Encyclopedia
A
digital circuit is based on a number of discrete
voltage levels, 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. They can also be used to process digital information without being connected up as a computer. Such circuits are referred to as "random logic".
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."
To most electronic engineers, the terms "digital circuit", "digital system" and "logic" are interchangeable in the context of digital circuits.
Properties of digital circuits
Digital circuits are distinct from analog circuits. In analog circuits, quantities are represented by continuously varying voltages, currents, or
frequencies.
The usual advantages of digital circuits when compared to analog circuits are:
- Digital circuits are less affected by noise. In fact, if the noise is below a certain level , 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.
- Digital signals can thus be regenerated to achieve lossless data transmission, within certain limits. Analog signal transmission and processing, by contrast, always introduces noise.
- Digital systems interface well with computers and are easy to control with software. It is often possible to add new features to a digital system without changing hardware, and to do this remotely, just by uploading new software. Design errors or bugs can be worked-around with a software upgrade, after the product is in customer hands.
- 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:
- 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 failure that corrupts the microcontroller's instruction pointer which could 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. This problem can usually be mitigated by designing the system to store enough digital data to represent the signal to the desired degree of fidelity. The Nyquist-Shannon sampling theorem provides an important guideline as to how much digital data is needed to accurately portray a given analog signal.
- 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. In particular, attention must be paid to all noise and timing margins, to parasitic inductances and capacitances, to proper filtering of power and ground connections, to electromagnetic coupling amongst datalines, and many other details. Inattention to these can cause intermittent problems such as "glitches", vanishingly-fast pulses that may trigger some logic but not others, "runt pulses" that do not reach valid switching voltages, or unexpected combinations of logic states.
- A corollary of the fact that digital circuits are made from analog components is the fact that digital circuits are slower to perform calculations than analog circuits that occupy a similar amount of physical space and consume the same amount of power. However, the digital circuit will perform the calculation with much better repeatability, due to the high noise immunity of digital circuitry.
- 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 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 radio techniques that digitize the signal essentially at the antenna and performs all channelization and demodulation via software-driven calculations. Such base stations can be reprogrammed, potentially via remote control, to process the signals used in future cellular standards as those standards become available.
- Digital circuits are sometimes more expensive, especially in small quantities.
Logic voltage 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 circuits 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.
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 |
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 .
Another form of digital circuit is constructed from lookup tables, . 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 .
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.
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.
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.
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 . 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.
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 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".
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.
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 , 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. 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 are inherently asynchronous in their design and must be analyzed as such.
As of now , 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.
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.
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.
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.
"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."
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.
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.
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.
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 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 typical.
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 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.
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 and capture the test result into
flip-flops and/or latches in the scan shift register. Finally, the result of the test is shifted out to the block boundary and compared against the predicted "good machine" result.
In a board-test environment, serial to parallel testing has been formalized with a standard called "
JTAG" .
Another common testing scheme provides a test mode that forces some part of the logic machine to enter a "test cycle." The test cycle usually exercises large independent parts of the machine.
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 the
Apollo Guidance Computer to control an
inertial guidance system for a spacecraft. The first integrated circuit logic gates cost nearly $50 . 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.
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.
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.
The "reliability" of a logic gate describes its mean time between failure . 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 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.
The "switching speed" describes how many times per second an inverter 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 , and some laboratory systems switch at more than a terahertz .
Non-electronic logic
It is possible to construct non-electronic digital mechanisms. In principle, any technology capable of representing discrete states and representing logic operations could be used to build mechanical logic.
Danny Hillis, co-author of The Connection Machine, once built a working computer from Tinker Toys, string, a brick, and a sharpened pencil, which is supposed to be in the Houston Museum of Science.
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 that would destroy any electrical circuits.
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.
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 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.
Branch pages
Electronics - Combinatorial logic -
Boolean algebra - Fuzzy electronics -
Logic analyzer -
Logic gate -
Glitch - Ringing -
Programmable logic device - Reconfigurable system - Register
See also
...
- De Morgan's laws - Digital - Digital signal processing - Electrical network -
Electronics -
Field effect transistor -
Finite state machine - Formal verification - Hardware description language -
Instruction pipelining -
Integrated circuit -
Logical effort - Sequential logic - Microelectronics -
Glitch - Ringing - NMOS -
Transistor -
Transistor-transistor logic - Transparent latch - Ternary logic - Runt pulse -
Transmission line - VHSIC
External links
