In electronics , a LOGIC GATE is an idealized or physical device
implementing a
Logic gates are primarily implemented using diodes or transistors
acting as electronic switches , but can also be constructed using
vacuum tubes , electromagnetic relays (relay logic ), fluidic logic ,
pneumatic logic , optics , molecules , or even mechanical elements.
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
Logic circuits include such devices as multiplexers , registers , arithmetic logic units (ALUs), and computer memory , all the way up through complete microprocessors , which may contain more than 100 million gates. In modern practice, most gates are made from field-effect transistors (FETs), particularly metal–oxide–semiconductor field-effect transistors (MOSFETs). Compound logic gates
In reversible logic , Toffoli gates are used. CONTENTS * 1 Electronic gates * 2 History and development * 3 Symbols * 4 Universal logic gates * 5 De Morgan equivalent symbols * 6 Data storage * 7 Three-state logic gates * 8 Implementations * 9 See also * 10 References * 11 Further reading ELECTRONIC GATES Main article:
To build a functionally complete logic system, relays , valves
(vacuum tubes), or transistors can be used. The simplest family of
logic gates using bipolar transistors is called resistor-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 early integrated
circuits . For higher speed and better density, the resistors used in
RTL were replaced by diodes resulting in diode-transistor logic (DTL).
For small-scale logic, designers now use prefabricated logic gates
from families of devices such as the TTL
Other types of logic gates include, but are not limited to: LOGIC FAMILY ABBREVIATION DESCRIPTION Tunnel diode logic
TDL
Exactly the same as
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 SCR’s to perform logic operations where high current and or high voltages are required.
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 voltage amplifier , 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 'fanout limit'. 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 a large number of inputs are connected to an output, due to the distributed capacitance of all the inputs and wiring and the finite amount of current that each output can provide. HISTORY AND DEVELOPMENT The binary number system was refined by Gottfried Wilhelm Leibniz
(published in 1705), influenced by the ancient
In an 1886 letter,
From 1934 to 1936,
Active research is taking place in molecular 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 in ANSI /IEEE Std 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 from MIL-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, IEC 60617-12, has been adopted by other standards, such as EN 60617-12:1999 in Europe, BS EN 60617-12:1999 in the United Kingdom, and DIN EN 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 was in use in Europe and is still widely used in European academia. See the column "DIN 40700" in the table in the German. In the 1980s, schematics were the predominant method to design both
circuit boards and custom ICs known as gate arrays . Today custom ICs
and the field-programmable gate array are typically designed with
Hardware Description Languages (HDL) such as
TYPE Distinctive shape (IEEE Std 91/91a-1991) Rectangular shape (IEEE Std 91/91a-1991 IEC 60617-12 : 1997) BOOLEAN ALGEBRA BETWEEN A "> A or A {displaystyle {overline {A}}{text{ or }}{sim }A} INPUT OUTPUT A NOT A 0 1 1 0 In electronics a
2-INPUT GATES AND A B or A B {displaystyle Aoplus B} INPUT OUTPUT A B A XOR B 0 0 0 0 1 1 1 0 1 1 1 0 The output of a two input exclusive-OR is true only when the two input values are different, 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. INVERTED 2-INPUT GATES NAND A B or A B {displaystyle {overline {Acdot B}}{text{ or }}Auparrow B} INPUT OUTPUT A B A NAND B 0 0 1 0 1 1 1 0 1 1 1 0 NOR A + B or A B {displaystyle {overline {A+B}}{text{ or }}A-B} INPUT OUTPUT A B A NOR B 0 0 1 0 1 0 1 0 0 1 1 0 XNOR A B or A B {displaystyle {overline {Aoplus B}}{text{ or }}{Aodot B}} INPUT OUTPUT A B A XNOR B 0 0 1 0 1 0 1 0 0 1 1 1 UNIVERSAL LOGIC GATES For more details on the theoretical basis, see Functional completeness . The 7400 chip, containing four NANDs. The two additional pins supply power (+5 V) and connect the ground.
DE MORGAN EQUIVALENT SYMBOLS By use of De Morgan\'s laws , an AND function is identical to an OR
function with negated inputs and outputs. Likewise, an OR function is
identical to an AND function with negated inputs and outputs. A NAND
gate is equivalent to an
This leads to an alternative set of symbols for basic gates that use the opposite core symbol (AND or OR) 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 N
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 Main article:
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 use clock signals and 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 logic system since its output can be influenced by its previous state(s), i.e. by the sequence of input states. In contrast, the output from combinational logic is purely a combination of its present inputs, unaffected by the previous input and output states. These logic circuits are known as computer memory . They vary in performance, based on factors of speed , 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. If B is on, the
switch is closed. If B is off, the switch is open. Main article:
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 buses of the CPU to allow multiple chips to send data. A group of three-states driving a line with a suitable control circuit is basically equivalent to a multiplexer , 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 Main article:
Since the 1990s, most logic gates are made in
There are several logic families with 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
Non-electronic implementations are varied, though few of them are
used in practical applications. Many early electromechanical digital
computers, such as the
In principle any method that leads to a gate that is functionally 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). SEE ALSO *
REFERENCES * ^ Jaeger, Microelectronic Circuit Design, McGraw-Hill 1997, ISBN
0-07-032482-4 , pp. 226-233
* ^ Tinder, Richard F. (2000). Engineering digital design: Revised
Second Edition. pp. 317–319. ISBN 0-12-691295-5 . Retrieved
2008-07-04.
* ^ Rowe, Jim. "Circuit Logic - Why and How" (December 1966).
FURTHER READING * Awschalom, D.D.; Loss, D.; Samarth, N. (5 August 2002). Semiconductor Spintronics and Quantum Computation. Berlin, Germany: Springer-Verlag. ISBN 978-3-540-42176-4 . Retrieved 28 November 2012. * Bostock, Geoff (1988). Programmable logic devices: technology and applications. New York: McGraw-Hill. ISBN 978-0-07-006611-3 . Retrieved 28 November 2012. * Brown, Stephen D.; Francis, Robert J.; Rose, Jonathan; Vranesic, Zvonko G. (1992). Field Programmable Gate Arrays. Boston, MA: Kluwer Academic Publishers. ISBN 978-0-7923-9248-4 . Retrieved 28 November 2012. * v * t * e COMPONENTS *
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