Read the introduction, look at the different logic families under "Electronic Gates" and study carefully the sections "Symbols" and "Truth Tables." Scan the rest of the article. Truth tables list the total possible input combinations of 1's and 0's and the corresponding outputs for each gate. Logic devices are physical implementations of Boolean logic and are built from components, which have gotten larger and more complex over time, for example: relays and transistors, gates, registers, multiplexors, adders, multipliers, ALUs (arithmetic logic units), data buses, memories, interfaces, and processors. These devices respond to control and data signals specified in machine instructions to perform the functions for which they were designed.
Alogic gateis an idealized or physicalelectronicdevice implementing aBoolean function, alogical operationperformed on one or morebinaryinputs that produces a single binary output. Depending on the context, the term may refer to anideal logic gate, one that has for instance zerorise timeand unlimitedfan-out, or it may refer to a non-ideal physical device(seeIdeal and real op-ampsfor comparison). Logic gates are primarily implemented usingdiodesortransistorsacting aselectronic switches, but can also be constructed usingvacuum tubes, electromagneticrelays(relay logic),fluidic logic, pneumatic logic,optics,molecules, or evenmechanicalelements. With amplification, logic gates can be cascaded in the same way that Boolean functions can be composed, allowing the construction of a physical model of all of Boolean logic, and therefore, all of the algorithms andmathematicsthat can be described with Boolean logic. Logic circuitsinclude such devices asmultiplexers,registers, arithmetic logic units(ALUs), andcomputer memory, all the way up through completemicroprocessors, which may contain more than 100 million gates. In modern practice, most gates are made fromMOSFETs(metal–oxide–semiconductorfield-effect transistors). Compound logic gatesAND-OR-Invert(AOI) and OR-AND-Invert (OAI) are often employed in circuit design because their construction using MOSFETs is simpler and more efficient than the sum of the individual gates. Inreversible logic,Toffoli gatesare used. Electronic gates Afunctionally completelogic system may be composed ofrelays,valves(vacuum tubes), ortransistors. The simplest family of logic gates usesbipolar transistors, and is calledresistor–transistor logic(RTL). Unlike simple diode logic gates (which do not have a gain element), RTL gates can be cascaded indefinitely to produce more complex logic functions. RTL gates were used in earlyintegrated circuits. For higher speed and better density, the resistors used in RTL were replaced by diodes resulting indiode–transistor logic(DTL). Transistor–transistor logic(TTL) then supplanted DTL. As integrated circuits became more complex, bipolar transistors were replaced with smallerfield-effect transistors( MOSFETs); seePMOSandNMOS. To reduce power consumption still further, most contemporary chip implementations of digital systems now useCMOSlogic. CMOS uses complementary (both n-channel and p-channel) MOSFET devices to achieve a high speed with low power dissipation. For small-scale logic, designers now use prefabricated logic gates from families of devices such as theTTL7400 seriesbyTexas Instruments, theCMOS 4000 seriesbyRCA, and their more recent descendants. Increasingly, these fixed-function logic gates are being replaced byprogrammable logic devices, which allow designers to pack many mixed logic gates into a single integrated circuit. The field-programmable nature ofprogrammable logic devicessuch asFPGAshas reduced the 'hard' property of hardware; it is now possible to change the logic design of a hardware system by reprogramming some of its components, thus allowing the features or function of a hardware implementation of a logic system to be changed. Other types of logic gates include, but are not limited to:
Logic family Abbreviation Description Diode logic DL Tunnel diode logic TDL Exactly the same as diode logic but can perform at a higher speed. Neon logic NL Uses neon bulbs or 3 element neon trigger tubes to perform logic. Core diode logic CDL Performed by semiconductor diodes and small ferrite toroidal cores for moderate speed and moderate power level. 4Layer Device Logic 4LDL Uses thyristors and SCRs to perform logic operations where high current and or high voltages are required. Direct-coupled transistor logic DCTL Uses transistors switching between saturated and cutoff states to perform logic. The transistors require carefully controlled parameters. Economical because few other components are needed, but tends to be susceptible to noise because of the lower voltage levels employed. Often considered to be the father to modern TTL logic. Metal-oxide-semiconductorlogic MOS UsesMOSFETs(metal-oxide-semiconductor field-effect transistors), the basis for most modern logic gates. The MOS logic family includesPMOS logic,NMOS logic,complementary MOS(CMOS), andBiCMOS(bipolar CMOS). Current-mode logic CML Uses transistors to perform logic but biasing is from constant current sources to prevent saturation and allow extremely fast switching. Has high noise immunity despite fairly low logic levels. Quantum-dot cellular automata QCA Uses tunnelable q-bits for synthesizing the binary logic bits. The electrostatic repulsive force in between two electrons in the quantum dots assigns the electron configurations (that defines high-level logic state 1 or low-level logic state 0) under the suitably driven polarizations. This is a transistorless, currentless, junctionless binary logic synthesis technique allowing it to have very fast operation speeds.
Electronic logic gates differ significantly from their relay-and-switch equivalents. They are much faster, consume much less power, and are much smaller (all by a factor of a million or more in most cases). Also, there is a fundamental structural difference. The switch circuit creates a continuous metallic path for current to flow (in either direction) between its input and its output. The semiconductor logic gate, on the other hand, acts as a high-gain voltageamplifier, which sinks a tiny current at its input and produces a low-impedance voltage at its output. It is not possible for current to flow between the output and the input of a semiconductor logic gate.
Another important advantage of standardized integrated circuit logic families, such as the 7400 and 4000 families, is that they can be cascaded. This means that the output of one gate can be wired to the inputs of one or several other gates, and so on. Systems with varying degrees of complexity can be built without great concern of the designer for the internal workings of the gates, provided the limitations of each integrated circuit are considered.
The output of one gate can only drive a finite number of inputs to other gates, a number called the 'fan-outlimit'. Also, there is always a delay, called the 'propagation delay', from a change in input of a gate to the corresponding change in its output. When gates are cascaded, the total propagation delay is approximately the sum of the individual delays, an effect which can become a problem in high-speed circuits. Additional delay can be caused when many inputs are connected to an output, due to the distributedcapacitanceof all the inputs and wiring and the finite amount of current that each output can provide.
History and development
Thebinary number systemwas refined byGottfried Wilhelm Leibniz(published in 1705), influenced by the ancientI Ching's binary system.Leibniz established that using the binary system combined the principles ofarithmeticandlogic.
In an 1886 letter,Charles Sanders Peircedescribed how logical operations could be carried out by electrical switching circuits.Eventually, vacuum tubesreplaced relays for logic operations.Lee De Forest's modification, in 1907, of theFleming valvecan be used as a logic gate.Ludwig Wittgensteinintroduced a version of the 16-rowtruth tableas proposition 5.101 ofTractatus Logico-Philosophicus(1921).Walther Bothe, inventor of thecoincidence circuit, got part of the 1954Nobel Prizein physics, for the first modern electronic AND gate in 1924.Konrad Zusedesigned and built electromechanical logic gates for his computerZ1(from 1935–38).
From 1934 to 1936,NECengineerAkira Nakashimaintroducedswitching circuit theoryin a series of papers showing thattwo-valued Boolean algebra, which he discovered independently, can describe the operation of switching circuits.His work was later cited byClaude E. Shannon, who elaborated on the use of Boolean algebra in the analysis and design of switching circuits in 1937.Using this property of electrical switches to implement logic is the fundamental concept that underlies all electronic digitalcomputers. Switching circuit theory became the foundation ofdigital circuitdesign, as it became widely known in the electrical engineering community during and afterWorld War II, with theoretical rigor superseding thead hocmethods that had prevailed previously.
Metal-oxide-semiconductor(MOS) logic originates from theMOSFET(metal-oxide-semiconductor field-effect transistor), invented byMohamed M. AtallaandDawon Kahngat Bell Labsin 1959.They first demonstrated bothPMOS logicandNMOS logicin 1960.Both types were later combined and adapted intocomplementary MOS(CMOS) logic byChih-Tang Sahand Frank WanlassatFairchild Semiconductorin 1963.
Active research is taking place inmolecular logic gates.
Symbols
A synchronous 4-bit up/down decade counter symbol (74LS192) in accordance with ANSI/IEEE Std. 91-1984 and IEC Publication 60617-12.
There are two sets of symbols for elementary logic gates in common use, both defined inANSI/IEEEStd 91-1984 and its supplement ANSI/IEEE Std 91a-1991. The "distinctive shape" set, based on traditional schematics, is used for simple drawings and derives fromUnited States Military StandardMIL-STD-806 of the 1950s and 1960s. It is sometimes unofficially described as "military", reflecting its origin. The "rectangular shape" set, based on ANSI Y32.14 and other early industry standards as later refined by IEEE and IEC, has rectangular outlines for all types of gate and allows representation of a much wider range of devices than is possible with the traditional symbols.The IEC standard,IEC60617-12, has been adopted by other standards, such asEN60617-12:1999 in Europe,BSEN 60617-12:1999 in the United Kingdom, andDINEN 60617-12:1998 in Germany.
The mutual goal of IEEE Std 91-1984 and IEC 60617-12 was to provide a uniform method of describing the complex logic functions of digital circuits with schematic symbols. These functions were more complex than simple AND and OR gates. They could be medium scale circuits such as a 4-bit counter to a large scale circuit such as a microprocessor.
IEC 617-12 and its successor IEC 60617-12 do not explicitly show the "distinctive shape" symbols, but do not prohibit them.These are, however, shown in ANSI/IEEE 91 (and 91a) with this note: "The distinctive-shape symbol is, according to IEC Publication 617, Part 12, not preferred, but is not considered to be in contradiction to that standard". IEC 60617-12 correspondingly contains the note (Section 2.1) "Although non-preferred, the use of other symbols recognized by official national standards, that is distinctive shapes in place of symbols, shall not be considered to be in contradiction with this standard. Usage of these other symbols in combination to form complex symbols (for example, use as embedded symbols) is discouraged". This compromise was reached between the respective IEEE and IEC working groups to permit the IEEE and IEC standards to be in mutual compliance with one another.
A third style of symbols, DIN 40700 (1976), was in use in Europe and is still widely used in European academia.
In the 1980s, schematics were the predominant method to design bothcircuit boardsand custom ICs known asgate arrays. Today custom ICs and thefield-programmable gate arrayare typically designed withHardware Description Languages(HDL) such asVerilogorVHDL.
| Type | Distinctive shape (IEEE Std 91/91a-1991) | Rectangular shape (IEEE Std 91/91a-1991) (IEC 60617-12:1997) | Boolean algebrabetween A & B | Truth table | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1-Input gates | ||||||||||||||||||||||
| Buffer |
|
|
| |||||||||||||||||||
| NOT (inverter) |
|
| or |
| ||||||||||||||||||
In electronics a NOT gate is more commonly called an inverter. The circle on the symbol is called abubbleand is used in logic diagrams to indicate a logic negation between the external logic state and the internal logic state (1 to 0 or vice versa). On a circuit diagram it must be accompanied by a statement asserting that thepositive logic conventionornegative logic conventionis being used (high voltage level = 1 or low voltage level = 1, respectively). Thewedgeis used in circuit diagrams to directly indicate an active-low (low voltage level = 1) input or output without requiring a uniform convention throughout the circuit diagram. This is calledDirect Polarity Indication. See IEEE Std 91/91A and IEC 60617-12. Both thebubbleand thewedgecan be used on distinctive-shape andrectangular-shape symbols on circuit diagrams, depending on the logic convention used. On pure logic diagrams, only thebubbleis meaningful. | ||||||||||||||||||||||
| ConjunctionandDisjunction | ||||||||||||||||||||||
| AND |
|
| or |
| ||||||||||||||||||
| OR |
|
| or |
| ||||||||||||||||||
| Alternative denialandJoint denial | ||||||||||||||||||||||
| NAND |
|
| or |
| ||||||||||||||||||
| NOR |  |  | or |
| ||||||||||||||||||
| Exclusive orandBiconditional | ||||||||||||||||||||||
| XOR |  |  | or |
| ||||||||||||||||||
The output of a two input exclusive-OR is true only when the two input values aredifferent, and false if they are equal, regardless of the value. If there are more than two inputs, the output of the distinctive-shape symbol is undefined. The output of the rectangular-shaped symbol is true if the number of true inputs is exactly one or exactly the number following the "=" in the qualifying symbol. | ||||||||||||||||||||||
| XNOR |  |  | or |
| ||||||||||||||||||
Truth tables
Output comparison of 1-input logic gates.
| INPUT | OUTPUT | |
| A | Buffer | Inverter |
| 0 | 0 | 1 |
| 1 | 1 | 0 |
Output comparison of 2-input logic gates.
| INPUT | OUTPUT | ||||||
| A | B | AND | NAND | OR | NOR | XOR | XNOR |
| 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 |
| 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 |
| 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 |
Universal logic gates
Further information on the theoretical basis:Functional completeness
The 7400 chip, containing four NANDs. The two additional pins supply power (+5 V) and connect the ground.
Charles Sanders Peirce(during 1880–81) showed thatNOR gates alone(or alternativelyNAND gates alone) can be used to reproduce the functions of all the other logic gates, but his work on it was unpublished until 1933.The first published proof was byHenry M. Shefferin 1913, so the NAND logical operation is sometimes calledSheffer stroke; thelogical NORis sometimes calledPeirce's arrow.Consequently, these gates are sometimes calleduniversal logic gates.
De Morgan equivalent symbols
By use ofDe Morgan's laws, anANDfunction is identical to anORfunction with negated inputs and outputs. Likewise, an ORfunction is identical to anANDfunction with negated inputs and outputs. A NAND gate is equivalent to an OR gate with negated inputs, and a NOR gate is equivalent to an AND gate with negated inputs.
This leads to an alternative set of symbols for basic gates that use the opposite core symbol (ANDorOR) but with the inputs and outputs negated. Use of these alternative symbols can make logic circuit diagrams much clearer and help to show accidental connection of an active high output to an active low input or vice versa. Any connection that has logic negations at both ends can be replaced by a negationless connection and a suitable change of gate or vice versa. Any connection that has a negation at one end and no negation at the other can be made easier to interpret by instead using the De Morgan equivalent symbol at either of the two ends. When negation or polarity indicators on both ends of a connection match, there is no logic negation in that path (effectively, bubbles "cancel"), making it easier to follow logic states from one symbol to the next. This is commonly seen in real logic diagrams – thus the reader must not get into the habit of associating the shapes exclusively as OR or AND shapes, but also take into account the bubbles at both inputs and outputs in order to determine the "true" logic function indicated.
A De Morgan symbol can show more clearly a gate's primary logical purpose and the polarity of its nodes that are considered in the "signaled" (active, on) state. Consider the simplified case where a two-input NAND gate is used to drive a motor when either of its inputs are brought low by a switch. The "signaled" state (motor on) occurs when either one OR the other switch is on. Unlike a regular NAND symbol, which suggests AND logic, the De Morgan version, a two negative-input OR gate, correctly shows that OR is of interest. The regular NAND symbol has a bubble at the output and none at the inputs (the opposite of the states that will turn the motor on), but the De Morgan symbol shows both inputs and output in the polarity that will drive the motor.
De Morgan's theorem is most commonly used to implement logic gates as combinations of only NAND gates, or as combinations of only NOR gates, for economic reasons.
Data storage
Logic gates can also be used to store data. A storage element can be constructed by connecting several gates in a "latch " circuit. More complicated designs that useclock signalsand that change only on a rising or falling edge of the clock are called edge-triggered " flip-flops". Formally, a flip-flop is called a bistable circuit, because it has two stable states which it can maintain indefinitely. The combination of multiple flip-flops in parallel, to store a multiple-bit value, is known as a register. When using any of these gate setups the overall system has memory; it is then called a sequential logicsystem since its output can be influenced by its previous state(s), i.e. by thesequence of input states. In contrast, the output from combinational logicis purely a combination of its present inputs, unaffected by the previous input and output states.
These logic circuits are known as computermemory. They vary in performance, based on factors ofspeed, complexity, and reliability of storage, and many different types of designs are used based on the application.
Three-state logic gates
A tristate buffer can be thought of as a switch. IfBis on, the switch is closed. If B is off, the switch is open.
A three-state logic gate is a type of logic gate that can have three different outputs: high (H), low (L) and high-impedance (Z). The high-impedance state plays no role in the logic, which is strictly binary. These devices are used on busesof theCPU to allow multiple chips to send data. A group of three-states driving a line with a suitable control circuit is basically equivalent to amultiplexer , which may be physically distributed over separate devices or plug-in cards.
In electronics, a high output would mean the output is sourcing current from the positive power terminal (positive voltage). A low output would mean the output is sinking current to the negative power terminal (zero voltage). High impedance would mean that the output is effectively disconnected from the circuit.
Implementations
Since the 1990s, most logic gates are made inCMOS(complementary metal oxide semiconductor) technology that uses both NMOS and PMOS transistors. Often millions of logic gates are packagedin a singleintegrated circuit .
There are severallogic familieswith different characteristics (power consumption, speed, cost, size) such as:RDL(resistor–diode logic),RTL(resistor-transistor logic),DTL(diode–transistor logic),TTL(transistor–transistor logic) and CMOS. There are also sub-variants, e.g. standard CMOS logic vs. advanced types using still CMOS technology, but with some optimizations for avoiding loss of speed due to slower PMOS transistors.
Non-electronic implementations are varied, though few of them are used in practical applications. Many early electromechanical digital computers, such as theHarvard Mark I, were built fromrelay logicgates, using electro-mechanicalrelays. Logic gates can be made usingpneumaticdevices, such as theSorteberg relayor mechanical logic gates, including on a molecular scale.Logic gates have been made out ofDNA(see DNA nanotechnology)and used to create a computer called MAYA (seeMAYA-II). Logic gates can be made fromquantum mechanicaleffects (thoughquantum computingusually diverges from boolean design; seequantum logic gate).Photonic logicgates usenonlinear opticaleffects.
In principle any method that leads to a gate that isfunctionally complete(for example, either a NOR or a NAND gate) can be used to make any kind of digital logic circuit. Note that the use of 3-state logic for bus systems is not needed, and can be replaced by digital multiplexers, which can be built using only simple logic gates (such as NAND gates, NOR gates, or AND and OR gates).
Source: Wikipedia, https://en.wikipedia.org/wiki/Logic_gate
This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 License.
