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Encyclopedia > Digital circuit

Digital circuits are electric circuits based on a number of discrete voltage levels. Digital circuits are the most common mechanical representation of Boolean algebra and are the basis of all digital computers. They can also be used to process digital information without being connected up as a computer. Such circuits are referred to as "random logic". (See also logic gate.) An electrical network or electrical circuit is an interconnection of analog electrical elements such as resistors, inductors, capacitors, diodes, switches and transistors. ... This article may be too technical for most readers to understand. ... Wikibooks has more about Boolean logic, under the somewhat misleading title Boolean Algebra For a basic intro to sets, Boolean operations, Venn diagrams, truth tables, and Boolean applications, see Boolean logic. ... A logic gate is an arrangement of controlled switches used to calculate operations using Boolean logic in digital circuits. ...

To most engineers, the terms "digital circuit", "digital system" and "logic" are interchangeable in the context of digital circuits. Logic, from Classical Greek Î»ÏŒÎ³Î¿Ï‚ (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of arguments, although the exact definition of logic is a matter of controversy among philosophers. ...

In most cases the number of states is two, and these states are represented by two voltage levels: one near to zero volts and one at a higher level depending on the supply voltage in use. These two levels are often represented as "Low" and "High." Electrical potential is the potential energy per unit charge associated with a static (time-invariant) electric field, also called the electrostatic potential or the electric potential, typically measured in volts. ...

## Properties of Digital Circuits GA_googleFillSlot("encyclopedia_square");

Digital circuits are distinct from analog circuits. In analog circuits, quantities are represented by continuously varying voltages, currents, or frequencies. An analog circuit (or analogue circuit) is an electric circuit that operates on analog signals. ... Electrical potential is the potential energy per unit charge associated with a static (time-invariant) electric field, also called the electrostatic potential or the electric potential, typically measured in volts. ... In electricity, current is the rate of flow of charges, usually through a metal wire or some other electrical conductor. ... Sine waves of various frequencies; the lower waves have higher frequencies than those above. ...

The usual advantages of digital circuits when compared to analog circuits are:

• Digital signals can be regenerated to achieve lossless data transmission.
• Digital systems interface well with computers and are easy to control with software.
• Digital circuits are less affected by noise. In fact, if the noise is below a certain level (the noise margin), a digital circuit behaves as if there was no noise at all --- this is a necessary and sufficient property for a circuit to be considered a digital circuit. However, if the noise exceeds this level, the digital circuit can give catastrophically wrong results.
• More digital circuitry can be fabricated per square millimeter of integrated-circuit material.
• Information storage can be much easier in digital systems than in analog ones. In particular, the great noise-immunity of digital systems makes it possible to store data and retrieve it later without degradation. In an analog system, aging and wear and tear will degrade the information in storage, but in a digital system, as long as the wear and tear is below a certain level, the information can be recovered perfectly.
• Theoretically, there is no data-loss when copying digital data. This is a great advantage over analog systems, which faithfully reproduce every bit of noise that makes its way into the signal.

The usual disadvantages include: A computer is a machine capable of undergoing complex calculations. ... Computer software (or simply software) refers to one or more computer programs and data held in the storage of a computer for some purpose. ...

• Digital circuits are more complex than most analog circuits, in the sense of having much higher component count and denser connections between components, and therefore are more susceptible to errors in design. Much of the modern art of designing digital systems involves careful architecture of a system into smaller, easier to understand modules that communicate in a few well-defined ways, then the careful design and thorough testing of those modules, first individually, then as integrated into the system. Depending on complexity, each module may first need to be architected as a collection of submodules, and so on, until the resulting building blocks are simple enough to be throroughly verified, and only then can detailed circuit design proceed. Sometimes, mathematical techniques can be used to formally prove that a circuit works to specification, but more often than not, a combination of judiciously chosen test cases as well as randomly-generated tests are used to verify operation.
• Digital systems can be fragile, in that if a single piece of digital data is lost or misinterpreted, the meaning of large blocks of related data can completely change. This problem can be mitigated by designing the digital system for robustness. For example, a parity-bit or other error-detecting or error-correcting code can be inserted into the signal path so that if less than a certain fraction of the data is corrupted, the system can determine that this has occurred and possibly uncorrupt the data, or ask for the corrupted data to be resent. In a state-machine, the state transition logic can be designed to catch all unused states and trigger a reset sequence or other error recovery routine. For example, it is standard practice in embedded software design to fill unused program memory with interrupt instructions that point to an error recovery routine, to help guard against a corrupted instruction pointer that would otherwise cause random code to be executed.
• The world in which we live is analog, and signals from this world such as light, temperature, sound, electrical conductivity, electric and magnetic fields, and phenomena such as the flow of time, are for most practical purposes continuous and thus analog quantities rather than discrete digital ones. For a digital system to do useful things in the real world, translation from the continuous realm to the discrete digital realm must occur, resulting in quantization errors as the analog signals from the real world are converted into a storable, regenerable digital form. This problem can usually be mitigated by designing the system to store enough digital data represent the signal to the desired degree of fidelity.
• Digital systems can use such subtle features to store digital states that digital systems errors can be hard to correctly regenerate. In most digital circuits, these problems show up as "glitches", vanishingly-fast pulses that may trigger some logic but not others, "runt pulses" that do not reach valid switching (threshold) voltages, or unexpected ("undecoded") combinations of logic states. In this realm, the analog nature of the components that make up the digital system start to manifest themselves.
• Digital circuits are slower to perform calculations than analog circuits using similar components, although they perform them with much better repeatability, due to the high noise immunity of digital circuits.
• Digital circuits use more energy than analog circuits to accomplish the same calculations and signal processing tasks, thus producing more heat as well. In portable or battery-powered systems this can be a major limiting factor, but in a situation where power is plentiful, a digital system is often preferred because of all the advantages listed above, especially that of (re-)programmability and ease of upgrading without requiring hardware changes. A particular example is the cellular telephone, which being a battery-powered portable device, uses a low-power analog front-end to acquire and tune in the radio signal from the base station. The base station, being in a fixed location with access to the power grid, can afford to use power-hungry software-defined (digital) radio techniques that digitize the signal essentially at the antenna and performs all channelization and signal acquisition via software-driven calculations. Such base stations can be reprogrammed, potentially via remote control, to process the signals used in future cellular standards.
• Digital circuits are sometimes more expensive, especially in small quantities.

For example, a digital music playback system, such as a CD player, stores the music as a long string of numbers, each representing speaker-cone positions. An analog music playback system, such as an LP record, stores the music as a continuously varying quantity. In LP records, this is the position of the sides of a V-shaped groove.

## Levels

The two states of a wire are usually represented by some measurement of electric current: Voltage is the most common, but current is used in some logic families. A threshold is designed for each logic family. When below that threshold, the wire is "low," when above "high." Digital circuit establish a "no man's area" or "exclusion zone" that is wider than the tolerances of the components. The circuits avoid that area, in order to avoid indeterminate results. In electricity, current is the rate of flow of charges, usually through a metal wire or some other electrical conductor. ... Electric potential is the potential energy per unit charge associated with a static (time-invariant) electric field, also called the electrostatic potential, typically measured in volts. ... In electricity, current is the rate of flow of charges, usually through a metal wire or some other electrical conductor. ...

It is usual to allow some tolerance in the voltage levels used; for example, 0 to 2 volts might represent logic 0, and 3 to 5 volts logic 1. A voltage of 2 to 3 volts would be invalid and would occur only in a fault condition or during a logic level transition, as most circuits are not purely resistive, and therefore cannot instantly change voltage levels. However, few logic circuits can detect such a fault, and most will just choose to interpret the signal randomly as either a 0 or a 1.

The levels represent the binary integers or logic levels of 0 and 1. In active-high logic, "low" represents binary 0 and "high" represents binary 1. Active-low logic uses the reverse representation.

Examples of binary logic levels:

Technology L voltage H voltage Notes
CMOS 0V to VCC/2 VCC/2 to VCC VCC = supply voltage
TTL 0V to 0.8V 2V to VCC VCC is 4.75V to 5.25V
ECL -1.175V to -VEE .75V to 0V VEE is about -5.2V VCC=Ground

Static CMOS Inverter CMOS (pronounced see-moss), which stands for complementary metal-oxide-semiconductor, is a major class of integrated circuits. ... VCC is an abbreviation for common-collector voltage. It most likely originated as the supply voltage for a common collector amplifier. ... A Motorola 68000-based computer with various TTL chips. ... In electronics, emitter coupled logic (or ECL) is a design which uses transistors to steer current through gates which compute logical functions (as does every logic family). ...

## Construction

A digital circuit is often constructed from small electronic circuits called logic gates. Each logic gate represents a function of boolean logic. A logic gate is an arrangement of electrically controlled switches. The output is an electrical flow or voltage, that can, in turn, control more logic gates. Logic gates often use the fewest number of transistors in order to reduce their size, power consumption and cost, and increase their reliability. Manufactured as integrated circuits, they are the least expensive implementation when made in large volumes. They are usually designed by engineers using electronic design automation software (See below for more information). A logic gate is an arrangement of controlled switches used to calculate operations using Boolean logic in digital circuits. ... Boolean logic is a system of syllogistic logic invented by 19th-century British mathematician George Boole, which attempts to incorporate the empty set, that is, a class of non-existent entities, such as round squares, without resorting to uncertain truth values. ... In electricity, current is the rate of flow of charges, usually through a metal wire or some other electrical conductor. ... Electrical potential is the potential energy per unit charge associated with a static (time-invariant) electric field, also called the electrostatic potential or the electric potential, typically measured in volts. ... Optical Microscope image of an integrated circuit showing defects in the aluminium layer deposition. ... Electronic design automation (EDA) is the category of tools for designing and producing electronic systems ranging from printed circuit boards (PCBs) to integrated circuits. ...

Another form of digital circuit is constructed from lookup tables, (many sold as "programmable logic devices", though other kinds of PLDs exist). Lookup tables can perform all the same functions as machines based on logic gates, but lookup tables can be easily reprogrammed without changing the wiring. This means that a designer can often repair errors without changing the arrangement of wires. Therefore, in small volume products, programmable logic devices are often the preferred solution. They are usually designed by engineers using electronic design automation software (See below for more information). A programmable logic device or PLD is an electronic component used to build digital circuits. ... Electronic design automation (EDA) is the category of tools for designing and producing electronic systems ranging from printed circuit boards (PCBs) to integrated circuits. ...

When the volumes are medium to large, and the logic can be slow, or involves complex algorithms or sequences, often a small microcontroller is programmed to make an embedded system. These are usually programmed by software engineers. A microcontroller is a computer-on-a-chip used to control electronic devices. ... A computer program or software program (usually abbreviated to a program) is a step-by-step list of instructions written for a particular computer architecture in a particular computer programming language. ... An embedded system is a special-purpose computer system, which is completely encapsulated by the device it controls. ... Software engineering (SE) is the profession that creates and maintains software applications by applying technologies and practices from computer science, project management, engineering, application domains and other fields. ...

When only one digital circuit is needed, and its design is totally customized, as for a factory production line controller, the conventional solution is a programmable logic controller, or PLC. These are usually programmed by electricians, using ladder logic. tsx17 TÃ©lÃ©mÃ©canique PLC PLC & input/output arrangements A programmable logic controller, PLC, or programmable controller is a small computer used for automation of real-world processes, such as control of machinery on factory assembly lines. ... Ladder logic or the Ladder programming language is a method of drawing electrical logic schematics. ...

### Structure of digital systems

Engineers use many methods to minimize logic functions, in order to reduce the complexity, and thus the number of errors and the expense of digital circuits. The most widely used methods include Truth tables, Karnaugh Maps, and Boolean Algebra. 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. ... Wikibooks has more about Boolean logic, under the somewhat misleading title Boolean Algebra For a basic intro to sets, Boolean operations, Venn diagrams, truth tables, and Boolean applications, see Boolean logic. ...

Representations are crucial to an engineer's design of digital circuits. Some analysis methods only work with particular representations.

The classical way to represent a digital circuit is with an equivalent set of logic gates. Another way, often with the least electronics, is to construct an equivalent system of electronic switches (usually transistors). One of the easiest ways is to simply have a memory containing a Truth table. The inputs are fed into the address of the memory, and the data outputs of the memory become the outputs. A logic gate is an arrangement of electronically-controlled switches used to calculate operations in Boolean algebra. ... Assorted component transistors The transistor is a solid state semiconductor device which can be used for amplification, switching, voltage stabilization, signal modulation and many other functions. ... Truth tables are a type of mathematical table used in logic to determine whether an expression is true or whether an argument is valid. ...

For automated analysis, these representations have digital file formats that can be processed by computer programs. Most digital engineers are very careful to select computer programs ("tools") with compatible file formats.

To choose representations, engineers consider types of digital systems. Most digital systems divide into "combinatorial systems" and "sequential systems". A combinatorial system always presents the same output when given the same inputs. It is basically a representation of a set of logic functions, as already discussed.

A sequential system is a combinatorial system with some of the outputs fed back as inputs. This makes the digital machine perform a "sequence" of operations. The simplest sequential system is probably a flip flop, a mechanism that represents a binary digit or "bit". In electronics and digital circuits, the flip-flop or bistable multivibrator is a pulsed digital circuit capable of serving as a one-bit memory. ... The binary or base-two numeral system is a system for representing numbers in which a radix of two is used; that is, each digit in a binary numeral may have either of two different values. ... A numeral is a symbol or group of symbols that represents a number. ... This article is about the unit of information. ...

Sequential systems are often designed as state machines. In this way, engineers can design a system's gross behavior, and even test it in a simulation, without considering all the details of the logic functions. In the theory of computation, a finite state machine (FSM) or finite state automaton (FSA) is an abstract machine that has only a finite, constant amount of memory. ...

Sequential systems divide into two further subcategories. "Synchronous" sequential systems change state all at once, when a "clock" signal changes state. "Asynchronous" sequential systems propagate changes whenever inputs change. Synchronous sequential systems are made of well-characterized asynchronous circuits such as flip-flops, that change only when the clock changes, and which have carefully designed timing margins.

The usual way to implement a synchronous sequential state machine is divide it into a piece of combinatorial logic and a set of flip flops called a "state register." Each time a clock signal ticks, the state register captures the feedback generated from the previous state of the combinatorial logic, and feeds it back as an unchanging input to the combinatorial part of the state machine. The fastest rate of the clock is set by the most time-consuming logic calculation in the combinatorial logic.

The state register is just a representation of a binary number. If the states in the state machine are numbered (easy to arrange), the logic function is just some logic that produces the number of the next state.

In comparison, asynchronous systems are very hard to design because all possible states, in all possible timings must be considered. The usual method is to construct a table of the minimum and maximum time that each such state can exist, and then adjust the circuit to minimize the number of such states, and force the circuit to periodically wait for all of its parts to enter a compatible state. (This is called "self-resynchronization.") Without such careful design, it is easy to accidentally produce asynchronous logic that is "unstable", that is, real electronics will have unpredictable results because of the cumulative delays caused by small variations in the values of the electronic components. Certain circuits (such as the synchronizer flip-flops, switch debouncers, and the like which allow external unsynchronized signals to enter synchronous logic circuits) are inherently asynchronous in their design and must be analyzed as such.

As of now (2005), almost all digital machines are synchronous designs because it is much easier to create and verify a synchronous design. However, asynchronous logic is thought to be superior, if it can be made to work, because its speed is not constrained by an arbitrary clock; instead, it simply runs at the maximum speed permitted by the propagation rates of the logic gates from which it is constructed. Building an asynchronous circuit using faster parts implicitly makes the circuit "go" faster.

More generally, many digital systems are data flow machines. These are usually designed using synchronous register transfer logic, using specialized programming languages such as VHDL or Verilog. VHDL or VHSIC Hardware Description Language, is commonly used as a design-entry language for FPGAs and ASICs in electronic design automation of digital circuits. ... Verilog is a hardware description language (HDL) used to model electronic systems. ...

In register transfer logic, binary numbers are stored in groups of flip flops called registers. The outputs of each register are a bundle of wires called a "bus" that carries that number to other calculations. A calculation is simply a piece of combinatorial logic. Each calculation also has an output bus, and these may be connected to the inputs of several registers. Sometimes a register will have a multiplexer on its input, so that it can store a number from any one of several buses. Alternatively, the outputs of several items may be connected to a bus through buffers that can turn off the output of all of the devices except one. A sequential state machine controls when each register accepts new data from its input. The binary or base-two numeral system is a system for representing numbers in which a radix of two is used; that is, each digit in a binary numeral may have either of two different values. ... Look up Number in Wiktionary, the free dictionary A number originally was a count or a measurement. ... 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 commonly used values—typically, the values being in the midst of a calculation at a given point in time. ... In computer architecture, a bus is a subsystem that transfers data or power between computer components inside a computer or between computers. ... A multiplexer combines more than one input into a single output. ... In electronics a 3-state digital logic gate is one in which the output circuit can be completely switched off, putting the output in a high-impedance state. ...

In the 1980s, some researchers discovered that almost all synchronous register-transfer machines could be converted to asynchronous designs by using first-in-first-out synchronization logic. In this scheme, the digital machine is characterized as a set of data flows. In each step of the flow, an asynchronous "synchronization circuit" determines when the outputs of that step are valid, and presents a signal that says, "grab the data" to the stages that use that stage's inputs. It turns out that just a few relatively simple synchronization circuits are needed.

The most general-purpose register-transfer logic machine is a computer. This is basically an automatic binary abacus. The control unit of a computer is usually designed as a microprogram run by a microsequencer. A microprogram is much like a player-piano roll. Each table entry or "word" of the microprogram commands the state of every bit that controls the computer. The sequencer then counts, and the count addresses the memory or combinatorial logic machine that contains the microprogram. The bits from the microprogram control the arithmetic logic unit, memory and other parts of the computer, including the microsequencer itself. A computer is a machine capable of undergoing complex calculations. ... A drummer automaton An automaton (plural: automata) is a self-operating machine. ... The binary or base-two numeral system is a system for representing numbers in which a radix of two is used; that is, each digit in a binary numeral may have either of two different values. ... This article is about the calculator. ... A control unit is the part of a CPU or other device that directs its operation. ... A microprogram is a program consisting of microcode that controls the different parts of a computers central processing unit (CPU). ... In the field of computer architecture and engineering, a sequencer or microsequencer, is a part of a control unit of a CPU. It generates the addresses used to step through the microprogram of a control store. ... The arithmetic logic unit/arithmetic-logic unit (ALU) of a computers CPU is a part of the execution unit, a core component of all CPUs. ... Memory is the ability of the brain to store, retain, and subsequently recall information. ... In the field of computer architecture and engineering, a sequencer or microsequencer, is a part of a control unit of a CPU. It generates the addresses used to step through the microprogram of a control store. ...

In this way, the complex task of designing the controls of a computer is reduced to a simpler task of programming a relatively independent collection of much simpler logic machines.

Computer architecture is a specialized engineering activity that tries to arrange the registers, calculation logic, buses and other parts of the computer in the best way for some purpose. Computer architects have applied large amounts of ingenuity to computer design to reduce the cost and increase the speed and immunity to programming errors of computers. An increasingly common goal is to reduce the power used in a battery-powered computer system, such as a cell-phone. Many computer architects serve an extended apprenticeship as microprogrammers. In computer science, computer architecture is the conceptual design and fundamental operational structure of a computer system. ...

"Specialized computers" are usually a conventional computer with a special-purpose microprogram.

### Automated design tools

To save costly engineering effort, much of the effort of designing large logic machines has been automated. The computer programs are called "electronic design automation tools" or just "EDA." Electronic design automation (EDA) is the category of tools for designing and producing electronic systems ranging from printed circuit boards (PCBs) to integrated circuits. ...

Simple truth table-style descriptions of logic are often optimized with EDA that automatically produces reduced systems of logic gates or smaller lookup tables that still produce the desired outputs.

Most practical algorithms for optimizing large logic systems use algebraic manipulations or binary decision diagrams, and there are promising experiments with genetic algorithms and annealing optimizations. Quine-McCluskey algorithm is a method used for minimization of Boolean functions. ... A binary decision diagram (BDD) is a data structure that is used to represent a Boolean function. ... A genetic algorithm (GA) is a search technique used in computer science to find approximate solutions to optimization and search problems. ... Simulated annealing (SA) is a generic probabilistic meta-algorithm for the global optimization problem, namely locating a good approximation to the global optimum of a given function in a large search space. ...

To automate costly engineering effort, some EDA can take state tables that describe state machines and automatically produce a truth table for the combinatorial part of a state machine. The state table is a piece of text that lists each state, and the conditions that can exit that state. This page meets Wikipedias criteria for speedy deletion. ... In the theory of computation, a finite state machine (FSM) or finite state automaton (FSA) is an abstract machine that has only a finite, constant amount of memory. ... Truth tables are a type of mathematical table used in logic to determine whether an expression is true or whether an argument is valid. ...

It is common for the truth tables of such computer-generated state-machines to be optimized with logic-minimization software. This is a simple example of how complex logic machines are broken into simpler parts. Often, real logic systems are designed as a series of sub-projects, which are combined using a "tool flow". The tool flow is usually a "script", a simplified computer language that can invoke the software design tools in the right order.

Tool flows for large logic systems such as microprocessors can be thousands of commands long, and combine the work of hundreds of engineers.

Writing and debugging tool flows is an established engineering specialty in companies that produce complex logic machines. The tool flow usually terminates in a detailed computer file or set of files that describe how to physically construct the logic machine. Often it consists of instructions to draw the transistors and wires on an integrated circuit or a printed circuit board. Photo of transistor types (tape measure marked in centimeters) Transistor in the SMD form factor The transistor is a solid state semiconductor device used for amplification and switching. ... Optical Microscope image of an integrated circuit showing defects in the aluminium layer deposition. ... Close-up photo of one side of a motherboard PCB, showing conductive traces, vias and solder points for through-hole components on the opposite side. ...

Parts of tool flows are "debugged" by testing the outputs of simulated logic machines against expected inputs. The test tools take computer files with sets of inputs and outputs, and highlight discrepancies between the simulated behavior and the expected behavior.

These test data are usually called "test vectors." Often, the test vectors are preserved and used in the factory to test that newly constructed logic machines work correctly.

### Design for Testability

A large logic machine (say, with more than a hundred logical variables) can have an astronomical number of possible states. Obviously, in the factory, testing every state is impractical if testing each state takes a microsecond, and there are more states than the number of microseconds since the universe began. Unfortunately, this ridiculous-sounding case is the typical case.

Fortunately, large logic machines are almost always designed as assemblies of smaller logic machines. To save time, the smaller sub-machines are isolated by permanently-installed "design for test" circuitry, and are tested independently.

One common test scheme known as "scan design" moves test bits serially (one after another) from external test equipment through one or more serial shift registers known as "scan chains". Serial scans have only one or two wires to carry the data, and minimize the physical size and expense of the infrequently-used test logic. In digital circuits a shift register is a group of registers set up in a linear fashion which have their inputs and outputs connected together in such a way that the data is shifted down the line when the circuit is activated. ...

After all the test data bits are in place, the design is reconfigured to be in "normal mode" and one or more clock pulses are applied, to test for faults (e.g. stuck-at low or stuck-at high) and capture the test result into flip-flops and/or latches in the scan shift register(s). Finally, the result of the test is shifted out to the block boundary and compared against the predicted "good machine" result. In electronics and digital circuits, the flip-flop or bistable multivibrator is a pulsed digital circuit capable of serving as a one-bit memory. ...

In a board-test environment, serial to parallel testing has been formalized with a standard called "JTAG" (named after the "Joint Testing Acting Group" that proposed it). JTAG, an initialism for Joint Test Action Group, is the usual name used for the IEEE 1149. ...

Another common testing scheme is provide a test mode that forces the logic machine or a part thereof to enter a "test cycle." The test cycle usually exercises large independent parts of the machine.

Several numbers determine the practicality of a system of digital logic. Engineers explored numerous electronic devices to get an ideal combination of speed, low cost and reliability.

The cost of a logic gate is crucial. In the 1930s, the earliest digital logic systems were constructed from telephone relays because these were inexpensive and relatively reliable. After that, engineers always used the cheapest available electronic switches that could still fulfill the requirements. // Events and trends A public speech by Benito Mussolini, founder of the Fascist movement The 1930s were described as an abrupt shift to more radical lifestyles, as countries were struggling to find a solution to the global depression. ...

The earliest integrated circuits were a happy accident. They were constructed not to save money, but to save weight, and permit the apollo guidance computer to control an inertial guidance system for a spacecraft. The first integrated circuit logic gates cost nearly \$50 (in 1960 dollars, when an engineer earned \$10,000/year). To everyone's surprise, by the time the circuits were mass-produced, they had become the least-expensive method of constructing digital logic. Improvements in this technology have driven all subsequent improvements in cost. Optical Microscope image of an integrated circuit showing defects in the aluminium layer deposition. ... The Apollo Guidance Computer (AGC) was the first recognizably modern embedded system, used in real-time by astronaut pilots to collect and provide flight information, and to automatically control all of the navigational functions of the Apollo spacecraft. ... An inertial navigation system (INS) provides the position, velocities and attitude of a vehicle by measuring the accelerations and rotations applied to the systems inertial frame. ...

With the rise of integrated circuits, reducing the absolute number of chips used represented another way to save costs. The goal of a designer is not just to make the simplest circuit, but to keep the component count down. Sometimes this results in slightly more complicated designs with respect to the underlying digital logic but nevertheless reduces the number of components, board size, and even power consumption. An integrated circuit (IC) is a thin chip consisting of at least two interconnected semiconductor devices, mainly transistors, as well as passive components like resistors. ...

For example, in some logic families, NAND gates are the simplest digital gate to build. All other logical operations can be implemented by NAND gates. If a circuit already required a single NAND gate, and a single chip normally carried four NAND gates, then the remaining gates could be used to implement other logical operations like logical and. This could eliminate the need for a separate chip containing those different types of gates. ... ... ... ... Logical conjunction (usual symbol and) is a logical operator that results in true if both of the operands are true. ...

The "reliability" of a logic gate describes its mean time between failure (MTBF). Digital machines often have millions of logic gates. Also, most digital machines are "optimized" to reduce their cost. The result is that often, the failure of a single logic gate will cause a digital machine to stop working.

Digital machines first became useful when the MTBF for a switch got above a few hundred hours. Even so, many of these machines had complex, well-rehearsed repair procedures, and would be nonfunctional for hours because a tube burned-out, or a moth got stuck in a relay. Modern transistorized integrated circuit logic gates have MTBFs of nearly a trillion (1x10^12) hours, and need them because they have so many logic gates.

The "fan out" describes how many logic inputs can be controlled by a single logic output. The minimum practical fan out is about five. Modern electronic logic using CMOS transistors for switches have fanouts near fifty, and can sometimes go much higher. Static CMOS Inverter CMOS (pronounced see-moss), which stands for complementary metal-oxide-semiconductor, is a major class of integrated circuits. ... Assorted component transistors The transistor is a solid state semiconductor device which can be used for amplification, switching, voltage stabilization, signal modulation and many other functions. ...

The "switching speed" describes how many times per second an inverter (an electronic representation of a "logical not" function) can change from true to false and back. Faster logic can accomplish more operations in less time. Digital logic first became useful when switching speeds got above fifty hertz, because that was faster than a team of humans operating mechanical calculators. Modern electronic digital logic routinely switches at five gigahertz (5x109 hertz), and some laboratory systems switch at more than a terahertz (1x1012 hertz). The hertz (symbol: Hz) is the SI unit of frequency. ... A gigahertz is a billion hertz or a thousand megahertz, a measure of frequency. ... A terahertz (THz) is 1012 hertz or a thousand gigahertz, a measure of frequency. ...

## Nonelectronic logic

It is possible to construct nonelectronic digital mechanisms. In principle, any technology capable of representing discrete states and representing logic operations could be used to build mechanical logic.

Hydraulic, pneumatic and mechanical versions of logic gates exist and are used in situations where electricity cannot be used. The first two types are considered under the heading of fluidics. One application of fluidic logic is in military hardware that is likely to be exposed to a nuclear electromagnetic pulse (nuclear EMP, or NEMP) that would destroy any electrical circuits. Fluidic logic , also known as fluidics , is the implementation of Boolean algebra functions using streams of fluid (such as water or air). ... In telecommunications and warfare, the term electromagnetic pulse (EMP) has the following meanings: The electromagnetic radiation from an explosion (especially nuclear explosions) or an intensely fluctuating magnetic field caused by Compton-recoil electrons and photoelectrons from photons scattered in the materials of the electronic or explosive device or in a...

Mechanical logic is frequently used in inexpensive controllers, such as those in washing machines. Famously, the first computer design, by Charles Babbage, was designed to use mechanical logic. Mechanical logic might also be used in very small computers that could be built by nanotechnology. Charles Babbage Charles Babbage (December 26, 1791 â€“ October 18, 1871) was an English mathematician, analytical philosopher, mechanical engineer and (proto-) computer scientist who originated the idea of a programmable computer. ... A mite next to a gear set produced using MEMS, the precursor to nanotechnology. ...

Another example is that if two particular enzymes are required to prevent the construction of a particular protein, this is the equivalent of a biological "NAND" gate.

## Recent developments

The discovery of superconductivity has enabled the development of Rapid Single Flux Quantum (RSFQ) circuit technology, which uses Josephson junctions instead of transistors. Most recently, attempts are being made to construct purely optical computing systems capable of processing digital information using nonlinear optical elements. A magnet levitating above a high-temperature superconductor (with boiling liquid nitrogen underneath) demonstrates the Meissner effect. ... In electronics, rapid single flux quantum (RSFQ) is a digital electronics technology that relies on quantum effects in superconducting materials to switch signals, instead of transistors. ... Josephson junctions, first postulated by B. D. Josephson and first made by John Rowell and Philip Anderson, are quantum-mechanical circuit elements of superconducting devices. ... An Optical Computer is a computer that performs its computation with photons as opposed to the more traditional electron-based computation. ... To do: 20th century mathematics chaos theory, fractals Lyapunov stability and non-linear control systems non-linear video editing See also: Aleksandr Mikhailovich Lyapunov Dynamical system External links http://www. ...

Results from FactBites:

 Circuit Builder (1230 words) Circuits and mechanisms were built to represent fixed mathematical problems with results appearing in the form of a final voltage or a rotation angle of a gear. That is, use the circuit builder to establish the logic behavior of AND, NOT, OR, NAND, NOR. The objective is to "etch" the circuit onto a single layer of a copper-coated circuit board which contains pin holes to accommodate the chips.
 Digital circuit Summary (5843 words) A digital circuit is based on a number of discrete voltage levels, usually two, as distinct from an analog circuit that uses continuous voltages to represent variables directly. Digital circuits are the most common mechanical representation of Boolean algebra and are the basis of all digital computers. Digital circuits are made from analog components, and care has to be taken in design so that the analog nature of these underlying components don't dominate over the desired digital behavior.
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