An advantage of digital circuits when compared to analog circuits is that signals represented digitally can be transmitted without degradation caused by noise.[29] For example, a continuous audio signal transmitted as a sequence of 1s and 0s, can be reconstructed without error, provided the noise picked up in transmission is not enough to prevent identification of the 1s and 0s.
In a digital system, a more precise representation of a signal can be obtained by using more binary digits to represent it. While this requires more digital circuits to process the signals, each digit is handled by the same kind of hardware, resulting in an easily scalable system. In an analog system, additional resolution requires fundamental improvements in the linearity and noise characteristics of each step of the signal chain.
With computer-controlled digital systems, new functions can be added through software revision and no hardware changes are needed. Often this can be done outside of the factory by updating the product's software. This way, the product's design errors can be corrected even after the product is in a customer's hands.
Information storage can be easier in digital systems than in analog ones. The noise immunity of digital systems permits data to be stored and retrieved without degradation. In an analog system, noise from aging and wear degrade the information stored. In a digital system, as long as the total noise is below a certain level, the information can be recovered perfectly. Even when more significant noise is present, the use of redundancy permits the recovery of the original data provided too many errors do not occur.
In some cases, digital circuits use more energy than analog circuits to accomplish the same tasks, thus producing more heat which increases the complexity of the circuits such as the inclusion of heat sinks. In portable or battery-powered systems this can limit the use of digital systems. For example, battery-powered cellular phones often use a low-power analog front-end to amplify and tune the radio signals from the base station. However, a base station has grid power and can use power-hungry, but very flexible software radios. Such base stations can easily be reprogrammed to process the signals used in new cellular standards.
Many useful digital systems must translate from continuous analog signals to discrete digital signals. This causes quantization errors. Quantization error can be reduced if the system stores 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.
If a single piece of digital data is lost or misinterpreted, in some systems only a small error may result, while in other systems the meaning of large blocks of related data can completely change. For example, a single-bit error in audio data stored directly as linear pulse-code modulation causes, at worst, a single audible click. But when using audio compression to save storage space and transmission time, a single bit error may cause a much larger disruption.
Because of the cliff effect, it can be difficult for users to tell if a particular system is right on the edge of failure, or if it can tolerate much more noise before failing. Digital fragility can be reduced by designing a digital system for robustness. For example, a parity bit or other error management method can be inserted into the signal path. These schemes help the system detect errors, and then either correct the errors, or request retransmission of the data.
Construction[edit]
A digital circuit is typically constructed from small electronic circuits called logic gates that can be used to create combinational logic. Each logic gate is designed to perform a function of boolean logic when acting on logic signals. A logic gate is generally created from one or more electrically controlled switches, usually transistors but thermionic valves have seen historic use. The output of a logic gate can, in turn, control or feed into more logic gates.
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 the same functions as machines based on logic gates, but can be easily reprogrammed without changing the wiring. This means that a designer can often repair design 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.
Integrated circuits consist of multiple transistors on one silicon chip, and are the least expensive way to make large number of interconnected logic gates. Integrated circuits are usually interconnected on a printed circuit board which is a board which holds electrical components, and connects them together with copper traces.
Design[edit]
Engineers use many methods to minimize logic redundancy in order to reduce the circuit complexity. Reduced complexity reduces component count and potential errors and therefore typically reduces cost. Logic redundancy can be removed by several well-known techniques, such as binary decision diagrams, Boolean algebra, Karnaugh maps, the Quine–McCluskey algorithm, and the heuristic computer method. These operations are typically performed within a computer-aided design system.
Embedded systems with microcontrollers and programmable logic controllers are often used to implement digital logic for complex systems that don't require optimal performance. These systems are usually programmed by software engineers or by electricians, using ladder logic.
Representation[edit]
A digital circuit's input-output relationship can be represented as a truth table. An equivalent high-level circuit uses logic gates, each represented by a different shape (standardized by IEEE/ANSI 91-1984).[30] A low-level representation uses an equivalent circuit of electronic switches (usually transistors).
Most digital systems divide into combinational and sequential systems. The output of a combinational system depends only on the present inputs. However, a sequential system has some of its outputs fed back as inputs, so its output may depend on past inputs in addition to present inputs, to produce a sequence of operations. Simplified representations of their behavior called state machines facilitate design and test.
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 using flip flops that store inputted voltages as a bit only when the clock changes.
Synchronous systems[edit]
The usual way to implement a synchronous sequential state machine is to divide it into a piece of combinational logic and a set of flip flops called a state register. The state register represents the state as a binary number. The combinational logic produces the binary representation for the next state. On each clock cycle, the state register captures the feedback generated from the previous state of the combinational logic and feeds it back as an unchanging input to the combinational part of the state machine. The clock rate is limited by the most time-consuming logic calculation in the combinational logic.
Asynchronous systems[edit]
Most digital logic is synchronous because it is easier to create and verify a synchronous design. However, asynchronous logic has the advantage of its speed not being constrained by an arbitrary clock; instead, it runs at the maximum speed of its logic gates.[a]
Nevertheless, most systems need to accept external unsynchronized signals into their synchronous logic circuits. This interface is inherently asynchronous and must be analyzed as such. Examples of widely used asynchronous circuits include synchronizer flip-flops, switch debouncers and arbiters.
Asynchronous logic components can be 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. The designer must force the circuit to periodically wait for all of its parts to enter a compatible state (this is called "self-resynchronization"). Without 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.
Register transfer systems[edit]
Many digital systems are data flow machines. These are usually designed using synchronous register transfer logic and written with hardware description languages such as VHDL or Verilog.
In register transfer logic, binary numbers are stored in groups of flip flops called registers. A sequential state machine
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