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A logic gate performs a logical operation on one or more logic inputs and produces a single logic output. Because the output is also a logic-level value, an output of one logic gate can connect to the input of one or more other logic gates. The logic normally performed is Boolean logic and is most commonly found in digital circuits. Boolean logic is a complete system for Logical operations It was named after George Boole, who first defined an algebraic system of Digital electronics are Electronics systems that use Digital signals Digital electronics are representations of Boolean algebra also see Logic gates are primarily implemented electronically using diodes or transistors, but can also be constructed using electromagnetic relays, fluidics, optics, molecules, or even mechanical elements. Electronics refers to the flow of charge (moving Electrons through Nonmetal conductors (mainly Semiconductors, whereas electrical Dioden2jpg|thumb|right|150px|Figure 2 Various semiconductor diodes In Electronics, a transistor is a Semiconductor device commonly used to amplify or switch electronic signals A relay is an electrical Switch that opens and closes under the control of another Electrical circuit. Fluidics (also known as Fluidic logic) is the use of a Fluid or compressible medium to perform analog or Digital operations similar to those A molecular logic gate is a molecule that performs a logical operation on one or more logic inputs and produces a single logic output The analytical engine, an important step in the History of computers, was the design of a mechanical general-purpose Computer by the British mathematician Charles

In electronic logic, a logic level is represented by a voltage or current, (which depends on the type of electronic logic in use). Each logic gate requires power so that it can source and sink currents to achieve the correct output voltage. In logic circuit diagrams the power is not shown, but in a full electronic schematic, power connections are required.

Contents

Truth table

Main article: Truth table

A truth table is a table that describes the behaviour of a logic gate. A truth table is a Mathematical table used in Logic — specifically in connection with Boolean algebra, Boolean functions and Propositional It lists the value of the output for every possible combination of the inputs and can be used to simplify the number of logic gates and level of nesting in an electronic circuit. In general the truth table does not lead to an efficient implementation; a minimization procedure, using Karnaugh maps, the Quine–McCluskey algorithm or a heuristic algorithm is required for reducing the circuit complexity. The Karnaugh map, also known as a Veitch diagram ( KV-map or K-map for short is a tool to facilitate the simplification of Boolean algebra The Quine–McCluskey algorithm (or the method of prime implicants) is a method used for minimization of Boolean functions which was developed by W The Espresso logic minimizer is a widely used computer program using heuristic and specific algorithms for efficiently reducing the complexity of digital electronic gate circuits

Background

Main article: Logic family

The simplest form of electronic logic is diode logic. In Computer engineering, a logic family may refer to one of two related concepts Diode logic or Diode-resistor logic, is a circuit style that uses Diodes to construct Boolean Logic gates for circuits. This allows AND and OR gates to be built, but not inverters, and so is an incomplete form of logic. Further, without some kind of amplification it is not possible to have such basic logic operations cascaded as required for more complex logic functions. To build a complete logic system, valves (vacuum tubes) or transistors can be used. This article is about the electronic device not an evacuated pipe used for experiments in Free-fall. In Electronics, a transistor is a Semiconductor device commonly used to amplify or switch electronic signals The simplest family of logic gates using bipolar transistors is called resistor-transistor logic, or RTL. Resistor–transistor logic ( RTL) is a class of Digital circuits built using Resistors as the input network and Bipolar junction transistors Unlike diode logic gates, RTL gates can be cascaded indefinitely to produce more complex logic functions. These gates were used in early integrated circuits. Microchipsjpg|right|thumb|200px|Microchips ( EPROM memory with a transparent window showing the integrated circuit inside For higher speed, the resistors used in RTL were replaced by diodes, leading to diode-transistor logic, or DTL. It was then discovered that one transistor could do the job of two diodes in the space of one diode even better, by more quickly switching off the following stage, so transistor-transistor logic, or TTL, was created. Transistor–transistor logic ( TTL) is a class of Digital circuits built from Bipolar junction transistors (BJT and Resistors It is called In virtually every type of contemporary chip implementation of digital systems, the bipolar transistors have been replaced by complementary field-effect transistors (MOSFETs) to reduce size and power consumption still further, thereby resulting in complementary metal-oxide-semiconductor (CMOS) logic. The field-effect transistor (FET is a type of Transistor that relies on an Electric field to control the shape and hence the conductivity of a 'channel' The metal–oxide–semiconductor field-effect transistor ( MOSFET, MOS-FET, or MOS FET) is a device used to amplify or switch electronic signals Complementary metal–oxide–semiconductor ( CMOS) (pronounced "see-moss" siːmɔːs ˈsiːmɒs is a major class of Integrated circuits CMOS technology

For small-scale logic, designers now use prefabricated logic gates from families of devices such as the TTL 7400 seriesby Texas Instruments and the CMOS 4000 series by RCA, and their more recent descendants. In Computer engineering, a logic family may refer to one of two related concepts Transistor–transistor logic ( TTL) is a class of Digital circuits built from Bipolar junction transistors (BJT and Resistors It is called The 7400 series of Transistor-transistor logic Integrated circuits are historically important as the first widespread family of TTL integrated circuit Texas Instruments ( better known in the electronics industry (and popularly as TI, is an American company based in Dallas, Texas, USA Complementary metal–oxide–semiconductor ( CMOS) (pronounced "see-moss" siːmɔːs ˈsiːmɒs is a major class of Integrated circuits CMOS technology The 4000 series is a family of industry standard Integrated circuits which implement a variety of logic functions using Complementary Metal–Oxide–Semiconductor RCA Corporation, founded as Radio Corporation of America, was an electronics company in existence from 1919 to 1986 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. A programmable logic device or PLD is an electronic component used to build reconfigurable Digital circuits Unlike a Logic gate, which has a Microchipsjpg|right|thumb|200px|Microchips ( EPROM memory with a transparent window showing the integrated circuit inside The field-programmable nature of programmable logic devices such as FPGAs has removed 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. A programmable logic device or PLD is an electronic component used to build reconfigurable Digital circuits Unlike a Logic gate, which has a FPGAs should not be confused with the Flip-chip pin grid array, a form of integrated circuit packaging

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. Electrical tension (or voltage after its SI unit, the Volt) is the difference of electrical potential between two points of an electrical An electronic amplifier is a device for increasing the power and/or Amplitude of a signal. It is not possible for current to flow between the output and the input of a semiconductor logic gate.

Another important advantage of standardised integrated circuit logic families, such as the 7400 and 4000 families, is that they are cascadable. Microchipsjpg|right|thumb|200px|Microchips ( EPROM memory with a transparent window showing the integrated circuit inside In Computer engineering, a logic family may refer to one of two related concepts This means that the output of one gate can be wired to the inputs of one or several other gates, and so on. Systems of arbitrary 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. Networking Propagation delay is defined as how long it takes for a certain amount of bytes to transfered over a medium 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. Capacitance is a measure of the amount of Electric charge stored (or separated for a given Electric potential.

Logic gates and hardware

NAND and NOR logic gates are the two pillars of logic, in that all other types of Boolean logic gates (i. Definition The NAND operation is a Logical operation on two Logical values typically the values of two Propositions that produces a value Symbols There are two symbols for NOR gates the American ('military' symbol and the IEC ('European' or 'rectangular' symbol e. , AND, OR, NOT, XOR, XNOR) can be created from a suitable network of just NAND or just NOR gate(s). Symbols There are two symbols for OR gates the 'military' symbol and the 'rectangular' symbol Symbols There are two symbols for XOR gates the 'military' symbol and the 'rectangular' symbol Symbols There are two symbols for XNOR gates the 'professional' symbol and the 'rectangular' symbol They can be built from relays or transistors, or any other technology that can create an inverter and a two-input AND or OR gate. Hence the NAND and NOR gates are called the universal gates.

For an input of 2 variables, there are 16 possible boolean algebraic functions. These 16 functions are enumerated below, together with their outputs for each combination of inputs variables.

INPUT A 0 0 1 1
B 0 1 0 1
OUTPUT 0 0 0 0 0
A AND B 0 0 0 1
A > B * 0 0 1 0
A 0 0 1 1
A < B * 0 1 0 0
B 0 1 0 1
A XOR B 0 1 1 0
A OR B 0 1 1 1
A NOR B 1 0 0 0
A XNOR B 1 0 0 1
NOT B 1 0 1 0
A ≥ B * 1 0 1 1
NOT A 1 1 0 0
A ≤ B * 1 1 0 1
A NAND B 1 1 1 0
1 1 1 1 1

The four functions labeled with a "*" are the logical implication functions: "A ≤ B" can be read as "A implies B"; it follows that "A > B" is "A does not imply B". In Logic and Mathematics, logical implication is a logical relation that holds between a set T of formulae and a formula B when every These four functions are less common and are usually not implemented directly as 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.
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 in common use, both now defined by ANSI/IEEE Std 91-1984 and its supplement ANSI/IEEE Std 91a-1991. The Institute of Electrical and Electronics Engineers or IEEE (read eye-triple-e) is an international Non-profit, professional organization The "distinctive shape" set, based on traditional schematics, is used for simple drawings and is quicker to draw by hand. It is sometimes unofficially described as "military", reflecting its origin if not its modern usage. The "rectangular shape" set, based on IEC 60617-12, 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 International Electrotechnical Commission ( IEC) is a not-for-profit, non-governmental international Standards organization that prepares and publishes The IEC's system has been adopted by other standards, such as EN 60617-12:1999 in Europe and BS EN 60617-12:1999 in the United Kingdom. European Committee for Standardization or Comité Européen de Normalisation ( CEN) is a private non-profit organisation whose mission is to foster the European economy British Standards are produced by BSI British Standards, a division of BSI Group that is incorporated under a Royal Charter and is formally designated

The goal of IEEE Std 91-1984 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 circuits such as a microprocessor. The 1984 version did not include the "distinctive shape" symbols. [1] These were added to the 1991 supplement 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. "

In the 1980s, schematics were the predominant method to design both circuit boards and custom ICs known as gate arrays. A gate array or uncommitted logic array ( ULA) is an approach to the design and manufacture of Application-specific integrated circuits (ASICs Today custom ICs and the field-programmable gate array are typically designed with Hardware Description Languages (HDL) such as Verilog or VHDL. FPGAs should not be confused with the Flip-chip pin grid array, a form of integrated circuit packaging In Electronics, a hardware description language or HDL is any language from a class of Computer languages and/or Programming languages for formal In the Semiconductor and electronic design industry Verilog is a Hardware description language (HDL used to model electronic systems. The need for complex logic symbols has diminished and distinctive shape symbols are still the predominate style.

Type Distinctive shape Rectangular shape Boolean algebra between A & B Truth table
AND AND symbol AND symbol A \cdot B
INPUT OUTPUT
A B A AND B
0 0 0
0 1 0
1 0 0
1 1 1
OR OR symbol OR symbol A + B
INPUT OUTPUT
A B A OR B
0 0 0
0 1 1
1 0 1
1 1 1
NOT NOT symbol NOT symbol \overline{A}
INPUT OUTPUT
A NOT A
0 1
1 0
In electronics a NOT gate is more commonly called an inverter. Symbols There are two symbols for OR gates the 'military' symbol and the 'rectangular' symbol The circle on the symbol is called a bubble, and is generally used in circuit diagrams to indicate an inverted (active-low) input or output. [1][2]
NAND NAND symbol NAND symbol \overline{A \cdot B}
INPUT OUTPUT
A B A NAND B
0 0 1
0 1 1
1 0 1
1 1 0
NOR NOR symbol NOR symbol \overline{A + B}
INPUT OUTPUT
A B A NOR B
0 0 1
0 1 0
1 0 0
1 1 0
In practice, the cheapest gate to manufacture is usually the NAND gate. Definition The NAND operation is a Logical operation on two Logical values typically the values of two Propositions that produces a value Symbols There are two symbols for NOR gates the American ('military' symbol and the IEC ('European' or 'rectangular' symbol Additionally, Charles Peirce showed that NAND gates alone (as well as NOR gates alone) can be used to reproduce the functions of all the other logic gates. Charles Sanders Peirce (pronounced purse) (September 10 1839 &ndash April 19 1914 was an American Logician mathematician, philosopher
The 7400 chip, containing four NANDs. The two additional pins supply power (+5 V) and connect the ground.
The 7400 chip, containing four NANDs. The two additional pins supply power (+5 V) and connect the ground.

Two more gates are the exclusive-OR or XOR function and its inverse, exclusive-NOR or XNOR. The two input Exclusive-OR is true only when the two input values are different, false if they are equal, regardless of the value. If there are more than two inputs, the gate generates a true at its output if the number of trues at its input is odd ([2]). In practice, these gates are built from combinations of simpler logic gates.

XOR XOR symbol XOR symbol A \oplus B
INPUT OUTPUT
A B A XOR B
0 0 0
0 1 1
1 0 1
1 1 0
XNOR XNOR symbol XNOR symbol \overline{A \oplus B}
INPUT OUTPUT
A B A XNOR B
0 0 1
0 1 0
1 0 0
1 1 1

DeMorgan equivalent symbols

By use of De Morgan's theorem, an AND gate can be turned into an OR gate by inverting the sense of the logic at its inputs and outputs. Symbols There are two symbols for XOR gates the 'military' symbol and the 'rectangular' symbol Symbols There are two symbols for XNOR gates the 'professional' symbol and the 'rectangular' symbol In Logic, De Morgan's laws or De Morgan's theorem are rules in Formal logic relating pairs of dual Logical operators in a systematic manner expressed This leads to a separate set of symbols with inverted inputs and the opposite core symbol. These symbols can make circuit diagrams for circuits using active low signals much clearer and help to show accidental connection of an active high output to an active low input or vice-versa. Symbolically, a NAND gate can also be shown using the OR shape with bubbles on its inputs, and a NOR gate can be shown as an AND gate with bubbles on its inputs. The bubble signifies a logic inversion. This reflects the equivalency due to De Morgans law, but it also allows a diagram to be read more easily, or a circuit to be mapped onto available physical gates in packages easily, since any circuit node that has bubbles at both ends can be replaced by a simple bubble-less connection and a suitable change of gate. In Logic, De Morgan's laws or De Morgan's theorem are rules in Formal logic relating pairs of dual Logical operators in a systematic manner expressed If the NAND is drawn as OR with input bubbles, and a NOR as AND with input bubbles, this gate substitution occurs automatically in the diagram (effectively, bubbles "cancel"). 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.


Storage of bits

Main article: sequential logic

Related to the concept of logic gates (and also built from them) is the idea of storing a bit of information. In Digital circuit theory sequential logic is a type of logic circuit whose output depends not only on the present input but also on the history of the input None of the gates discussed up to here can store a value by itself: when the inputs change, the outputs immediately react. It is possible to make a storage element either through a capacitor (which stores charge due to its physical properties) or by feedback. A capacitor is a passive electrical component that can store Energy in the Electric field between a pair of conductors Connecting the output of a gate to the input causes it to be put through the logic again, and choosing the feedback correctly allows it to be preserved or modified through the use of other inputs. A set of gates arranged in this fashion is known as a "latch", and more complicated designs that utilize clocks (signals that oscillate with a known period) and change only on the rising edge are called edge-triggered "flip-flops". In Electronics, a latch is a kind of Bistable Multivibrator, an Electronic circuit which has two stable states and thereby can store In Electronics and especially synchronous Digital circuits a clock signal is a signal used to coordinate the actions of two or more circuits In Digital circuits a flip-flop is a term referring to an Electronic circuit (a Bistable Multivibrator) that has two stable states and thereby 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). In Digital circuit theory sequential logic is a type of logic circuit whose output depends not only on the present input but also on the history of the input

These registers or capacitor-based circuits are known as computer memory. Computer data storage, often called storage or memory, refers to Computer components devices and recording media that retain digital 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.
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

Three-state, or 3-state, logic gates have three states of the output: high (H), low (L) and high-impedance (Z). In digital Electronics three-state, tri-state, or 3-state logic allows output ports to have a value of logical 0 1 or Hi-Z The high-impedance state plays no role in the logic, which remains strictly binary. These devices are used on buses to allow multiple chips to send data. An electrical bus (sometimes spelled incorrectly as buss) is a physical electrical interface where many devices share the same electric connection 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 multiplexer or mux ( occasionally the term muldex is also found for a combination multiplexer-demultiplexer

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.

'Tri-state', a widely-used synonym of 'three-state', is a trademark of the National Semiconductor Corporation. National Semiconductor ( is a Semiconductor manufacturer specializing in analog devices and subsystems headquartered in Santa Clara, California,

Miscellaneous

Logic circuits include such devices as multiplexers, registers, arithmetic logic units (ALUs), and computer memory, all the way up through complete microprocessors which can contain more than a 100 million gates. In Electronics, a multiplexer or mux ( occasionally the term muldex is also found for a combination multiplexer-demultiplexer In Computer architecture, a processor register is a small amount of storage available on the CPU whose contents can be accessed more quickly than storage In Computing, an arithmetic logic unit ( ALU) is a Digital circuit that performs Arithmetic and Logical operations Computer data storage, often called storage or memory, refers to Computer components devices and recording media that retain digital A microprocessor incorporates most or all of the functions of a Central processing unit (CPU on a single Integrated In practice, the gates are made from field effect transistors (FETs), particularly metal-oxide-semiconductor FETs (MOSFETs). The field-effect transistor (FET is a type of Transistor that relies on an Electric field to control the shape and hence the conductivity of a 'channel' The metal–oxide–semiconductor field-effect transistor ( MOSFET, MOS-FET, or MOS FET) is a device used to amplify or switch electronic signals

In reversible logic, Toffoli gates are used. Reversible computing includes any Computational process that is (at least to some close approximation Reversible, i In Computer science, the Toffoli gate, invented by Tommaso Toffoli, is a universal reversible Logic gate, which means that any reversible circuit

History and development

The earliest logic gates were made mechanically. Charles Babbage, around 1837, devised the Analytical Engine. The analytical engine, an important step in the History of computers, was the design of a mechanical general-purpose Computer by the British mathematician Charles His logic gates relied on mechanical gearing to perform operations. Electromagnetic relays were later used for logic gates. In 1891, Almon Strowger patented a device containing a logic gate switch circuit (U.S. Patent 0,447,918 ). Almon Brown Strowger (1839 &ndash May 26 1902 gave his name to the electromechanical Telephone exchange technology that his invention and Patent inspired Strowger's patent was not in widespread use until the 1920s. Starting in 1898, Nikola Tesla filed for patents of devices containing logic gate circuits (see List of Tesla patents). There have already been discussions about Tesla's ethnicity on the talk page A patent is a set of Exclusive rights granted by a State to an inventor or his assignee for a fixed period of time in exchange for a disclosure of an Below is a list of Tesla patents. Dr Nikola Tesla was an Inventor who obtained around 300 Patents ref>Snezana Sarbo Tesla's Patents, Sixth Eventually, vacuum tubes replaced relays for logic operations. This article is about the electronic device not an evacuated pipe used for experiments in Free-fall. Lee De Forest's modification, in 1907, of the Fleming valve can be used as AND logic gate. Lee De Forest, ( August 26, 1873 – June 30, 1961) was an American Inventor with over 300 patents to his credit This article is about the electronic device not an evacuated pipe used for experiments in Free-fall. Ludwig Wittgenstein introduced a version of the 16-row truth table, which is shown above, as proposition 5. A truth table is a Mathematical table used in Logic — specifically in connection with Boolean algebra, Boolean functions and Propositional 101 of Tractatus Logico-Philosophicus (1921). Tractatus Logico-Philosophicus is the only book-length work published by Austrian Philosopher Ludwig Wittgenstein. Claude E. Shannon introduced the use of Boolean algebra in the analysis and design of switching circuits in 1937. Claude Elwood Shannon (April 30 1916 – February 24 2001 an American Electronic engineer and Mathematician, is "the father of Information Year 1937 ( MCMXXXVII) was a Common year starting on Friday (link will display the full calendar of the Gregorian calendar. 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. Walther Wilhelm Georg Bothe (8 January 1891 in Oranienburg &ndash 8 February 1957 in Heidelberg) was a German nuclear physicst In Physics, a coincidence circuit is an Electronic device with one Output and two (or more Inputs The output is activated only when signals Year 1954 ( MCMLIV) was a Common year starting on Friday (link will display full 1954 Gregorian calendar) The Nobel Prize (Nobelpriset (Nobelprisen is a Swedish prize established in the 1895 will of Swedish chemist Alfred Nobel; it was first awarded in Peace, Literature Year 1924 ( MCMXXIV) was a Leap year starting on Tuesday (link will display the full calendar of the Gregorian calendar. Active research is taking place in molecular logic gates. A molecular logic gate is a molecule that performs a logical operation on one or more logic inputs and produces a single logic output

See also

References

Further reading

External links

electronic_gate at HowStuffWorks

Dictionary

logic gate

-noun

  1. a physical device, typically electronic, which computes a Boolean logical output (0 or 1) from Boolean input or inputs according to there rules of some logical operator.
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