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Encyclopedia > Logic gate

A logic gate is a combination of different electronic components, that takes one or more logic-level inputs and produces a single logic-level 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.

In electronic logic, a logic level is represented by a certain voltage (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. There are 7 positive logic gates and each gate has two laws or rules.

## Truth table

Main article: Truth table

A truth table is a table that describes the behaviour of a logic gate. 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. Truth tables are a type of mathematical table used in logic to determine whether an expression is true or whether an argument is valid. ... The Karnaugh map, also known as a Veitch diagram (K-map or KV-map for short), is a tool to facilitate management of Boolean algebraic expressions. ... The Quineâ€“McCluskey algorithm is a method used for minimization of boolean functions. ... The Espresso heuristic logic minimizer is a widely used computer program for efficiently reducing the complexity of digital electronic gate circuits. ...

## Background

The simplest form of electronic logic is diode logic. This allows AND and OR gates to be built, but not inverters, and so is an incomplete form of logic. To build a complete logic system, valves (vacuum tubes) or transistors can be used. The simplest family of logic gates using bipolar transistors is called resistor-transistor logic, or RTL. Unlike diode logic gates, RTL gates can be cascaded indefinitely to produce more complex logic functions. These gates were used in early integrated circuits. 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, so transistor-transistor logic, or TTL, was created. In some types of chip, to reduce size and power consumption still further, the bipolar transistors were replaced with complementary field-effect transistors (MOSFETs), resulting in complementary metal-oxide-semiconductor (CMOS) logic. Diode logic is an outdated technology which makes use of diodes to contruct logic gates. ... In electronics, a vacuum tube (American English) or (thermionic) valve (British English) is a device generally used to amplify a signal. ... Assorted discrete transistors A transistor is a semiconductor device, commonly used as an amplifier or an electrically controlled switch. ... Resistor-transistor logic (RTL) is a class of digital circuits built from bipolar junction transistors (BJT), and resistors; it is the earliest transistorized digital logic used. ... Integrated circuit of Atmel Diopsis 740 System on Chip showing memory blocks, logic and input/output pads around the periphery Microchips with a transparent window, showing the integrated circuit inside. ... Diode-Transistor Logic (DTL) Diode-Transistor Logic, or DTL, refers to the technology for designing and fabricating digital circuits wherein logic gates employ both diodes and transistors. ... A Motorola 68000-based computer with various TTL chips. ... Large power N-channel field effect transistor 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 in a semiconductor material. ... The metalâ€“oxideâ€“semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET) is by far the most common field-effect transistor in both digital and analog circuits. ... For other uses, see CMOS (disambiguation). ...

For small-scale logic, designers now use prefabricated logic gates from families of devices such as the TTL 7400 series invented by Texas Instruments and the CMOS 4000 series invented by RCA, and their more recent descendants. These devices usually contain transistors with multiple emitters, used to implement the AND function, which are not available as separate components. Increasingly, these fixed-function logic gates are being replaced by programmable logic devices, which allow designers to pack a huge number of mixed logic gates into a single integrated circuit. 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. This article needs to be cleaned up to conform to a higher standard of quality. ... A Motorola 68000-based computer with various TTL chips. ... The 7400 chip, containing four NANDs. ... Texas Instruments (NYSE: TXN), better known in the electronics industry (and popularly) as TI, is an American company based in Dallas, Texas, USA, renowned for developing and commercializing semiconductor and computer technology. ... For other uses, see CMOS (disambiguation). ... The 4000 series is the general classification referring to the industry standard integrated circuits which implement a variety of logic functions using CMOS technology. ... RCA, formerly an acronym for the Radio Corporation of America, is now a trademark owned by Thomson SA through RCA Trademark Management S.A., a company owned by Thomson. ... A programmable logic device or PLD is an electronic component used to build digital circuits. ... Integrated circuit of Atmel Diopsis 740 System on Chip showing memory blocks, logic and input/output pads around the periphery Microchips with a transparent window, showing the integrated circuit inside. ... A programmable logic device or PLD is an electronic component used to build digital circuits. ... A field-programmable gate array or FPGA is a gate array that can be reprogrammed after it is manufactured, rather than having its programming fixed during the manufacturing &#8212; a programmable logic device. ...

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. International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ... The term amplifier as used in this article can mean either a circuit (or stage) using a single active device or a complete system such as a packaged audio hi-fi amplifier. ...

Another important advantage of standardised semiconductor logic gates, such as the 7400 and 4000 families, is that they are cascadable. This means that the output of one gate can be wired to the inputs of one or several other gates, and so on ad infinitum, enabling the construction of circuits of arbitrary complexity without requiring the designer to understand the internal workings of the gates.

In practice, the output of one gate can only drive a finite number of inputs to other gates, a number called the 'fanout limit', but this limit is rarely reached in the newer CMOS logic circuits, as compared to TTL circuits. 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. Fanout is a measure of the ability of a logic gate output, implemented electronically, to drive a number of inputs of other logic gates of the same type. ... For other uses, see CMOS (disambiguation). ... A Motorola 68000-based computer with various TTL chips. ... In computer science, the propogation delay is the amount of time starting from when the input to a logic gate becomes stable and valid to the time that the output of that logic gate is stable and valid. ...

## 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.e., AND, OR, NOT, XOR, XNOR) can be created from a suitable network of just NAND or just NOR gate(s). 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. NAND Logic gate The Sheffer stroke, written | or â†‘, denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as not both. It is also called the alternative denial, since it says in effect that at least one of its operands is false. ... The NOR gate is a digital logic gate that implements logical NOR - it behaves according to the truth table to the right. ... Media:Example. ... // Function The OR gate is a digital logic gate that behaves according to the truth table to the right. ... The NOT gate is a digital logic gate that behaves according to the truth table to the right. ... This article is about XOR in the sense of an electronic logic gate (e. ... The XNOR gate is a digital logic gate whose function is the inverse of the exclusive OR (XOR) gate. ...

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". These four functions are less common and are usually not implemented directly as logic gates. In logical calculus of mathematics, the logical conditional (also known as the material implication, sometimes material conditional) is a binary logical operator connecting two statements, if p then q where p is a hypothesis (or antecedent) and q is a conclusion (or consequent). ...

Logic gates are a vital part of many digital circuits, and as such, every kind is available as an IC. For examples, see the 4000 series of CMOS logic chips or the 7400 TTL series. The 4000 series is the general classification referring to the industry standard integrated circuits which implement a variety of logic functions using CMOS technology. ... For other uses, see CMOS (disambiguation). ...

## 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 in common use, both now defined by 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 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 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. Image File history File links Size of this preview: 720 Ã— 600 pixelsFull resolution (900 Ã— 750 pixel, file size: 22 KB, MIME type: image/png) {{{title}}}. (All user names refer to en. ... Image File history File links Size of this preview: 720 Ã— 600 pixelsFull resolution (900 Ã— 750 pixel, file size: 22 KB, MIME type: image/png) {{{title}}}. (All user names refer to en. ... The American National Standards Institute or ANSI (pronounced an-see) is a nonprofit organization that oversees the development of standards for products, services, processes and systems in the United States. ... Not to be confused with the Institution of Electrical Engineers (IEE). ... The International Electrotechnical Commission (IEC) is an international standards organization dealing with electrical, electronic and related technologies. ... EN can mean: Air Dolomiti, IATA airline designator A standard established by the European Committee for Standardization Engineer Estonia (FIPS 10-4 and obsolete NATO country code) Evaluation notice Exanewton, an SI unit of force. ... British Standards is the new name of the British Standards Institute and is part of BSI Group which also includes a testing organisation. ...

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 predominate 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. The need for complex logic symbols has diminished and distinctive shape symbols are still the predominate style.[citation needed] A Gate array is an approach to the design and manufacture of ASICs. ... An Altera Stratix II GX FPGA. A field-programmable gate array is a semiconductor device containing programmable logic components called logic blocks, and programmable interconnects. ... In electronics, a hardware description language or HDL is any language from a class of computer languages for formal description of electronic circuits. ... Verilog is a hardware description language (HDL) used to model electronic systems. ... VHDL, or VHSIC Hardware Description Language, is commonly used as a design-entry language for field-programmable gate arrays and application-specific integrated circuits in electronic design automation of digital circuits. ...

Type Distinctive shape Rectangular shape Boolean algebra between A & B Truth table
AND $A cdot B$
 INPUT OUTPUT A B A AND B 0 0 0 0 1 0 1 0 0 1 1 1
OR A + B
 INPUT OUTPUT A B A OR B 0 0 0 0 1 1 1 0 1 1 1 1
NOT $overline{A}$
 INPUT OUTPUT A NOT A 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 generally used in circuit diagrams to indicate an inverted (active-low) input or output.[1][2]
NAND $overline{A cdot B}$
 INPUT OUTPUT A B A NAND B 0 0 1 0 1 1 1 0 1 1 1 0
NOR $overline{A + B}$
 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. 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.

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 $A oplus B$
 INPUT OUTPUT A B A XOR B 0 0 0 0 1 1 1 0 1 1 1 0
XNOR $overline{A oplus B}$
 INPUT OUTPUT A B A XNOR B 0 0 1 0 1 0 1 0 0 1 1 1
The 7400 chip, containing four NANDs. The two additional pins supply power (+5 V) and connect the ground.

### List of logic gate ICs

The 7400 series has several ICs that contain just two-input logic gates: The 7400 chip, containing four NANDs. ...

IC No. Gate
7400 NAND
7402 NOR
7404 NOT gate
7408 AND
7432 OR
7486 XOR

## 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. 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. note that demorgans laws are also a big part in circut design. ... Active-low signals are used in electronic logic circuits to represent binary values by means of two different voltages. ...

## Storage of bits

Related to the concept of logic gates (and also built from them) is the idea of storing a bit of information. The gates discussed up to here cannot store a value: 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. 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 utilise clocks (signals that oscillate with a known period) and change only on the rising edge are called edge-triggered "flip-flops". 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 system since its output can be influenced by its previous state(s). See Capacitor (component) for a discussion of specific types. ... In digital circuits, the latch is a particular usage of the simple (non clocked) flip-flop or bistable multivibrator. ... 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, the flip-flop, latch, or bistable multivibrator is an electronic circuit which has two stable states and thereby is capable of serving as one bit of memory. ...

These registers or capacitor-based 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. This article does not cite any references or sources. ...

## 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

Three-state, or 3-state, logic gates have three states of the output: high (H), low (L) and high-impedance (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. 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. Image File history File links This is a lossless scalable vector image. ... Image File history File links This is a lossless scalable vector image. ... It has been suggested that this article or section be merged with Three-state logic. ... An electrical bus (sometimes spelled buss) is a physical electrical interface where many devices share the same electric connection. ... MUX redirects here. ...

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. Categories: Electronics companies of the United States | Companies based in California | Corporation stubs ...

## 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 practice, the gates are made from field effect transistors (FETs), particularly metal-oxide-semiconductor FETs (MOSFETs). MUX redirects here. ... In computer architecture, a processor register is a small amount of very fast computer memory used to speed the execution of computer programs by providing quick access to frequently used valuesâ€”typically, these values are involved in multiple expression evaluations occurring within a small region on the program. ... A typical schematic symbol for an ALU: A & B are operands; R is the output; F is the input from the Control Unit; D is an output status In computing, an arithmetic logic unit (ALU) is a digital circuit that performs arithmetic and logical operations. ... This article does not cite any references or sources. ... A microprocessor is a programmable digital electronic component that incorporates the functions of a central processing unit (CPU) on a single semiconducting integrated circuit (IC). ... Large power N-channel field effect transistor The field-effect transistor (FET) is a transistor that relies on an electric field to control the shape and hence the conductivity of a channel in a semiconductor material. ... The metalâ€“oxideâ€“semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET) is by far the most common field-effect transistor in both digital and analog circuits. ...

In reversible logic, Toffoli gates are used. The term reversible computing refers to 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 can be constructed from Toffoli gates. ...

## History and development

The earliest logic gates were made mechanically. Charles Babbage, around 1837, devised the Analytical Engine. 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 ). 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). Eventually, vacuum tubes replaced relays for logic operations. Lee De Forest's modification, in 1907, of the Fleming valve can be used as AND logic gate. Ludwig Wittgenstein introduced a version of the 16-row truth table in #Logic gates and hardware above, as proposition 5.101 of Tractatus Logico-Philosophicus (1921). Claude E. Shannon introduced the use of Boolean algebra in the analysis and design of switching circuits in 1937. 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. Active research is taking place in molecular logic gates. Babbage redirects here. ... The analytical engine, an important step in the history of computers, was the design of a mechanical general-purpose computer by the British professor of mathematics Charles Babbage. ... Almon Brown Strowger (1839 â€“ May 26, 1902) gave his name to the electromechanical telephone exchange technology that his invention and patent inspired. ... Nikola Tesla (1856-1943)[1] was a world-renowned Serbian inventor, physicist, mechanical engineer and electrical engineer. ... For other uses, see Patent (disambiguation). ... Nikola Tesla with his invention, a wireless lightbulb powered by the electric field surrounding it. ... Lee De Forest, (August 26, 1873 â€“ June 30, 1961) was an American inventor with over 300 patents to his credit. ... Structure of a vacuum tube diode Structure of a vacuum tube triode In electronics, a vacuum tube, electron tube, or (outside North America) thermionic valve or just valve, is a device used to amplify, switch or modify a signal by controlling the movement of electrons in an evacuated space. ... Ludwig Josef Johann Wittgenstein (IPA: ) (April 26, 1889 in Vienna, Austria â€“ April 29, 1951 in Cambridge, England) was an Austrian philosopher who contributed several ground-breaking ideas to philosophy, primarily in the foundations of logic, the philosophy of mathematics, the philosophy of language, and the philosophy of mind. ... Truth tables are a type of mathematical table used in logic to determine whether an expression is true or whether an argument is valid. ... Book cover of the Dover edition of Tractatus Logico-Philosophicus (Ogden translation) Tractatus Logico-Philosophicus is the only book-length work published by the philosopher Ludwig Wittgenstein in his lifetime. ... Claude Elwood Shannon (April 30, 1916 - February 24, 2001) has been called the father of information theory, and was the founder of practical digital circuit design theory. ... Year 1937 (MCMXXXVII) was a common year starting on Friday (link will display the full calendar) of the Gregorian calendar. ... Walther Wilhelm Georg Bothe (January 8, 1891 â€“ February 8, 1957) was a German physicist, mathematician, chemist, and Nobel Prize winner. ... In physics, a coincidence circuit is an electronic device with one output and two (or more) inputs. ... Year 1954 (MCMLIV) was a common year starting on Friday (link will display full calendar) of the Gregorian calendar. ... The Nobel Prize (Swedish: ) was established in Alfred Nobels will in 1895, and it was first awarded in Physics, Chemistry, Physiology or Medicine, Literature, and Peace in 1901. ... For the rap album, see 1924 (album). ... A molecular logic gate in nanotechnology is a logic gate on a molecular level. ...

An and-inverter graph (AIG) is a directed, acyclic graph that represents a structural implementation of the logical functionality of a circuit or network. ... Algebra of sets Ampheck Boole, George Boolean algebra Boolean domain Boolean function Boolean logic Boolean implicant Boolean prime ideal theorem Boolean-valued function Boolean-valued model Boolean satisfiability problem Booles syllogistic Canonical form (Boolean algebra) Characteristic function Compactness theorem Complete Boolean algebra De Morgan, Augustus De Morgans laws... A Boolean function describes how to determine a Boolean value output based on some logical calculation from Boolean inputs. ... Digital circuits are electric circuits based on a number of discrete voltage levels. ... The Espresso heuristic logic minimizer is a widely used computer program for efficiently reducing the complexity of digital electronic gate circuits. ... Fanout is a measure of the ability of a logic gate output, implemented electronically, to drive a number of inputs of other logic gates of the same type. ... In digital circuits, the flip-flop, latch, or bistable multivibrator is an electronic circuit which has two stable states and thereby is capable of serving as one bit of memory. ... An example Karnaugh map The Karnaugh map, also known as a Veitch diagram (K-map or KV-map for short), is a tool to facilitate management of Boolean algebraic expressions. ... In computer engineering, a logic family of monolithic digital integrated circuit devices is a group of electronic logic gates constructed using one of several different designs, usually with compatible logic levels and power supply characteristics within a family. ... A logical graph is a special type of graph-theoretic structure in any one of several systems of graphical syntax that Charles Sanders Peirce developed for logic. ... nMOS logic uses n-type metal-oxide-semiconductor field effect transistors (MOSFETs) to implement logic gates and other digital circuits. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... The term reversible computing refers to any computational process that is (at least to some close approximation) reversible, i. ... Truth tables are a type of mathematical table used in logic to determine whether an expression is true or whether an argument is valid. ... A Venn diagram of sets A, B, and C Venn diagrams are illustrations used in the branch of mathematics known as set theory. ... Zeroth-order logic is a term in popular use among practitioners for the subject matter otherwise known as boolean functions, monadic predicate logic, propositional calculus, or sentential calculus. ...

## References

1. ^ Winfield Hill and Paul Horowitz (1989). The Art of Electronics. Cambridge University Press. ISBN 0521377099.
2. ^ another site that describes the logic gate bubble

• Awschalom, D., D. Loss, and N. Samarth, Semiconductor Spintronics and Quantum Computation (2002), Springer-Verlag, Berlin, Germany.
• Bostock, Geoff, Programmable Logic Devices. Technology and Applications (1988), McGraw-Hill, New York, NY.
• Brown, Stephen D. et al., Field-Programmable Gate Arrays (1992), Kluwer Academic Publishers, Boston, MA.

Results from FactBites:

 Fluid chip does binary logic TRN 100604 (960 words) Logic gates convert one or two inputs into an output based on a rule. The researchers' microfluidic logic gates convert "flow" or "not flow" inputs to outputs of "dyed" or "not dyed" liquid. The NOT gate is the simplest logic gate because it only has one input and so all the channels can be flowing at the same rate, said Vestad.
 Logic gate - Wikipedia, the free encyclopedia (2765 words) In the NOT gate the output is the logical opposite of the input. The NOR gate is the NOT of an OR gate. Logic circuits are often classified in two groups: combinatorial logic, in which the outputs are continuous-time functions of the inputs, and sequential logic, in which the outputs depend on information stored by the circuits as well as on the inputs.
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