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 (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
AND-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
In reversible logic, Toffoli gates are used.
1 Electronic gates
2 History and development
4 Universal logic gates
5 De Morgan equivalent symbols
6 Data storage
7 Three-state logic gates
9 See also
11 Further reading
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).
Transistor–transistor logic (TTL) then supplanted DTL. As integrated
circuits became more complex, bipolar transistors were replaced with
smaller field-effect transistors (MOSFETs); see PMOS and NMOS. To
reduce power consumption still further, most contemporary chip
implementations of digital systems now use
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 the TTL
7400 series by Texas
4000 series by RCA, and their more recent
descendants. Increasingly, these fixed-function logic gates are being
replaced by programmable logic devices, which allow designers to pack
a large number of mixed logic gates into a single integrated circuit.
The field-programmable nature of programmable logic devices such as
FPGAs has 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:
Tunnel diode logic
Exactly the same as diode logic but can perform at a higher speed.[not
in citation given]
Uses neon bulbs or 3 element neon trigger tubes to perform logic.
Core diode logic
Performed by semiconductor diodes and small ferrite toroidal cores for
moderate speed and moderate power level.
4Layer Device Logic
Uses thyristors and SCRs to perform logic operations where high
current and or high voltages are required.
Direct-coupled transistor logic
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.
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
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. This is a transistorless, currentless, junctionless
binary logic syntheeis technique. This device has the lighting speed
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
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
The binary number system was refined by Gottfried Wilhelm Leibniz
(published in 1705), influenced by the ancient I Ching's binary
system. Leibniz established that, by using the binary system,
the principles of arithmetic and logic could be combined.
In an 1886 letter,
Charles Sanders Peirce
Charles Sanders Peirce described how logical
operations could be carried out by electrical switching circuits.
Eventually, vacuum tubes replaced relays for logic operations. Lee De
Forest's modification, in 1907, of the
Fleming valve can be used as a
Ludwig Wittgenstein introduced a version of the 16-row
truth table as proposition 5.101 of Tractatus Logico-Philosophicus
(1921). Walther Bothe, inventor of the coincidence circuit, got part
of the 1954
Nobel Prize in physics, for the first modern electronic
AND gate in 1924.
Konrad Zuse designed and built electromechanical
logic gates for his computer Z1 (from 1935–38).
From 1934 to 1936,
Akira Nakashima introduced switching
circuit theory in a series of papers showing that two-valued Boolean
algebra, which he discovered independently, can describe the operation
of switching circuits. His work was later cited by
Claude 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 digital computers. Switching
circuit theory became the foundation of digital circuit design, as it
became widely known in the electrical engineering community during and
after World War II, with theoretical rigor superseding the ad hoc
methods that had prevailed previously.
Active research is taking place in molecular logic gates.
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 [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
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
Verilog or VHDL.
(IEEE Std 91/91a-1991)
(IEEE Std 91/91a-1991
IEC 60617-12 : 1997)
Boolean algebra between A & B
displaystyle overline A text or sim A
In electronics a
NOT gate is more commonly called an inverter. The
circle on the symbol is called a bubble and 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 the positive logic
convention or negative logic convention is being used (high voltage
level = 1 or low voltage level = 1, respectively). The wedge is 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 called Direct Polarity
Indication. See IEEE Std 91/91A and IEC 60617-12. Both the bubble and
the wedge can be used on distinctive-shape and rectangular-shape
symbols on circuit diagrams, depending on the logic convention used.
On pure logic diagrams, only the bubble is meaningful.
Conjunction and Disjunction
displaystyle Acdot B
A AND B
A OR B
Alternative denial and Joint denial
displaystyle overline Acdot B text or Auparrow B
A NAND B
displaystyle overline A+B text or Adownarrow B
A NOR B
Exclusive or and Biconditional
displaystyle Aoplus B
A XOR B
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
displaystyle overline Aoplus B text or Aodot B
A XNOR B
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
Charles Sanders Peirce (during 1880–81) showed that NOR gates alone
(or alternatively NAND 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 by Henry M.
Sheffer in 1913, so the NAND logical operation is sometimes called
Sheffer stroke; the logical NOR is sometimes called Peirce's
arrow. Consequently, these gates are sometimes called universal
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
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 (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
AND 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.
Main article: Sequential logic
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
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: 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
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.
Main article: Unconventional computing
Since the 1990s, most logic gates are made in
metal oxide semiconductor) technology that uses both NMOS and PMOS
transistors. Often millions of logic gates are packaged in a single
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 CMOS. There are also sub-variants,
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 the Harvard Mark I, were built from relay logic
gates, using electro-mechanical relays. Logic gates can be made using
pneumatic devices, such as the Sorteberg relay or mechanical logic
gates, including on a molecular scale. Logic gates have been made
DNA nanotechnology) and used to create a computer
called MAYA (see MAYA-II). Logic gates can be made from quantum
mechanical effects (though quantum computing usually diverges from
Photonic logic gates use nonlinear optical effects.
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).
Boolean algebra topics
Espresso heuristic logic minimizer
4000 series integrated circuits
7400 series integrated circuits
Programmable Logic Controller
Programmable Logic Controller (PLC)
Programmable Logic Device
Programmable Logic Device (PLD)
^ 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
^ Rowe, Jim. "Circuit Logic - Why and How" (December 1966).
Electronics Australia. access-date= requires url= (help)
^ Roy, S. S. (September 2016). "Simplification of master power
expression and effective power detection of QCA device (Wave nature
tunneling of electron in QCA device)". 2016 IEEE Students #8217;
Technology Symposium (TechSym): 272–277.
^ Nylan, Michael (2001). The Five "Confucian" Classics. Yale
University Press. pp. 204–206. ISBN 978-0-300-08185-5.
Retrieved 8 June 2010.
^ Perkins, Franklin. Leibniz and China: A Commerce of Light.
Cambridge: Cambridge University Press, 2004. p 117. Print.
^ Peirce, C. S., "Letter, Peirce to A. Marquand", dated 1886, Writings
of Charles S. Peirce, v. 5, 1993, pp. 421–23. See Burks, Arthur W.,
"Review: Charles S. Peirce, The new elements of mathematics", Bulletin
of the American Mathematical Society v. 84, n. 5 (1978), pp. 913–18,
see 917. PDF Eprint.
^ History of Research on Switching Theory in Japan, IEEJ Transactions
on Fundamentals and Materials, Vol. 124 (2004) No. 8, pp. 720-726,
Institute of Electrical Engineers of Japan
^ Switching Theory/
Relay Circuit Network Theory/Theory of Logical
Computer Museum, Information Processing Society of
^ a b Radomir S. Stanković (University of Niš), Jaakko T. Astola
(Tampere University of Technology), Mark G. Karpovsky (Boston
University), Some Historical Remarks on Switching Theory, 2007, DOI
^ a b Radomir S. Stanković, Jaakko Astola (2008), Reprints from the
Early Days of Information Sciences: TICSP Series On the Contributions
Akira Nakashima to Switching Theory, TICSP Series #40, Tampere
International Center for Signal Processing, Tampere University of
^ a b Overview of IEEE Standard 91-1984 Explanation of Logic Symbols,
Doc. No. SDYZ001A,
Texas Instruments Semiconductor Group, 1996
^ Peirce, C. S. (manuscript winter of 1880–81), "A Boolean Algebra
with One Constant", published 1933 in Collected Papers v. 4,
paragraphs 12–20. Reprinted 1989 in Writings of Charles S. Peirce v.
4, pp. 218-21, Google Preview. See Roberts, Don D. (2009), The
Existential Graphs of Charles S. Peirce, p. 131.
^ Hans Kleine Büning; Theodor Lettmann (1999). Propositional logic:
deduction and algorithms. Cambridge University Press. p. 2.
^ John Bird (2007). Engineering mathematics. Newnes. p. 532.
^ Mechanical Logic gates (focused on molecular scale)
DNA Logic gates Archived 2010-06-18 at the Wayback Machine.
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
Integrated circuit (IC)
Digital signal (electronics)
Logic in computer science
Digital signal (signal processing)
Digital signal processing
Switching circuit theory
Formal equivalence checking