most widely used type of transistor and the most critical device component in integrated circuit chips. Planar process, developed by Jean Hoerni at Fairchild Semiconductor in early 1959, was critical to the invention of the monolithic integrated circuit chip by Robert Noyce later in 1959. The same year, Mohamed M. Atalla used his surface passivation process to make the first working MOSFET with Dawon Kahng at Bell Labs. This was followed by the development of clean rooms to reduce contamination to levels never before thought necessary, and coincided with the development of photolithography which, along with surface passivation and the planar process, allowed circuits to be made in few steps.
|
4,711
|
Atalla realised that the main advantage of a MOS transistor was its ease of fabrication, particularly suiting it for use in the recently invented integrated circuits. In contrast to bipolar transistors which required a number of steps for the p–n junction isolation of transistors on a chip, MOSFETs required no such steps but could be easily isolated from each other. Its advantage for integrated circuits was re-iterated by Dawon Kahng in 1961. The Si–SiO2 system possessed the technical attractions of low cost of production and ease of integration. These two factors, along with its rapidly scaling miniaturization and low energy consumption, led to the MOSFET becoming the most widely used type of transistor in IC chips.
|
4,712
|
The earliest experimental MOS IC to be demonstrated was a 16-transistor chip built by Fred Heiman and Steven Hofstein at RCA in 1962. General Microelectronics later introduced the first commercial MOS integrated circuits in 1964, consisting of 120 p-channel transistors. It was a 20-bit shift register, developed by Robert Norman and Frank Wanlass. In 1967, Bell Labs researchers Robert Kerwin, Donald Klein and John Sarace developed the self-aligned gate MOS transistor, which Fairchild Semiconductor researchers Federico Faggin and Tom Klein used to develop the first silicon-gate MOS IC.
|
4,713
|
There are various different types of MOS IC chips, which include the following.
|
4,714
|
With its high scalability, and much lower power consumption and higher density than bipolar junction transistors, the MOSFET made it possible to build high-density IC chips. By 1964, MOS chips had reached higher transistor density and lower manufacturing costs than bipolar chips. MOS chips further increased in complexity at a rate predicted by Moore's law, leading to large-scale integration with hundreds of MOSFETs on a chip by the late 1960s. MOS technology enabled the integration of more than 10,000 transistors on a single LSI chip by the early 1970s, before later enabling very large-scale integration .
|
4,715
|
The MOSFET is the basis of every microprocessor, and was responsible for the invention of the microprocessor. The origins of both the microprocessor and the microcontroller can be traced back to the invention and development of MOS technology. The application of MOS LSI chips to computing was the basis for the first microprocessors, as engineers began recognizing that a complete computer processor could be contained on a single MOS LSI chip.
|
4,716
|
The earliest microprocessors were all MOS chips, built with MOS LSI circuits. The first multi-chip microprocessors, the Four-Phase Systems AL1 in 1969 and the Garrett AiResearch MP944 in 1970, were developed with multiple MOS LSI chips. The first commercial single-chip microprocessor, the Intel 4004, was developed by Federico Faggin, using his silicon-gate MOS IC technology, with Intel engineers Marcian Hoff and Stan Mazor, and Busicom engineer Masatoshi Shima. With the arrival of CMOS microprocessors in 1975, the term "MOS microprocessors" began to refer to chips fabricated entirely from PMOS logic or fabricated entirely from NMOS logic, contrasted with "CMOS microprocessors" and "bipolar bit-slice processors".
|
4,717
|
Complementary metal–oxide–semiconductor logic was developed by Chih-Tang Sah and Frank Wanlass at Fairchild Semiconductor in 1963. CMOS had lower power consumption, but was initially slower than NMOS, which was more widely used for computers in the 1970s. In 1978, Hitachi introduced the twin-well CMOS process, which allowed CMOS to match the performance of NMOS with less power consumption. The twin-well CMOS process eventually overtook NMOS as the most common semiconductor manufacturing process for computers in the 1980s. By the 1980s CMOS logic consumed over 7 times less power than NMOS logic, and about 100,000 times less power than bipolar transistor-transistor logic .
|
4,718
|
The growth of digital technologies like the microprocessor has provided the motivation to advance MOSFET technology faster than any other type of silicon-based transistor. A big advantage of MOSFETs for digital switching is that the oxide layer between the gate and the channel prevents DC current from flowing through the gate, further reducing power consumption and giving a very large input impedance. The insulating oxide between the gate and channel effectively isolates a MOSFET in one logic stage from earlier and later stages, which allows a single MOSFET output to drive a considerable number of MOSFET inputs. Bipolar transistor-based logic does not have such a high fanout capacity. This isolation also makes it easier for the designers to ignore to some extent loading effects between logic stages independently. That extent is defined by the operating frequency: as frequencies increase, the input impedance of the MOSFETs decreases.
|
4,719
|
The MOSFET's advantages in digital circuits do not translate into supremacy in all analog circuits. The two types of circuit draw upon different features of transistor behavior. Digital circuits switch, spending most of their time either fully on or fully off. The transition from one to the other is only of concern with regards to speed and charge required. Analog circuits depend on operation in the transition region where small changes to Vgs can modulate the output current. The JFET and bipolar junction transistor are preferred for accurate matching , higher transconductance and certain temperature characteristics which simplify keeping performance predictable as circuit temperature varies.
|
4,720
|
Nevertheless, MOSFETs are widely used in many types of analog circuits because of their own advantages . The characteristics and performance of many analog circuits can be scaled up or down by changing the sizes of the MOSFETs used. By comparison, in bipolar transistors the size of the device does not significantly affect its performance. MOSFETs' ideal characteristics regarding gate current and drain-source offset voltage also make them nearly ideal switch elements, and also make switched capacitor analog circuits practical. In their linear region, MOSFETs can be used as precision resistors, which can have a much higher controlled resistance than BJTs. In high power circuits, MOSFETs sometimes have the advantage of not suffering from thermal runaway as BJTs do. Also, MOSFETs can be configured to perform as capacitors and gyrator circuits which allow op-amps made from them to appear as inductors, thereby allowing all of the normal analog devices on a chip to be built entirely out of MOSFETs. This means that complete analog circuits can be made on a silicon chip in a much smaller space and with simpler fabrication techniques. MOSFETS are ideally suited to switch inductive loads because of tolerance to inductive kickback.
|
4,721
|
Some ICs combine analog and digital MOSFET circuitry on a single mixed-signal integrated circuit, making the needed board space even smaller. This creates a need to isolate the analog circuits from the digital circuits on a chip level, leading to the use of isolation rings and silicon on insulator . Since MOSFETs require more space to handle a given amount of power than a BJT, fabrication processes can incorporate BJTs and MOSFETs into a single device. Mixed-transistor devices are called bi-FETs if they contain just one BJT-FET and BiCMOS if they contain complementary BJT-FETs. Such devices have the advantages of both insulated gates and higher current density.
|
4,722
|
In the late 1980s, Asad Abidi pioneered RF CMOS technology, which uses MOS VLSI circuits, while working at UCLA. This changed the way in which RF circuits were designed, away from discrete bipolar transistors and towards CMOS integrated circuits. As of 2008, the radio transceivers in all wireless networking devices and modern mobile phones are mass-produced as RF CMOS devices. RF CMOS is also used in nearly all modern Bluetooth and wireless LAN devices.
|
4,723
|
MOSFET analog switches use the MOSFET to pass analog signals when on, and as a high impedance when off. Signals flow in both directions across a MOSFET switch. In this application, the drain and source of a MOSFET exchange places depending on the relative voltages of the source/drain electrodes. The source is the more negative side for an N-MOS or the more positive side for a P-MOS. All of these switches are limited on what signals they can pass or stop by their gate–source, gate–drain, and source–drain voltages; exceeding the voltage, current, or power limits will potentially damage the switch.
|
4,724
|
This analog switch uses a four-terminal simple MOSFET of either P or N type.
|
4,725
|
In the case of an n-type switch, the body is connected to the most negative supply and the gate is used as the switch control. Whenever the gate voltage exceeds the source voltage by at least a threshold voltage, the MOSFET conducts. The higher the voltage, the more the MOSFET can conduct. An N-MOS switch passes all voltages less than Vgate − Vtn. When the switch is conducting, it typically operates in the linear mode of operation, since the source and drain voltages will typically be nearly equal.
|
4,726
|
In the case of a P-MOS, the body is connected to the most positive voltage, and the gate is brought to a lower potential to turn the switch on. The P-MOS switch passes all voltages higher than Vgate − Vtp .
|
4,727
|
This "complementary" or CMOS type of switch uses one P-MOS and one N-MOS FET to counteract the limitations of the single-type switch. The FETs have their drains and sources connected in parallel, the body of the P-MOS is connected to the high potential and the body of the N-MOS is connected to the low potential . To turn the switch on, the gate of the P-MOS is driven to the low potential and the gate of the N-MOS is driven to the high potential. For voltages between VDD − Vtn and gnd − Vtp, both FETs conduct the signal; for voltages less than gnd − Vtp, the N-MOS conducts alone; and for voltages greater than VDD − Vtn, the P-MOS conducts alone.
|
4,728
|
The voltage limits for this switch are the gate–source, gate–drain and source–drain voltage limits for both FETs. Also, the P-MOS is typically two to three times wider than the N-MOS, so the switch will be balanced for speed in the two directions.
|
4,729
|
Tri-state circuitry sometimes incorporates a CMOS MOSFET switch on its output to provide for a low-ohmic, full-range output when on, and a high-ohmic, mid-level signal when off.
|
4,730
|
The advent of the MOSFET enabled the practical use of MOS transistors as memory cell storage elements, a function previously served by magnetic cores in computer memory. The first modern computer memory was introduced in 1965, when John Schmidt at Fairchild Semiconductor designed the first MOS semiconductor memory, a 64-bit MOS SRAM . SRAM became an alternative to magnetic-core memory, but required six MOS transistors for each bit of data.
|
4,731
|
MOS technology is the basis for DRAM . In 1966, Dr. Robert H. Dennard at the IBM Thomas J. Watson Research Center was working on MOS memory. While examining the characteristics of MOS technology, he found it was capable of building capacitors, and that storing a charge or no charge on the MOS capacitor could represent the 1 and 0 of a bit, while the MOS transistor could control writing the charge to the capacitor. This led to his development of a single-transistor DRAM memory cell. In 1967, Dennard filed a patent under IBM for a single-transistor DRAM memory cell, based on MOS technology. MOS memory enabled higher performance, was cheaper, and consumed less power, than magnetic-core memory, leading to MOS memory overtaking magnetic core memory as the dominant computer memory technology by the early 1970s.
|
4,732
|
Frank Wanlass, while studying MOSFET structures in 1963, noted the movement of charge through oxide onto a gate. While he did not pursue it, this idea would later become the basis for EPROM technology. In 1967, Dawon Kahng and Simon Sze proposed that floating-gate memory cells, consisting of floating-gate MOSFETs , could be used to produce reprogrammable ROM . Floating-gate memory cells later became the basis for non-volatile memory technologies including EPROM, EEPROM and flash memory.
|
4,733
|
There are various different types of MOS memory. The following list includes various different MOS memory types.
|
4,734
|
A number of MOSFET sensors have been developed, for measuring physical, chemical, biological and environmental parameters. The earliest MOSFET sensors include the open-gate FET introduced by Johannessen in 1970, the ion-sensitive field-effect transistor invented by Piet Bergveld in 1970, the adsorption FET patented by P.F. Cox in 1974, and a hydrogen-sensitive MOSFET demonstrated by I. Lundstrom, M.S. Shivaraman, C.S. Svenson and L. Lundkvist in 1975. The ISFET is a special type of MOSFET with a gate at a certain distance, and where the metal gate is replaced by an ion-sensitive membrane, electrolyte solution and reference electrode.
|
4,735
|
By the mid-1980s, numerous other MOSFET sensors had been developed, including the gas sensor FET , surface accessible FET , charge flow transistor , pressure sensor FET , chemical field-effect transistor , reference ISFET , biosensor FET , enzyme-modified FET and immunologically modified FET . By the early 2000s, BioFET types such as the DNA field-effect transistor , gene-modified FET and cell-potential BioFET had been developed.
|
4,736
|
The two main types of image sensors used in digital imaging technology are the charge-coupled device and the active-pixel sensor . Both CCD and CMOS sensors are based on MOS technology, with the CCD based on MOS capacitors and the CMOS sensor based on MOS transistors.
|
4,737
|
MOS technology is the basis for modern image sensors, including the charge-coupled device and the CMOS active-pixel sensor , used in digital imaging and digital cameras. Willard Boyle and George E. Smith developed the CCD in 1969. While researching the MOS process, they realized that an electric charge was the analogy of the magnetic bubble and that it could be stored on a tiny MOS capacitor. As it was fairly straightforward to fabricate a series of MOS capacitors in a row, they connected a suitable voltage to them so that the charge could be stepped along from one to the next. The CCD is a semiconductor circuit that was later used in the first digital video cameras for television broadcasting.
|
4,738
|
The MOS active-pixel sensor was developed by Tsutomu Nakamura at Olympus in 1985. The CMOS active-pixel sensor was later developed by Eric Fossum and his team at NASA's Jet Propulsion Laboratory in the early 1990s.
|
4,739
|
MOS image sensors are widely used in optical mouse technology. The first optical mouse, invented by Richard F. Lyon at Xerox in 1980, used a 5 µm NMOS sensor chip. Since the first commercial optical mouse, the IntelliMouse introduced in 1999, most optical mouse devices use CMOS sensors.
|
4,740
|
MOS sensors, also known as MOSFET sensors, are widely used to measure physical, chemical, biological and environmental parameters. The ion-sensitive field-effect transistor , for example, is widely used in biomedical applications.
|
4,741
|
MOSFETs are also widely used in microelectromechanical systems , as silicon MOSFETs could interact and communicate with the surroundings and process things such as chemicals, motions and light. An early example of a MEMS device is the resonant-gate transistor, an adaptation of the MOSFET, developed by Harvey C. Nathanson in 1965.
|
4,742
|
Common applications of other MOS sensors include the following.
|
4,743
|
The power MOSFET, which is commonly used in power electronics, was developed in the early 1970s. The power MOSFET enables low gate drive power, fast switching speed, and advanced paralleling capability.
|
4,744
|
The power MOSFET is the most widely used power device in the world. Advantages over bipolar junction transistors in power electronics include MOSFETs not requiring a continuous flow of drive current to remain in the ON state, offering higher switching speeds, lower switching power losses, lower on-resistances, and reduced susceptibility to thermal runaway. The power MOSFET had an impact on power supplies, enabling higher operating frequencies, size and weight reduction, and increased volume production.
|
4,745
|
Switching power supplies are the most common applications for power MOSFETs. They are also widely used for MOS RF power amplifiers, which enabled the transition of mobile networks from analog to digital in the 1990s. This led to the wide proliferation of wireless mobile networks, which revolutionised telecommunication systems. The LDMOS in particular is the most widely used power amplifier in mobile networks such as 2G, 3G, 4G and 5G, as well as broadcasting and amateur radio. Over 50 billion discrete power MOSFETs are shipped annually, as of 2018. They are widely used for automotive, industrial and communications systems in particular. Power MOSFETs are commonly used in automotive electronics, particularly as switching devices in electronic control units, and as power converters in modern electric vehicles. The insulated-gate bipolar transistor , a hybrid MOS-bipolar transistor, is also used for a wide variety of applications.
|
4,746
|
LDMOS, a power MOSFET with lateral structure, is commonly used in high-end audio amplifiers and high-power PA systems. Their advantage is a better behaviour in the saturated region than the vertical MOSFETs. Vertical MOSFETs are designed for switching applications.
|
4,747
|
Power MOSFETs, including DMOS, LDMOS and VMOS devices, are commonly used for a wide range of other applications, which include the following.
|
4,748
|
RF DMOS, also known as RF power MOSFET, is a type of DMOS power transistor designed for radio-frequency applications. It is used in various radio and RF applications, which include the following.
|
4,749
|
MOSFETs are fundamental to the consumer electronics industry. According to Colinge, numerous consumer electronics would not exist without the MOSFET, such as digital wristwatches, pocket calculators, and video games, for example.
|
4,750
|
MOSFETs are commonly used for a wide range of consumer electronics, which include the following devices listed. Computers or telecommunication devices are not included here, but are listed separately in the Information and communications technology section below.
|
4,751
|
One of the earliest influential consumer electronic products enabled by MOS LSI circuits was the electronic pocket calculator, as MOS LSI technology enabled large amounts of computational capability in small packages. In 1965, the Victor 3900 desktop calculator was the first MOS LSI calculator, with 29 MOS LSI chips. In 1967 the Texas Instruments Cal-Tech was the first prototype electronic handheld calculator, with three MOS LSI chips, and it was later released as the Canon Pocketronic in 1970. The Sharp QT-8D desktop calculator was the first mass-produced LSI MOS calculator in 1969, and the Sharp EL-8 which used four MOS LSI chips was the first commercial electronic handheld calculator in 1970. The first true electronic pocket calculator was the Busicom LE-120A HANDY LE, which used a single MOS LSI calculator-on-a-chip from Mostek, and was released in 1971. By 1972, MOS LSI circuits were commercialized for numerous other applications.
|
4,752
|
MOSFETs are commonly used for a wide range of audio-visual media technologies, which include the following list of applications.
|
4,753
|
Power MOSFETs are commonly used for a wide range of consumer electronics. Power MOSFETs are widely used in the following consumer applications.
|
4,754
|
MOSFETs are fundamental to information and communications technology , including modern computers, modern computing, telecommunications, the communications infrastructure, the Internet, digital telephony, wireless telecommunications, and mobile networks. According to Colinge, the modern computer industry and digital telecommunication systems would not exist without the MOSFET. Advances in MOS technology has been the most important contributing factor in the rapid rise of network bandwidth in telecommunication networks, with bandwidth doubling every 18 months, from bits per second to terabits per second .
|
4,755
|
MOSFETs are commonly used in a wide range of computers and computing applications, which include the following.
|
4,756
|
MOSFETs are commonly used in a wide range of telecommunications, which include the following applications.
|
4,757
|
The insulated-gate bipolar transistor is a power transistor with characteristics of both a MOSFET and bipolar junction transistor . As of 2010, the IGBT is the second most widely used power transistor, after the power MOSFET. The IGBT accounts for 27% of the power transistor market, second only to the power MOSFET , and ahead of the RF amplifier and bipolar junction transistor . The IGBT is widely used in consumer electronics, industrial technology, the energy sector, aerospace electronic devices, and transportation.
|
4,758
|
The IGBT is widely used in the following applications.
|
4,759
|
In quantum physics and quantum mechanics, the MOSFET is the basis for two-dimensional electron gas and the quantum Hall effect. The MOSFET enables physicists to study electron behavior in a two-dimensional gas, called a two-dimensional electron gas. In a MOSFET, conduction electrons travel in a thin surface layer, and a "gate" voltage controls the number of charge carriers in this layer. This allows researchers to explore quantum effects by operating high-purity MOSFETs at liquid helium temperatures.
|
4,760
|
In 1978, the Gakushuin University researchers Jun-ichi Wakabayashi and Shinji Kawaji observed the Hall effect in experiments carried out on the inversion layer of MOSFETs. In 1980, Klaus von Klitzing, working at the high magnetic field laboratory in Grenoble with silicon-based MOSFET samples developed by Michael Pepper and Gerhard Dorda, made the unexpected discovery of the quantum Hall effect.
|
4,761
|
The MOSFET is used in quantum technology. A quantum field-effect transistor or quantum well field-effect transistor is a type of MOSFET that takes advantage of quantum tunneling to greatly increase the speed of transistor operation.
|
4,762
|
MOSFETs are widely used in transportation. For example, they are commonly used for automotive electronics in the automotive industry. MOS technology is commonly used for a wide range of vehicles and transportation, which include the following applications.
|
4,763
|
MOSFETs are widely used in the automotive industry, particularly for automotive electronics in motor vehicles. Automotive applications include the following.
|
4,764
|
Power MOSFETs are widely used in transportation technology, which includes the following vehicles.
|
4,765
|
In the automotive industry, power MOSFETs are widely used in automotive electronics, which include the following.
|
4,766
|
The insulated-gate bipolar transistor is a power transistor with characteristics of both a MOSFET and bipolar junction transistor . IGBTs are widely used in the following transportation applications.
|
4,767
|
In the space industry, MOSFET devices were adopted by NASA for space research in 1964, for its Interplanetary Monitoring Platform program and Explorers space exploration program. The use of MOSFETs was a major step forward in the electronics design of spacecraft and satellites. The IMP D , launched in 1966, was the first spacecraft to use the MOSFET. Data gathered by IMP spacecraft and satellites were used to support the Apollo program, enabling the first crewed Moon landing with the Apollo 11 mission in 1969.
|
4,768
|
The Cassini–Huygens to Saturn in 1997 had spacecraft power distribution accomplished 192 solid-state power switch devices, which also functioned as circuit breakers in the event of an overload condition. The switches were developed from a combination of two semiconductor devices with switching capabilities: the MOSFET and the ASIC . This combination resulted in advanced power switches that had better performance characteristics than traditional mechanical switches.
|
4,769
|
MOSFETs are commonly used for a wide range of other applications, which include the following.
|
4,770
|
Housed in special high-speed memory, microcode translates machine instructions, state machine data, or other input into sequences of detailed circuit-level operations. It separates the machine instructions from the underlying electronics, thereby enabling greater flexibility in designing and altering instructions. Moreover, it facilitates the construction of complex multi-step instructions, while simultaneously reducing the complexity of computer circuits. The act of writing microcode is often referred to as microprogramming, and the microcode in a specific processor implementation is sometimes termed a microprogram.
|
4,771
|
Through extensive microprogramming, microarchitectures of smaller scale and simplicity can emulate more robust architectures with wider word lengths, additional execution units, and so forth. This approach provides a relatively straightforward method of ensuring software compatibility between different products within a processor family.
|
4,772
|
Some hardware vendors, notably IBM/Lenovo, use the term microcode interchangeably with firmware. In this context, all code within a device is termed microcode, whether it is microcode or machine code. For instance, updates to a hard disk drive's microcode often encompass updates to both its microcode and firmware.
|
4,773
|
At the hardware level, processors contain a number of separate areas of circuity, or "units", that perform different tasks. Commonly found units include the arithmetic logic unit which performs instructions such as addition or comparing two numbers, circuits for reading and writing data to external memory, and small areas of onboard memory to store these values while they are being processed. In most designs, additional high-performance memory, the register file, is used to store temporary values, not just those needed by the current instruction.
|
4,774
|
To properly perform an instruction, the various circuits have to be activated in order. For instance, it is not possible to add two numbers if they have not yet been loaded from memory. In RISC designs, the proper ordering of these instructions is largely up to the programmer, or at least to the compiler of the programming language they are using. So to add two numbers, for instance, the compiler may output instructions to load one of the values into one register, the second into another, call the addition function in the ALU, and then write the result back out to memory.
|
4,775
|
As the sequence of instructions needed to complete this higher-level concept, "add these two numbers in memory", may require multiple instructions, this can represent a performance bottleneck if those instructions are stored in main memory. Reading those instructions one by one is taking up time that could be used to read and write the actual data. For this reason, it is common for non-RISC designs to have many different instructions that differ largely on where they store data. For instance, the MOS 6502 has eight variations of the addition instruction, ADC, which differ only in where they look to find the two operands.
|
4,776
|
Using the variation of the instruction, or "opcode", that most closely matches the ultimate operation can reduce the number of instructions to one, saving memory used by the program code and improving performance by leaving the data bus open for other operations. Internally, however, these instructions are not separate operations, but sequences of the operations the units actually perform. Converting a single instruction read from memory into the sequence of internal actions is the duty of the control unit, another unit within the processor.
|
4,777
|
The basic idea behind microcode is to replace the custom logic implementing the instruction sequencing with a series of simple instructions run in a "microcode engine" in the processor. Whereas a custom logic system might have a series of diodes and gates that output a series of voltages on various control lines, the microcode engine is connected to these lines instead, and these are turned on and off as the engine reads the microcode instructions in sequence. The microcode instructions are often bit encoded to those lines, for instance, if bit 8 is true, that might mean that the ALU should be paused awaiting data. In this respect microcode is somewhat similar to the paper rolls in a player piano, where the holes represent which key should be pressed.
|
4,778
|
The distinction between custom logic and microcode may seem small, one uses a pattern of diodes and gates to decode the instruction and produce a sequence of signals, whereas the other encodes the signals as microinstructions that are read in sequence to produce the same results. The critical difference is that in a custom logic design, changes to the individual steps require the logic to be redesigned. Using microcode, all that changes is the code stored in the associated read only memory . This makes it much easier to fix problems in a microcode system. It also means that there is no effective limit to the complexity of the instructions, it is only limited by the amount of ROM one is willing to use.
|
4,779
|
The lowest layer in a computer's software stack is traditionally raw machine code instructions for the processor. In microcoded processors, fetching and decoding those instructions, and executing them, may be done by microcode. To avoid confusion, each microprogram-related element is differentiated by the micro prefix: microinstruction, microassembler, microprogrammer, etc.
|
4,780
|
Complex digital processors may also employ more than one control unit in order to delegate sub-tasks that must be performed essentially asynchronously in parallel. For example, the VAX 9000 has an IBox unit to fetch and decode instructions, which it hands to a microcoded EBox unit to be executed, and the VAX 8800 has both a microcoded IBox and a microcoded EBox.
|
4,781
|
A high-level programmer, or even an assembly language programmer, does not normally see or change microcode. Unlike machine code, which often retains some backward compatibility among different processors in a family, microcode only runs on the exact electronic circuitry for which it is designed, as it constitutes an inherent part of the particular processor design itself.
|
4,782
|
Engineers normally write the microcode during the design phase of a processor, storing it in a read-only memory or programmable logic array structure, or in a combination of both. However, machines also exist that have some or all microcode stored in static random-access memory or flash memory. This is traditionally denoted as writeable control store in the context of computers, which can be either read-only or read–write memory. In the latter case, the CPU initialization process loads microcode into the control store from another storage medium, with the possibility of altering the microcode to correct bugs in the instruction set, or to implement new machine instructions.
|
4,783
|
Microprograms consist of series of microinstructions, which control the CPU at a very fundamental level of hardware circuitry. For example, a single typical horizontal microinstruction might specify the following operations:
|
4,784
|
To simultaneously control all processor's features in one cycle, the microinstruction is often wider than 50 bits; e.g., 128 bits on a 360/85 with an emulator feature. Microprograms are carefully designed and optimized for the fastest possible execution, as a slow microprogram would result in a slow machine instruction and degraded performance for related application programs that use such instructions.
|
4,785
|
Microcode was originally developed as a simpler method of developing the control logic for a computer. Initially, CPU instruction sets were hardwired. Each step needed to fetch, decode, and execute the machine instructions was controlled directly by combinational logic and rather minimal sequential state machine circuitry. While such hard-wired processors were very efficient, the need for powerful instruction sets with multi-step addressing and complex operations made them difficult to design and debug; highly encoded and varied-length instructions can contribute to this as well, especially when very irregular encodings are used.
|
4,786
|
Microcode simplified the job by allowing much of the processor's behaviour and programming model to be defined via microprogram routines rather than by dedicated circuitry. Even late in the design process, microcode could easily be changed, whereas hard-wired CPU designs were very cumbersome to change. Thus, this greatly facilitated CPU design.
|
4,787
|
From the 1940s to the late 1970s, a large portion of programming was done in assembly language; higher-level instructions mean greater programmer productivity, so an important advantage of microcode was the relative ease by which powerful machine instructions can be defined. The ultimate extension of this are "Directly Executable High Level Language" designs, in which each statement of a high-level language such as PL/I is entirely and directly executed by microcode, without compilation. The IBM Future Systems project and Data General Fountainhead Processor are examples of this. During the 1970s, CPU speeds grew more quickly than memory speeds and numerous techniques such as memory block transfer, memory pre-fetch and multi-level caches were used to alleviate this. High-level machine instructions, made possible by microcode, helped further, as fewer more complex machine instructions require less memory bandwidth. For example, an operation on a character string can be done as a single machine instruction, thus avoiding multiple instruction fetches.
|
4,788
|
Architectures with instruction sets implemented by complex microprograms included the IBM System/360 and Digital Equipment Corporation VAX. The approach of increasingly complex microcode-implemented instruction sets was later called complex instruction set computer . An alternate approach, used in many microprocessors, is to use one or more programmable logic array or read-only memory mainly for instruction decoding, and let a simple state machine do most of the sequencing. The MOS Technology 6502 is an example of a microprocessor using a PLA for instruction decode and sequencing. The PLA is visible in photomicrographs of the chip, and its operation can be seen in the transistor-level simulation.
|
4,789
|
Microprogramming is still used in modern CPU designs. In some cases, after the microcode is debugged in simulation, logic functions are substituted for the control store. Logic functions are often faster and less expensive than the equivalent microprogram memory.
|
4,790
|
A processor's microprograms operate on a more primitive, totally different, and much more hardware-oriented architecture than the assembly instructions visible to normal programmers. In coordination with the hardware, the microcode implements the programmer-visible architecture. The underlying hardware need not have a fixed relationship to the visible architecture. This makes it easier to implement a given instruction set architecture on a wide variety of underlying hardware micro-architectures.
|
4,791
|
The IBM System/360 has a 32-bit architecture with 16 general-purpose registers, but most of the System/360 implementations use hardware that implements a much simpler underlying microarchitecture; for example, the System/360 Model 30 has 8-bit data paths to the arithmetic logic unit and main memory and implemented the general-purpose registers in a special unit of higher-speed core memory, and the System/360 Model 40 has 8-bit data paths to the ALU and 16-bit data paths to main memory and also implemented the general-purpose registers in a special unit of higher-speed core memory. The Model 50 has full 32-bit data paths and implements the general-purpose registers in a special unit of higher-speed core memory. The Model 65 through the Model 195 have larger data paths and implement the general-purpose registers in faster transistor circuits. In this way, microprogramming enabled IBM to design many System/360 models with substantially different hardware and spanning a wide range of cost and performance, while making them all architecturally compatible. This dramatically reduces the number of unique system software programs that must be written for each model.
|
4,792
|
A similar approach was used by Digital Equipment Corporation in their VAX family of computers. As a result, different VAX processors use different microarchitectures, yet the programmer-visible architecture does not change.
|
4,793
|
Microprogramming also reduces the cost of field changes to correct defects in the processor; a bug can often be fixed by replacing a portion of the microprogram rather than by changes being made to hardware logic and wiring.
|
4,794
|
In 1947, the design of the MIT Whirlwind introduced the concept of a control store as a way to simplify computer design and move beyond ad hoc methods. The control store is a diode matrix: a two-dimensional lattice, where one dimension accepts "control time pulses" from the CPU's internal clock, and the other connects to control signals on gates and other circuits. A "pulse distributor" takes the pulses generated by the CPU clock and breaks them up into eight separate time pulses, each of which activates a different row of the lattice. When the row is activated, it activates the control signals connected to it.
|
4,795
|
In 1951, Maurice Wilkes enhanced this concept by adding conditional execution, a concept akin to a conditional in computer software. His initial implementation consisted of a pair of matrices: the first one generated signals in the manner of the Whirlwind control store, while the second matrix selected which row of signals to invoke on the next cycle. Conditionals were implemented by providing a way that a single line in the control store could choose from alternatives in the second matrix. This made the control signals conditional on the detected internal signal. Wilkes coined the term microprogramming to describe this feature and distinguish it from a simple control store.
|
4,796
|
Microcode remained relatively rare in computer design as the cost of the ROM needed to store the code was not significantly different than using a custom control store. This changed through the early 1960s with the introduction of mass-produced core memory and core rope, which was far less expensive that dedicated logic based on diode arrays or similar solutions. The first to take real advantage of this was IBM in their 1964 System/360 series. This allowed the machines to have a very complex instruction set, including operations that matched high-level language constructs like formatting binary values as decimal strings, storing the complex series of instructions needed for this task in low cost memory.
|
4,797
|
But the real value in the 360 line was that one could build a series of machines that were completely different internally, yet run the same ISA. For a low-end machine, one might use an 8-bit ALU that requires multiple cycles to complete a single 32-bit addition, while a higher end machine might have a full 32-bit ALU that performs the same addition in a single cycle. These differences could be implemented in control logic, but the cost of implementing a completely different decoder for each machine would be prohibitive. Using microcode meant all that changed was the code in the ROM. For instance, one machine might include a floating point unit and thus its microcode for multiplying two numbers might be only a few lines line, whereas on the same machine without the FPU this would be a program that did the same using multiple additions, and all that changed was the ROM.
|
4,798
|
The outcome of this design was that customers could use a low-end model of the family to develop their software, knowing that if more performance was ever needed, they could move to a faster version and nothing else would change. This lowered the barrier to entry and the 360 was a runaway success. By the end of the decade, the use of microcode was de rigueur across the mainframe industry.
|
4,799
|
Early minicomputers were far too simple to require microcode, and were more similar to earlier mainframes in terms of their instruction sets and the way they were decoded. But it was not long before their designers began using more powerful integrated circuits that allowed for more complex ISAs. By the mid-1970s, most new minicomputers and superminicomputers were using microcode as well, such as most models of the PDP-11 and, most notably, most models of the VAX, which included high-level instruction not unlike those found in the 360.
|
4,800
|
The same basic evolution occurred with microprocessors as well. Early designs were extremely simple, and even the more powerful 8-bit designs of the mid-1970s like the Zilog Z80 had instruction sets that were simple enough to be implemented in dedicated logic. By this time, the control logic could be patterned into the same die as the CPU, making the difference in cost between ROM and logic less of an issue. However, it was not long before these companies were also facing the problem of introducing higher-performance designs but still wanting to offer backward compatibility. Among early examples of microcode in micros was the Intel 8086.
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.