In electronics, a logic gate is an idealized or physical device
implementing a Boolean function; that is, it performs a logical
operation on one or more binary inputs and produces a single binary
output. Depending on the context, the term may refer to an ideal logic
gate, one that has for instance zero rise time and unlimited fan-out,
or it may refer to a non-ideal physical device[1] (see Ideal and real
op-amps for comparison).
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 Boolean logic, and therefore, all of the
algorithms and mathematics that can be described with Boolean logic.
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
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[edit]
Main article: Logic family
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).
Logic family Abbreviation Description Tunnel diode logic TDL Exactly the same as diode logic but can perform at a higher speed.[not in citation given] 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. 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 the tunnelable q-bits for synthesizng 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 suitable driven prolarizations.[4] This is a transistorless, currentless, junctionless binary logic syntheeis technique. This device has the lighting speed of operation. 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 'fan-out 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[edit]
The binary number system was refined by Gottfried Wilhelm Leibniz
(published in 1705), influenced by the ancient I Ching's binary
system.[5][6] Leibniz established that, by using the binary system,
the principles of arithmetic and logic could be combined.
In an 1886 letter,
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.[12] 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.[12] 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 [list of basic gates], 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)
Negation NOT A ¯ or ∼ A displaystyle overline A text or sim A INPUT OUTPUT A NOT A 0 1 1 0 In electronics a
Conjunction and Disjunction AND A ⋅ B displaystyle Acdot B INPUT OUTPUT A B A AND B 0 0 0 0 1 0 1 0 0 1 1 1 OR A + B displaystyle A+B INPUT OUTPUT A B A OR B 0 0 0 0 1 1 1 0 1 1 1 1 Alternative denial and Joint denial 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 Adownarrow B INPUT OUTPUT A B A NOR B 0 0 1 0 1 0 1 0 0 1 1 0
XOR 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. 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[edit] 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.
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: Tri-state buffer
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[edit]
Main article: Unconventional computing
Since the 1990s, most logic gates are made in
And-inverter graph
References[edit] ^ 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[edit] 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 Digital electronics Components Combinational logic
Theory Digital signal (electronics)
Boolean algebra
Logic synthesis
Logic in computer science
Design Logic synthesis Register-transfer level Formal equivalence checking Synchronous logic Asynchronous logic Finite-state machine Applications
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