Digital circuits are electric circuits based on a number of discrete voltage levels. In most cases there are 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 L and H. An electrical network or electrical circuit is an interconnection of analog electrical elements such as resistors, inductors, capacitors, diodes, switches and transistors. ... In the physical sciences, potential difference is the difference in potential between two points in a conservative vector field. ...

Levels

The two levels are used to represent the binary integers or logic levels of 0 and 1. In active-high logic, L represents binary 0 and H represents binary 1. Active-low logic uses the reverse representation. 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.

Examples of binary logic levels:

CMOS (pronounced see-moss) is the name used for a major class of integrated circuits. ... The abbreviation TTL can refer to: time to live, when talking about Internet Protocol packets, or the Ping Internet diagnostic tool, transistor-transistor logic, the first widespread semiconductor integrated circuit technology, through the lens when talking about photography. ...

Construction

Electronic logic 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 large volumes, they are the least expensive implementation. They are usually designed by engineers using electronic design automation software. A logic gate is an arrangement of electronically-controlled switches used to calculate operations in Boolean algebra. ... In mathematics and computer science, Boolean algebras, or Boolean lattices, are algebraic structures which capture the essence of the logical operations AND, OR and NOT as well as the corresponding set theoretic operations intersection, union and complement. ... 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. ... 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 electronic logic is constructed from lookup tables, usually described as "programmable logic devices". These 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. 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 optimised to control devices. ... A computer program (often simply called a program) is an example of computer software that prescribes the actions (computations) that are to be carried out by a computer. ... An embedded system is a special-purpose computer system, which is completely encapsulated by the device it controls. ... Software engineering (SE) is the profession, practiced by software engineers, concerned with creating and maintaining software applications by applying technologies and practices from computer science, project management, engineering and other fields. ...

When only one logic machine 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. PLC 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 is a method of drawing electrical logic schematics. ...

Structure of Digital Systems

Complicated digital systems, such as computers, are constructed from large numbers of small logic gates or lookup tables. How these are organized is crucial, because the most likely reason for a project to fail is because it is too complex to understand. The tower of a personal computer (specifically a Power Mac G5). ...

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.

One of the easiest ways to design a combinatorial system 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. To save money, truth table-style descriptions are often given to computer programs that automatically produce systems of logic gates or lookup tables that produce the desired outputs. Interestingly, the only known way to get a perfect optimization is to enumerate all possible designs. This means that many needed systems are too large to be perfectly optimized with known algorithms on real computers. Larger systems have problems with partitioning the logic system, or run out of memory or time. 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. Truth tables are a type of mathematical table used in logic to determine whether an expression is true or whether an argument is valid. ... Quine-McCluskey algorithm is a method used for minimisation 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 heuristic used to find approximate solutions to difficult-to-solve problems through application of the principles of evolutionary biology to computer science. ...

Engineers use many methods to minimize logic functions, in order to reduce the complexity and expense of digital machines. The most widely used cost-reduction 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), was invented in 1950 by Maurice Karnaugh, a telecommunications engineer at Bell Labs. ... In mathematics and computer science, Boolean algebras, or Boolean lattices, are algebraic structures which capture the essence of the logical operations AND, OR and NOT as well as the corresponding set theoretic operations intersection, union and complement. ...

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 bit. This article is about the electronic component. ... A bit (abbreviated b) is the most basic information unit used in computing and information theory. ...

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. Asynchronous systems are very hard to design, because all possible states, in all possible timings must be considered.

Now (2005), almost all digital machines are synchronous, because it is much easier to design. However, asynchronous logic is thought to be superior, if it can be made to work, because it runs at the speed of its slowest part. Theoretically, this means that a machine could run as fast as the logic permitted.

In the 1980s, some researchers discovered that almost all synchronous digital machines could be convereted 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.

More generally, many digital systems are data flow machines. These are now designed using 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. ... The Verilog HDL is a hardware description language, used for the design of ASICs and FPGAs. ...

The most general-purpose data flow machine is a computer. This is basically an automatic binary abacus. The control unit of a computer is usually designed as a microprogram running on a microsequencer, and this controls the arithmetic logic unit. An abacus is a calculation tool, often constructed as a wooden frame with beads sliding on wires. ... 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. ... ALU redirects here. ...

Trade Offs

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. The earliest integrated circuits were a happy accident. They were constructed not to save money, but to save weight, and permit a computer to fly 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. 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. ... The Apollo Guidance Computer (AGC) was the first recognizably modern embedded system. ... An inertial navigation system measures the position and altitude of a vehicle by measuring the accelerations and rotations applied to the systems inertial frame. ...

The "reliability" of a logic gate describes its mean time between failure (MTBF). Digital machines often need thousands, sometimes 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. CMOS (pronounced see-moss) is the name used for a major class of integrated circuits. ... Through hole transistors (tape measure marked in centimeters) The transistor is a solid state semiconductor device which can be used for amplification, switching, voltage stabilisation, 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 fall 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 billion (5x10^9) Hertz, and some laboratory systems switch at more than a trillion (1x10^12) Hertz. The hertz (symbol Hz) is the SI unit 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). ... EMP redirects here. ...

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 – October 18, 1871) was an English mathematician, analytical philosopher and (proto-) computer scientist who was the first person to come up with the idea of a programmable computer. ... A mite next to a gear chain produced using nanotechnology Nanotechnology as a collective term refers to technological developments on the nanometer scale, usually 0. ...

Logic systems

Logic systems can be constructed from diverse systems including optical, magnetic, chemical, biochemical and quantum systems. In each case, the desired logic function can be found in the interactions of the physical components. For example if two particular enzymes are required to prevent the construction of a particular protein, this is the equivalent of a biological "NAND" gate. They can even be constructed in computer games. David Deutsch (Q3A Electronics (http://www.skore.de)) constructed logic circuits for use in the game Quake 3 Arena. Although not present in the game, as a level designer, he found a way of doing it, thus allowing complex triggering of game events. This article or section should include material from Anarki For an overview of the Quake game franchise go to Quake series. ...

Digital circuits are the most common hardware realisation of Boolean algebra and are the basis of all digital computers. (See also logic gate.) In mathematics and computer science, Boolean algebras, or Boolean lattices, are algebraic structures which capture the essence of the logical operations AND, OR and NOT as well as the corresponding set theoretic operations intersection, union and complement. ... A logic gate is an arrangement of electronically-controlled switches used to calculate operations in Boolean algebra. ...

They can also be used to process digital information without being connected up as a computer. Such circuits are referred to as "random logic".

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. Superconductivity is a phenomenon occurring in certain materials at low temperatures, characterised by the complete absence of electrical resistance and the damping of the interior magnetic field (the Meissner effect. ... 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 developed by B. D. Josephson, 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. ...

See also

• List of electronics topics

Analog circuit | Boolean algebra | Circuit | CMOS | Combinatorial logic | Data strobe encoding | De Morgan's laws | Digital | Electrical network | Electronics | Field effect transistor | Finite state machine | Formal verification | Glitch Ringing | Hardware description language | Instruction pipelining | Integrated circuit | Sequential logic  | Logic analyzer | Logic gate | Microelectronics | Multiplexer | Multiplication ALU | Multivibrator | NMOS | Programmable logic device | Reconfigurable system | Register | Transistor | Transistor-transistor logic | Transparent latch | Ternary logic | Runt pulse | Transmission line | VHSIC This is a list of communications, computers, electronic circuits, fiberoptics, microelectronics, medical electronics, reliablity, and semiconductors. ... For the Analog Science Fiction and Science Fact publication, see Astounding Magazine. ... In mathematics and computer science, Boolean algebras, or Boolean lattices, are algebraic structures which capture the essence of the logical operations AND, OR and NOT as well as the corresponding set theoretic operations intersection, union and complement. ... There are many kinds of circuit An electric circuit interconnects electrical elements. ... CMOS (pronounced see-moss) is the name used for a major class of integrated circuits. ... This article is not about combinatory logic, a topic in mathematical logic. ... Data strobe encoding (or D/S encoding) is an encoding scheme for transmitting data in digital circuits. ... In logic, De Morgans laws (or De Morgans theorem) are the two rules of propositional logic, boolean algebra and set theory not (P and Q) = (not P) or (not Q) not (P or Q) = (not P) and (not Q) which allow us to move a negation over a... A digital system is one that uses discrete values rather than a continuous spectrum of values: compare analog. ... An electrical network or electrical circuit is an interconnection of analog electrical elements such as resistors, inductors, capacitors, diodes, switches and transistors. ... Electronics is the study and use of electrical devices that operate by controlling the flow of electrons or other electrically charged particles in devices such as thermionic valves and semiconductors. ... The field-effect transistor (FET) is a transistor that relies on an electric field to control the shape of the nonconductive depletion layer within a semiconductor material, thus controlling the conductivity of a channel in that material. ... Fig. ... In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of a system with respect to a certain formal specification or property, using formal methods. ... Glitch City, a Pokémon programming error that creates a jumble of pixels A glitch is a short-lived fault in a system. ... In electrical circuits, ringing is an unwanted oscillation of a voltage or current. ... In electronics, a hardware description language or HDL is any language from a class of computer languages for formal description of electronic circuits. ... Instruction pipelining is a method for increasing the throughput of a digital circuit, particularly a CPU, and implements a form of instruction level parallelism. ... 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. ... 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. ... A logic analyzer captures digital data from a digital system and presents it to a user so that the user can locate failure of the digital system. ... A logic gate is an arrangement of electronically-controlled switches used to calculate operations in Boolean algebra. ... Microelectronics is a subfield of electronics. ... The term multiplexer has uses in several fields of application: Electronics In electronics, a multiplexer or mux is a device that combines several electrical signals into a single signal. ... In digital design, a multiplier or multiplication ALU is a hardware circuit dedicated to multiplying two binary values. ... A multivibrator is an electronic circuit used to implement a variety of simple two-state systems such as oscillators, timers and flip-flops. ... NMOS logic uses n-type metal-oxide-semiconductor field effect transistors (MOSFETs) to implement logic gates and other digital circuits. ... A programmable logic device or PLD is an electronic component used to build digital circuits. ... In electronics and computing, a reconfigurable system is a computer that can, by executing code, change the function of the digital circuits of which it is composed. ... 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. ... Through hole transistors (tape measure marked in centimeters) The transistor is a solid state semiconductor device which can be used for amplification, switching, voltage stabilisation, signal modulation and many other functions. ... A Motorola 68000-based computer with various TTL chips. ... A transparent latch is an electronic data storage device with a data input (D), an enable input (E) and a data output (Q). ... Ternary logic is a multi-valued logic in which there are three truth values indicating true, false and unknown. ... In digital circuits, a runt pulse is a narrow pulse that, due to non-zero rise and fall times of the signal, does not reach a valid high or low level. ... A transmission line is the material medium or structure that forms all or part of a path from one place to another for directing the transmission of energy, such as electric currents, magnetic fields, acoustic waves, or electromagnetic waves. ... A VHSIC is a Very-High-Speed Integrated Circuit, a type of digital logic circuit. ...

• Claude E. Shannon : used Boolean algebra for building digital circuits.
• List of electrical Input/Output standards