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14 décembre 2010 2 14 /12 /décembre /2010 02:57

Digital electronics represent signals by discrete bands of analog levels, rather than by a continuous range. All levels within a band represent the same signal state. Relatively small changes to the analog signal levels due to manufacturing tolerance, signal attenuation or parasitic noise do not leave the discrete envelope, and as result are ignored by signal state sensing circuitry  (Dell XPS M1210 Batteryhttp://www.hdd-shop.co.uk .

In most cases the number of these states is two, and they are represented by two voltage bands: one near zero volts and a higher level near the supply voltage, corresponding to the "false" ("0") and "true" ("1") values of the boolean domain respectively (Dell Studio XPS 1340 Battery)    .

Digital techniques are useful because it is easier to get an electronic device to switch into one of a number of known states than to accurately reproduce a continuous range of values.

Digital electronic circuits are usually made from large assemblies of logic gates, simple electronic representations of Boolean logic functions (Dell Studio XPS 1640 Battery)   .

Advantages

One advantage of digital circuits when compared to analog circuits is that signals represented digitally can be transmitted without degradation due to noise. 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  (Dell Vostro 1710 Battery)    .

An hour of music can be stored on a compact disc as about 6 billion binary digits.

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  (Sony VGP-BPS13 battery) .

In an analog system, additional resolution requires fundamental improvements in the linearity and noise characteristics of each step of the signal chain.

Computer-controlled digital systems can be controlled by software, allowing new functions to be added without changing hardware. Often this can be done outside of the factory by updating the product's software  (Sony VGP-BPS13/B battery)  .

So, the product's design errors can be corrected 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 (Sony VGP-BPS13/S battery)   .

In a digital system, as long as the total noise is below a certain level, the information can be recovered perfectly.

Disadvantages

In some cases, digital circuits use more energy than analog circuits to accomplish the same tasks, thus producing more heat. In portable or battery-powered systems this can limit use of digital systems  (Sony VGP-BPS13A/B battery).

For example, battery-powered cellular telephones often use a low-power analog front-end to amplify and tune in 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 be easily reprogrammed to process the signals used in new cellular standards  (Sony VGP-BPS13B/B battery)   .

Digital circuits are sometimes more expensive, especially in small quantities.

Most 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  (Sony VGP-BPL9 battery)    .

The Nyquist-Shannon sampling theorem provides an important guideline as to how much digital data is needed to accurately portray a given analog signal.

In some systems, if a single piece of digital data is lost or misinterpreted, the meaning of large blocks of related data can completely change    (Sony VGP-BPS13B/B battery)    .

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  (Sony VGP-BPL11 battery)   .

These schemes help the system detect errors, and then either correct the errors, or at least ask for a new copy of the data. In a state-machine, the state transition logic can be designed to catch unused states and trigger a reset sequence or other error recovery routine      (Sony VGP-BPL15 battery)   .

Digital memory and transmission systems can use techniques such as error detection and correction to use additional data to correct any errors in transmission and storage.

On the other hand, some techniques used in digital systems make those systems more vulnerable to single-bit errors. These techniques are acceptable when the underlying bits are reliable enough that such errors are highly unlikely  (Dell Inspiron E1505 battery)    .

A single-bit error in audio data stored directly as linear pulse code modulation (such as on a CD-ROM) causes, at worst, a single click. Instead, many people useaudio compression to save storage space and download time, even though a single-bit error may corrupt the entire song    (Dell Latitude E6400 battery)  .

Analog issues in digital circuits

Digital circuits are made from analog components. The design must assure that the analog nature of the components doesn't dominate the desired digital behavior. Digital systems must manage noise and timing margins, parasitic inductances and capacitances, and filter power connections     (HP Pavilion dv6000 Battery)     .

Bad designs have intermittent problems such as "glitches", vanishingly-fast pulses that may trigger some logic but not others, "runt pulses" that do not reach valid "threshold" voltages, or unexpected ("undecoded") combinations of logic states  (Sony Vaio VGN-FZ31S battery)      .

Additionally, where clocked digital systems interface to analogue systems or systems that are driven from a different clock, the digital system can be subject to metastability where a change to the input violates the set-up time for a digital input latch. This situation will self-resolve, but will take a random time, and while it persists can result in invalid signals being propagated within the digital system for a short time    (Sony VGN-FZ31S battery)  .

Since digital circuits are made from analog components, digital circuits calculate more slowly than low-precision analog circuits that use a similar amount of space and power. However, the digital circuit will calculate more repeatably, because of its high noise immunity    (SONY VGN-FZ38M Battery)  .

On the other hand, in the high-precision domain (for example, where 14 or more bits of precision are needed), analog circuits require much more power and area than digital equivalents      (SONY VGN-FZ31z Battery)     .

Construction

A digital circuit is often constructed from small electronic circuits called logic gates that can be used to create combinational logic. Each logic gate represents a function of boolean logic. A logic gate is an arrangement of electrically controlled switches, better known as transistors      (Sony VGN-FZ31Z Battery)        .

Each logic symbol is represented by a different shape. The actual set of shapes was introduced in 1984 under IEEE\ANSI standard 91-1984. "The logic symbol given under this standard are being increasingly used now and have even started appearing in the literature published by manufacturers of digital integrated circuits   (SONY VAIO VGN-FZ38M Battery)   ."

The output of a logic gate 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      (SONY VGN-FZ31E Battery)     .

Integrated circuits are the least expensive way to make logic gates in large volumes. Integrated circuits are usually designed by engineers using electronic design automation software (see below for more information).

Another form of digital circuit is constructed from lookup tables, (many sold as "programmable logic devices", though other kinds of PLDs exist)  (SONY  VGN-FZ31J Battery)    .

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  (SONY VGN-FZ31M Battery)     .

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  (SONY VGN-FZ31B Battery)     .

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 circuit's complexity  (SONY VGP-BPS13 Battery)   .

When the complexity is less, the circuit also has fewer errors and less electronics, and is therefore less expensive.

The most widely used simplification is a minimization algorithm like the Espresso heuristic logic minimizer within a CAD system, although historically, binary decision diagrams, an automated Quine–McCluskey algorithm, truth tables, Karnaugh Maps, and Boolean algebra have been used     (Dell Inspiron 1320 Battery)     .

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 (usuallytransistors)     (Dell Inspiron 1320n Battery)      .

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 ("tools") with compatible file formats    (Dell Inspiron 1464 Battery)  .

To choose representations, engineers consider types of digital systems. Most digital systems divide into "combinational systems" and "sequential systems." A combinational 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      (Dell Inspiron 1564 Battery) .

A sequential system is a combinational 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    (Dell Inspiron 1764 Battery)   .

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      (Dell Studio 1450 Battery)      .

"Asynchronous" sequential systemspropagate 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   (Dell Studio 1457 Battery)      .

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." Each time a clock signal ticks, 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  (Dell Latitude D610 Battery)   .

The fastest rate of the clock is set by the most time-consuming logic calculation in the combinational 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 some combinational logic that produces the number of the next state    (Toshiba NB100 Battery)      .

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")     (Toshiba Satellite M65 battery)    .

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  (Toshiba Satellite M60 battery)    .

Certain circuits (such as the synchronizer flip-flops, switch debouncers, arbiters, 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 2005, almost all digital machines are synchronous designs because it is much easier to create and verify a synchronous design—the software currently used to simulate digital machines does not yet handle asynchronous designs   (Dell Latitude D830 Battery) .

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 runs at the maximum speed of its logic gates. Building an asynchronous circuit using faster parts makes the circuit faster      (Dell Latitude D620 Battery)    .

Many digital systems are data flow machines. These are usually designed using synchronous register transfer logic, using hardware description 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     (Dell Inspiron Mini 10 Battery)   .

A calculation is simply a piece of combinational logic. Each calculation also has an output bus, and these may be connected to the inputs of several registers. Sometimes a register will have amultiplexer on its input, so that it can store a number from any one of several buses       (Sony VGN-FW11S Battery)     .

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   (Sony VGN-FW11M Battery)     .

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      (Sony VGN-FW139E/H battery) .

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 amicrosequencer. 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  (Dell Latitude E5400 Battery)    .

The sequencer then counts, and the count addresses the memory or combinational 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  (Dell Latitude E4200 Battery)        .

In this way, the complex task of designing the controls of a computer is reduced to a simpler task of programming a 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     (Dell Vostro A840 Battery)    .

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      (Dell Inspiron 300M Battery)     .

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  (Dell Studio 1737 battery).

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      (Dell Inspiron E1505 battery)    .

The most common example of this kind of software is the Espresso heuristic logic minimizer       .

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     (Dell RM791 battery)  .

To automate costly engineering processes, some EDA can take state tables that describe state machines and automatically produce a truth table or a function table for the combinational logic of a state machine. The state table is a piece of text that lists each state, together with the conditions controlling the transitions between them and the belonging output signals      (Dell XPS M1530 battery) .

It is common for the function tables of such computer-generated state-machines to be optimized with logic-minimization software such as Minilog.

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      (Dell XPS M2010 battery)  .

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 digital designs. The tool flow usually terminates in a detailed computer file or set of files that describe how to physically construct the logic  (Dell Vostro 1000 battery)   .

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 verifying the outputs of simulated logic 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  (Acer Aspire One battery)        .

Once the input data is believed correct, the design itself must still be verified for correctness. Some tool flows verify designs by first producing a design, and then scanning the design to produce compatible input data for the tool flow. If the scanned data matches the input data, then the tool flow has probably not introduced errors      (Toshiba Satellite P10 Battery)   .

The functional verification data are usually called "test vectors." The functional test vectors may be preserved and used in the factory to test that newly constructed logic works correctly. However, functional test patterns don't discover common fabrication faults. Production tests are often designed by software tools called "test pattern generators"  (SONY VGN-FZ210CE Battery)    .

These generate test vectors by examining the structure of the logic and systematically generating tests for particular faults. This way the fault coverage can closely approach 100%, provided the design is properly made testable (see next section).

Once a design exists, and is verified and testable, it often needs to be processed to be manufacturable as well  (Dell Precision M70 Battery)   .

Modern integrated circuits have features smaller than the wavelength of the light used to expose the photoresist. Manufacturability software adds interference patterns to the exposure masks to eliminate open-circuits, and enhance the masks' resolution and contrast    (Toshiba Satellite L305 Battery)  .

Design for testability

"There are several reasons for testing a logic circuit. When the circuit is first developed, it is necessary to verify that the design circuit meets the required functional and timing specifications. When multiple copies of a correctly designed circuit are being manufactured, it is essential to test each copy to ensure that the manufacturing process has not introduced any flaws   (Toshiba Satellite T4900 Battery)     .

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 typical  (Toshiba PA3399U-2BRS battery)   .

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" (Toshiba Satellite A200 Battery)     .

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 (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)  (Toshiba Satellite 1200 Battery)     .

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" (named after the "Joint Test Action Group" that proposed it)      (Toshiba Satellite M300 Battery)  .

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     (Dell KM958 battery).

Trade-offs

Several numbers determine the practicality of a system of digital logic. Engineers explored numerous electronic devices to get an ideal combination of fanout, speed, low cost and reliability        WD passport essential (500GB/640GB) .

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        WD passport essential (250GB/320GB) .

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 systemfor a spacecraft. The first integrated circuit logic gates cost nearly $50 (in 1960 dollars, when an engineer earned $10,000/year)     WD  passport essential SE (750GB/1TB)   .

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  WD  passport elite(250GB/320GB) .

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      WD passport elite(500GB/640GB) .

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  WD  passport studio for Mac(320GB/500GB) .

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 (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     WD  passport studio for Mac(500GB/640GB) .

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        WD  Elements series(250GB/320GB) .

Modern transistorized integrated circuit logic gates have MTBFs greater than 82 billion hours (8.2×1010) hours, and need them because they have so many logic gates.

Fanout describes how many logic inputs can be controlled by a single logic output without exceeding the current ratings of the gateWD  Elements SE(500GB/640GB) .

The minimum practical fanout 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 (an electronic representation of a "logical not" function) can change from true to false and back       WD Elements SE(750GB/1TB) .

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 (5×109 hertz), and some laboratory systems switch at more than a terahertz (1×1012 hertz)   WD  Elements desktop(500GB/640GB) .

Logic families

Design started with relays. Relay logic was relatively inexpensive and reliable, but slow. Occasionally a mechanical failure would occur. Fanouts were typically about ten, limited by the resistance of the coils and arcing on the contacts from high voltages.

Later, vacuum tubes were used      WD  Elements desktop(750GB/1TB) .

These were very fast, but generated heat, and were unreliable because the filaments would burn out. Fanouts were typically five to seven, limited by the heating from the tubes' current. In the 1950s, special "computer tubes" were developed with filaments that omitted volatile elements like silicon. These ran for hundreds of thousands of hours     WD  Elements desktop(1.5 TB/2TB) .

The first semiconductor logic family was resistor-transistor logic. This was a thousand times more reliable than tubes, ran cooler, and used less power, but had a very low fan-in of three. Diode-transistor logic improved the fanout up to about seven, and reduced the power       WD  passport essential SE (750GB/1TB)--USB 3.0)      .

Some DTL designs used two power-supplies with alternating layers of NPN and PNP transistors to increase the fanout.

Transistor transistor logic (TTL) was a great improvement over these. In early devices, fanout improved to ten, and later variations reliably achieved twenty. TTL was also fast, with some variations achieving switching times as low as twenty nanoseconds. TTL is still used in some designs      WD  passport essential (500GB/640GB) .

Emitter coupled logic is very fast but uses a lot of power. It was extensively used for high-performance computers made up of many medium-scale components ( such as the Illiac IV).

Modern integrated circuits mostly use variations of CMOS, which is fast, small and low-power. Fanouts of forty or more are possible, with some speed penalty      WD  passport for Mac(320GB/500GB) .

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. MIT students Erlyne Gee, Edward Hardebeck, Danny Hillis (co-author of The Connection Machine), Margaret Minsky and brothers Barry and Brian Silverman, built two working computers fromTinker toys, string, a brick, and a sharpened pencil       WD  passport for Mac(640GB/1TB) .

The Tinkertoy computer is in the Boston 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        My book essential 4 generation  (640GB/1TB) .

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 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        WD  My book essential 4 generation( 1.5TB/2TB) .

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       WD  My book elite( 1TB/1.5TB) .

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        WD  My book studio(1TB/2TB) .

Digital

A digital system is a data technology that uses discrete (discontinuous) values. By contrast, non-digital (or analog) systems use a continuous range of values to represent information. Although digital representations are discrete, the information represented can be either discrete, such as numbers, letters or icons, or continuous, such as sounds, images, and other measurements of continuous systems       WD  My book essential 4 generation( 1.5TB/2TB) .

The word digital comes from the same source as the word digit and digitus (the Latin word for finger), as fingers are used for discrete counting. It is most commonly used in computing and electronics, especially where real-world information is converted to binary numeric form as in digital audio and digital photography          WD  My book elite(640GB/2TB) .

Digital noise

When data is transmitted, or indeed handled at all, a certain amount of noise enters into the signal. Noise can have several causes: data transmitted wirelessly, such as by radio, may be received inaccurately, suffer interference from other wireless sources, or pick up background noise from the rest of the universe     Seagate  expansion portable (320GB/500GB) .

Microphones pick up both the intended signal as well as background noise without discriminating between signal and noise, so when audio is encoded digitally, it typically already includes noise.

Electric pulses transmitted via wires are typically attenuated by the resistance of the wire, and changed by its capacitance or inductance. Temperature variations can increase or reduce these effects    Seagate  expansion (1.5TB/2TB) .

While digital transmissions are also degraded, slight variations do not matter since they are ignored when the signal is received. With an analog signal, variances cannot be distinguished from the signal and so provide a kind of distortion. In a digital signal, similar variances will not matter, as any signal close enough to a particular value will be interpreted as that value   Seagate  Freeagent Desktop (500GB/1TB) .

Care must be taken to avoid noise and distortion when connecting digital and analog systems, but more when using analog systems.

Symbol to digital conversion

Since symbols (for example, alphanumeric characters) are not continuous, representing symbols digitally is rather simpler than conversion of continuous or analog information to digital        Seagate  Freeagent Go(250GB/320GB) .

Instead ofsampling and quantization as in analog-to-digital conversion, such techniques as polling and encoding are used.

A symbol input device usually consists of a number of switches that are polled at regular intervals to see which switches are pressed. Data will be lost if, within a single polling interval, two switches are pressed, or a switch is pressed, released, and pressed again  Seagate  Freeagent Go(500GB/640GB) .

This polling can be done by a specialized processor in the device to prevent burdening the main CPU. When a new symbol has been entered, the device typically sends an interrupt to alert the CPU to read it.

For devices with only a few switches (such as the buttons on a joystick), the status of each can be encoded as bits (usually 0 for released and 1 for pressed) in a single word         Seagate  Freeagent Go(750GB/1TB) .

This is useful when combinations of key presses are meaningful, and is sometimes used for passing the status of modifier keys on a keyboard (such as shift and control). But it does not scale to support more keys than the number of bits in a single byte or word.

Devices with many switches (such as a computer keyboard) usually arrange these switches in a scan matrix, with the individual switches on the intersections of x and y lines       Seagate  Freeagent Goflex(250GB/320GB) .

When a switch is pressed, it connects the corresponding x and y lines together. Polling (often called scanning in this case) is done by activating each x line in sequence and detecting which y lines then have a signal, thus which keys are pressed. When the keyboard processor detects that a key has changed state, it sends a signal to the CPU indicating the scan code of the key and its new state      Seagate Freeagent Goflex(500GB/640GB) .

The symbol is then encoded, or converted into a number, based on the status of modifier keys and the desired character encoding.

A custom encoding can be used for a specific application with no loss of data. However, using a standard encoding such as ASCII is problematic if a symbol such as 'ß' needs to be converted but is not in the standard     Seagate  Freeagent Goflex(750GB/1TB) .

Properties of digital information

All digital information possesses common properties that distinguish it from analog communications methods:

  • Synchronization: Since digital information is conveyed by the sequence in which symbols are ordered, all digital schemes have some method for determining the beginning of a sequence      Seagate  Freeagent Goflex Pro(500GB/750GB) .
  • In written or spoken human languages synchronization is typically provided by pauses (spaces), capitalization, and punctuation. Machine communications typically use special synchronization sequences     Seagate  Freeagent Goflex desktop(1TB/2TB) .
  • Language: All digital communications require a language, which in this context consists of all the information that the sender and receiver of the digital communication must both possess, in advance, in order for the communication to be successful. Languages are generally arbitrary and specify the meaning to be assigned to particular symbol sequences, the allowed range of values, methods to be used for synchronization, etc       Seagate  Freeagent go for Mac(320GB/640GB) .
  • Errors: Disturbances (noise) in analog communications invariably introduce some, generally small deviation or error between the intended and actual communication. Disturbances in a digital communication do not result in errors unless the disturbance is so large as to result in a symbol being misinterpreted as another symbol or disturb the sequence of symbols  Samsung  G2 protable (250gb/320GB) .
  • It is therefore generally possible to have an entirely error-free digital communication. Further, techniques such as check codes may be used to detect errors and guarantee error-free communications through redundancy or retransmission. Errors in digital communications can take the form of substitution errors in which a symbol is replaced by another symbol  Samsung  G2 protable (500GB/640GB) .
  • or insertion/deletion errors in which an extra incorrect symbol is inserted into or deleted from a digital message. Uncorrected errors in digital communications have unpredictable and generally large impact on the information content of the communication       Samsung  S2 protable (320GB/500GB) .
  • Copying: Because of the inevitable presence of noise, making many successive copies of an analog communication is infeasible because each generation increases the noise. Because digital communications are generally error-free, copies of copies can be made indefinitely       Samsung S1 Mini (120GB/160GB) .
  • Granularity: When a continuously variable analog value is represented in digital form there is always a decision as to the number of symbols to be assigned to that value. The number of symbols determines the precision or resolution of the resulting datum      Samsung  S1 Mini (250GB/320GB) .
  • The difference between the actual analog value and the digital representation is known as quantization error. Example: the actual temperature is 23.234456544453 degrees but if only two digits (23) are assigned to this parameter in a particular digital representation     Samsung story station (1TB/1.5TB) .

Historical digital systems

Although digital signals are generally associated with the binary electronic digital systems used in modern electronics and computing, digital systems are actually ancient, and need not be binary nor electronic       Samsung Story station (1.5TB/2TB) .

  • Written text in books (due to the limited character set and the use of discrete symbols - the alphabet in most cases)
  • An abacus was created sometime between 1000 BC and 500 BC , it later become a form of calculation frequency, nowadays it can be used as a very advanced, yet basic digital calculator that uses beads on rows to represent numbers  Samsung story station Esata(1TB/1.5TB) .
  • Beads only have meaning in discrete up and down states, not in analog in-between states.
  • A beacon is perhaps the simplest non-electronic digital signal, with just two states (on and off). In particular, smoke signals are one of the oldest examples of a digital signal, where an analog "carrier" (smoke) is modulated with a blanket to generate a digital signal (puffs) that conveys information     Samsung  G3 station (1TB/1.5TB) .
  • Morse code uses six digital states—dot, dash, intra-character gap (between each dot or dash), short gap (between each letter), medium gap (between words), and long gap (between sentences)—to send messages via a variety of potential carriers such as electricity or light, for example using an electrical telegraph or a flashing light        Maxtor  one touch 4 plus (500GB/750GB) .
  • The Braille system was the first binary format for character encoding, using a six-bit code rendered as dot patterns.
  • Flag semaphore uses rods or flags held in particular positions to send messages to the receiver watching them some distance away      Maxtor one touch 4 plus (1TB/1.5TB) .
  • International maritime signal flags have distinctive markings that represent letters of the alphabet to allow ships to send messages to each other.
  • More recently invented, a modem modulates an analog "carrier" signal (such as sound) to encode binary electrical digital information, as a series of binary digital sound pulses     Maxtor cool black(640GB/1TB) .
  • A slightly earlier, surprisingly reliable version of the same concept was to bundle a sequence of audio digital "signal" and "no signal" information (i.e. "sound" and "silence") on magnetic cassette tape for use with early home computers.

Digital physics

In physics and cosmology, digital physics is a collection of theoretical perspectives based on the premise that the universe is, at heart, describable by information, and is therefore computable     Maxtor Black diamond (320GB/500GB) .

Therefore, the universe can be conceived as either the output of a computer program or as a vast, digital computation device (or, at least, mathematically isomorphic to such a device).

Digital physics is grounded in one or more of the following hypotheses, listed in order of increasing boldness    Hitachi  simple touch (250GB/320GB) .

The universe, or reality, is:

  • Essentially informational (although not every informational ontology need be digital);
  • Essentially digital;
  • Itself a colossal computer;
  • The output of a simulated reality exercise     Hitachi simple touch (320GB/500GB) .

History

Every computer must obviously be compatible with the principles of information theory, statistical thermodynamics, and quantum mechanics. A fundamental link among these fields was proposed byEdwin Jaynes in two seminal 1957 papers     Hitachi  life studio (320GB/500GB) .

Moreover, Jaynes elaborated an interpretation of probability theory as generalized Aristotelian logic, a view very convenient for linking fundamental physics with digital computers, because these are designed to implement the operations of classical logic and, equivalently, of Boolean algebra     Hitachi life studio (250GB/320GB) .

The hypothesis that the universe is a digital computer was pioneered by Konrad Zuse in his book Rechnender Raum (translated into English as Calculating Space). The term digital physics was first employed by Edward Fredkin, who later came to prefer the term digital philosophy Hitachi  life studio platinum (250GB/320GB) .

Others who have modeled the universe as a giant computer include Stephen Wolfram, Juergen Schmidhuber,and Nobel laureate Gerard 't Hooft. These authors hold that the apparently probabilistic nature of quantum physics is not necessarily incompatible with the notion of computability      Hitachi life studio platinum (320GB/500GB) .

Quantum versions of digital physics have recently been proposed by Seth Lloyd, David Deutsch, and Paola Zizzi.

Related ideas include Carl Friedrich von Weizsäcker's binary theory of ur-alternatives, pancomputationalism, computational universe theory, John Archibald Wheeler's "It from bit", and Max Tegmark'sultimate ensemble    Hitachi life studio desk (500GB/1TB).

Digital physics

Overview

Digital physics suggests that there exists, at least in principle, a program for a universal computer which computes the evolution of the universe. The computer could be, for example, a huge cellular automaton (Zuse 1967), or a universal Turing machine, as suggested by Schmidhuber (1997), who pointed out that there exists a very short program that can compute all possible computable universes in an asymptotically optimal way       Hitachi life studio plus (320GB/500GB) .

Some try to identify single physical particles with simple bits. For example, if one particle, such as an electron, is switching from one quantum state to another, it may be the same as if a bit is changed from one value (0, say) to the other (1). A single bit suffices to describe a single quantum switch of a given particle       Hitachi life studio plus (320GB/500GB) .

As the universe appears to be composed of elementary particles whose behavior can be completely described by the quantum switches they undergo, that implies that the universe as a whole can be described by bits. Every state is information, and every change of state is a change in information (requiring the manipulation of one or more bits)      Hitachi X mobile (250GB/320GB) .

Setting aside dark matter and dark energy, which are poorly understood at present, the known universe consists of about 1080protons and the same number of electrons. Hence, the universe could be simulated by a computer capable of storing and manipulating about 1090 bits. If such a simulation is indeed the case, thenhypercomputation would be impossible   Hitachi X mobile(320GB/500GB) .

Loop quantum gravity could lend support to digital physics, in that it assumes space-time is quantized. Paola Zizzi has formulated a realization of this concept in what has come to be called "computational loop quantum gravity", or CLQG . Other theories that combine aspects of digital physics with loop quantum gravity are those of Marzuoli and Rasetti and Girelli and Livine Hitachi  XL (1TB/2TB) .

Weizsacker's ur-alternatives

Physicist Carl Friedrich von Weizsäcker's theory of ur-alternatives (archetypal objects), first publicized in his book The Unity of Nature (1980) , further developed through the 1990s , is a kind of digital ph

ysics as it axiomatically constructs quantum physics from the distinction between empirically observable, binary alternatives    Toshiba canvio portable(320GB/500GB) .

Weizsäcker used his theory to derive the 3-dimensionality of space and to estimate the entropy of a proton falling into a black hole.

Pancomputationalism or the Computational universe theory

Pancomputationalism (also known as Pan-computationalism, Naturalist computationalism) is a view that the universe is a huge computational machine, or rather a network of computational processes which, following fundamental physical laws, computes (dynamically develop) its own next state from the current one      Toshiba  canvio portable(750GB/1TB) .

For instance, in his book, Programming the Universe, Seth Lloyd contends that the universe itself is one big quantum computer producing what we see around us, and ourselves, as it runs a cosmicprogram. According to Lloyd, once we understand the laws of physics completely, we will be able to use small-scale quantum computing to understand the universe completely as well  Toshiba  anvio for Mac(500GB/750GB) .

A computational universe is also proposed by Jürgen Schmidhuber in a paper based on Konrad Zuse's assumption (1967) that the history of the universe is computable. He pointed out that the simplest explanation of the universe would be a very simple Turing machine programmed to systematically execute all possible programs computing all possible histories for all types of computable physical laws        Toshiba  canvio for Mac(750GB/1TB) .

He also pointed out that there is an optimally efficient way of computing all computable universes based on Leonid Levin's universal search algorithm (1973). In 2000 he expanded this work by combining Ray Solomonoff's theory of inductive inference with the assumption that quickly computable universes are more likely than others      Toshiba External HDD –portable(320GB/500GB) .

This work on digital physics also led to limit-computable generalizations of algorithmic information or Kolmogorov Complexity and the concept of Super Omegas, which are limit-computable numbers that are even more random (in a certain sense) than Gregory Chaitin's number of wisdom Omega      Toshiba portable(500GB/640GB) .

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