Logic gate

A logic gate is a device that performs a Boolean function, a logical

operation performed on one or more binary inputs that 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).

The primary way of building logic gates uses diodes or transistors acting
as electronic switches. Today, most logic gates are made from MOSFETs
(metal–oxide–semiconductor field-effect transistors).[2] They can also be
constructed using vacuum tubes, electromagnetic relays with relay logic,
fluidic logic, pneumatic logic, optics, molecules, acoustics,[3] or even
mechanical or thermal[4] elements.

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 A logic circuit diagram for a 4-bit
carry lookahead binary adder design
Boolean logic, and therefore, all of the algorithms and mathematics that
using only the AND, OR, and XOR
can be described with Boolean logic. Logic circuits include such devices logic gates.
as multiplexers, registers, arithmetic logic units (ALUs), and computer
memory, all the way up through complete microprocessors, which may
contain more than 100 million logic gates.

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 gates.[5]

Electronic gates
A functionally complete logic system may be composed of relays, valves
(vacuum tubes), or transistors. The simplest family of logic gates uses
bipolar transistors, and 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 CMOS diagram of a NOT gate, also
supplanted DTL. As integrated circuits became more complex, bipolar known as an inverter. MOSFETs are
transistors were replaced with smaller field-effect transistors (MOSFETs); the most common way to make logic
see PMOS and NMOS. To reduce power consumption still further, most gates.
contemporary chip implementations of digital systems now use CMOS
logic. 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 the TTL 7400
series by Texas Instruments, the CMOS 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
many 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:[6]

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.

Performed by semiconductor diodes and small ferrite toroidal cores for moderate
Core diode logic CDL
speed and moderate power level.

4Layer Device Uses thyristors and SCRs to perform logic operations where high current and or
4LDL
Logic high voltages are required.
Uses transistors switching between saturated and cutoff states to perform logic.
The transistors require carefully controlled parameters. Economical because few
Direct-coupled
DCTL other components are needed, but tends to be susceptible to noise because of the
transistor logic
lower voltage levels employed. Often considered to be the father to modern TTL
logic.

Metal–oxide– Uses MOSFETs (metal–oxide–semiconductor field-effect transistors), the basis for

semiconductor MOS most modern logic gates. The MOS logic family includes PMOS logic, NMOS
logic logic, complementary MOS (CMOS), and BiCMOS (bipolar CMOS).

Uses transistors to perform logic but biasing is from constant current sources to
Current-mode
CML prevent saturation and allow extremely fast switching. Has high noise immunity
logic
despite fairly low logic levels.
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
Quantum-dot
QCA configurations (that defines state 1 or state 0) under the suitably driven
cellular automata
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 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 synchronous circuits. Additional delay can
be caused when many 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.
Logic built with FeFET (ferroelectric FET) transistors can retain their state to speed recovery in case of a power
loss.[7]

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.[8][9] Leibniz established that using the binary system combined the principles of
arithmetic and logic.

In an 1886 letter, Charles Sanders Peirce described how logical operations could be carried out by electrical
switching circuits.[10] Early electro-mechanical computers were constructed from switches and relay logic rather
than the later innovations of vacuum tubes (thermionic valves) or transistors (from which later electronic
computers were constructed). 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 to 1938).

From 1934 to 1936, NEC engineer Akira Nakashima, Claude Shannon and Victor Shestakov introduced
switching circuit theory in a series of papers showing that two-valued Boolean algebra, which they discovered
independently, can describe the operation of switching circuits.[11][12][13][14] 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.[14]

Metal–oxide–semiconductor (MOS) devices in the forms of PMOS and NMOS were demonstrated by Bell Labs
engineers Mohamed M. Atalla and Dawon Kahng in 1960.[15] Both types were later combined and adapted into
complementary MOS (CMOS) logic by Chih-Tang Sah and Frank Wanlass at Fairchild Semiconductor in
1963.[16]

Active research is taking place in molecular logic gates.

Symbols
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 United States Military
Standard MIL-STD-806 of the 1950s and 1960s.[17] 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.[18] The IEC standard, IEC 60617- A synchronous 4-bit up/down decade
12, has been adopted by other standards, such as EN 60617-12:1999 in counter symbol (74LS192) in
Europe, BS EN 60617-12:1999 in the United Kingdom, and DIN EN accordance with ANSI/IEEE Std. 91-
60617-12:1998 in Germany. 1984 and IEC Publication 60617-12.

The mutual goal of IEEE Std 91-1984 and IEC 617-12 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 renumbered successor IEC 60617-12 do not explicitly show the "distinctive shape" symbols,
but do not prohibit them.[18] These are, however, shown in ANSI/IEEE Std 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.

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.
 Boolean
Rectangular shape
Distinctive shape algebra
Type (IEEE Std 91/91a-1991) Truth table
(IEEE Std 91/91a-1991) between A
(IEC 60617-12:1997)
and B

Single-input gates

Input Output

A Q
Buffer
0 0
1 1

Input Output

NOT A Q
(inverter) or
0 1
1 0

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

Input Output

A B Q

or 0 0 0
AND
0 1 0

1 0 0

1 1 1

Input Output
A B Q

or 0 0 0
OR
0 1 1
1 0 1

1 1 1

Alternative denial and joint denial

NAND or
 Input Output
A B Q

0 0 1

0 1 1
1 0 1

1 1 0

Input Output

A B Q
0 0 1
NOR or
0 1 0

1 0 0
1 1 0

Exclusive or and biconditional

Input Output
A B Q

or 0 0 0
XOR
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.

Input Output
A B Q

0 0 1
XNOR or
0 1 0
1 0 0

1 1 1

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
1 0
1 0 1 0

1 1 1 0 0 1

Universal logic gates

Charles Sanders Peirce (during 1880–1881) 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.[19] 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.[20] Consequently, these gates are sometimes called
universal logic gates.[21]

The 7400 chip, containing four

NANDs. The two additional
pins supply power (+5 V) and
connect the ground.
 type NAND construction NOR construction

NOT

AND

NAND

OR

NOR

XOR

XNOR

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 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 and sequential logic

Logic gates can also be used to hold a state, allowing data storage. A
storage element can be constructed by connecting several gates in a
"latch" circuit. Latching circuitry is used in static random-access memory.
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 Animation of how an SR NOR gate
called a sequential logic system since its output can be influenced by its latch works.
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 used in 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 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 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.
effectively disconnected from the circuit.

Manufacturing
Since the 1990s, most logic gates are made in CMOS (complementary metal oxide semiconductor) technology
that uses both NMOS and PMOS transistors. Often millions of logic gates are packaged in a single integrated
circuit.

Non-electronic logic gates

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.[22] Various types of fundamental logic gates have been constructed
using molecules (molecular logic gates), which are based on chemical inputs and spectroscopic outputs.[23] Logic
gates have been made out of DNA (see DNA nanotechnology)[24] and used to create a computer called MAYA
(see MAYA-II). Logic gates can be made from quantum mechanical effects, see quantum logic gate. 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).

Logic families
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, 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.

See also
And-inverter graph
Boolean algebra topics
Boolean function
Depletion-load NMOS logic
Digital circuit
Espresso heuristic logic minimizer
Emitter-coupled logic
Fan-out
Field-programmable gate array (FPGA)
Flip-flop (electronics)
Functional completeness
Integrated injection logic
 Karnaugh map
Combinational logic
List of 4000 series integrated circuits
List of 7400 series integrated circuits
Logic family
Logic level
Logical graph
NMOS logic
Parametron
Processor design
Programmable logic controller (PLC)
Programmable logic device (PLD)
Propositional calculus
Quantum logic gate
Race hazard
Reversible computing
Superconducting computing
Truth table

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Further reading
Awschalom, D. D.; Loss, D.; Samarth, N. (2002). Semiconductor Spintronics and Quantum
Computation (https://books.google.com/books?id=tlDSx_8_5v4C). Springer. ISBN 978-3-540-
42176-4.
Bostock, Geoff (1988). Programmable logic devices: technology and applications (https://books.go
ogle.com/books?id=XEFTAAAAMAAJ). McGraw-Hill. ISBN 978-0-07-006611-3.
Brown, Stephen D.; Francis, Robert J.; Rose, Jonathan; Vranesic, Zvonko G. (1992). Field
Programmable Gate Arrays (https://books.google.com/books?id=8s4M-qYOWZIC). Kluwer
Academic. ISBN 978-0-7923-9248-4.

External links
Media related to Logic gates at Wikimedia Commons

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