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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Digital data</span></span>
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</style><div role="note" class="hatnote navigation-not-searchable">This article is about the concept in information theory and information systems. For the electronics concept, see <a href="Digital_signal" title="Digital signal">Digital signal</a>. For other uses, see <a href="Digital_(disambiguation)" class="mw-redirect mw-disambig" title="Digital (disambiguation)">Digital</a>.</div>
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<p><b>Digital data</b>, in <a href="Information_theory" title="Information theory">information theory</a> and <a href="Information_systems" class="mw-redirect" title="Information systems">information systems</a>, is information represented as a string of <a href="Discrete_mathematics" title="Discrete mathematics">discrete</a> symbols, each of which can take on one of only a finite number of values from some <a href="Alphabet_(formal_languages)" title="Alphabet (formal languages)">alphabet</a>, such as letters or digits. An example is a <a href="Text_document" class="mw-redirect" title="Text document">text document</a>, which consists of a string of <a href="Alphanumeric_character" class="mw-redirect" title="Alphanumeric character">alphanumeric characters</a>. The most common form of digital data in modern information systems is <i><a href="Binary_data" title="Binary data">binary data</a></i>, which is represented by a string of <a href="Binary_digit" class="mw-redirect" title="Binary digit">binary digits</a> (bits) each of which can have one of two values, either 0 or 1.
</p><p>Digital data can be contrasted with <i>analog data</i>, which is represented by a value from a <a href="Continuous_variable" class="mw-redirect" title="Continuous variable">continuous</a> range of <a href="Real_number" title="Real number">real numbers</a>. Analog data is transmitted by an <a href="Analog_signal" title="Analog signal">analog signal</a>, which not only takes on continuous values but can vary continuously with time, a continuous <a href="Real-valued_function" title="Real-valued function">real-valued function</a> of time. An example is the air pressure variation in a <a href="Sound_wave" class="mw-redirect" title="Sound wave">sound wave</a>.
</p><p>The word <i>digital</i> comes from the same source as the words <a href="Digit_(anatomy)" title="Digit (anatomy)">digit</a> and <i>digitus</i> (the <a href="Latin" title="Latin">Latin</a> word for <i>finger</i>), as fingers are often used for counting. Mathematician <a href="George_Stibitz" title="George Stibitz">George Stibitz</a> of <a href="Bell_Labs" title="Bell Labs">Bell Telephone Laboratories</a> used the word <i>digital</i> in reference to the fast electric pulses emitted by a device designed to aim and fire anti-aircraft guns in 1942.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> The term is most commonly used in <a href="Computing" title="Computing">computing</a> and <a href="Electronics" title="Electronics">electronics</a>, especially where real-world information is converted to <a href="Binary_numeral_system" class="mw-redirect" title="Binary numeral system">binary</a> numeric form as in <a href="Digital_audio" title="Digital audio">digital audio</a> and <a href="Digital_photography" title="Digital photography">digital photography</a>.
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<div class="mw-heading mw-heading2"><h2 id="Symbol_to_digital_conversion">Symbol to digital conversion</h2></div>
<p>Since symbols (for example, <a href="Alphanumeric" class="mw-redirect" title="Alphanumeric">alphanumeric</a> <a href="Character_(computing)" title="Character (computing)">characters</a>) are not continuous, representing symbols digitally is rather simpler than conversion of continuous or analog information to digital. Instead of <a href="Sampling_(signal_processing)" title="Sampling (signal processing)">sampling</a> and <a href="Quantization_(signal_processing)" title="Quantization (signal processing)">quantization</a> as in <a href="Analog-to-digital_conversion" class="mw-redirect" title="Analog-to-digital conversion">analog-to-digital conversion</a>, such techniques as <a href="Polling_(computer_science)" title="Polling (computer science)">polling</a> and <a href="Character_encoding" title="Character encoding">encoding</a> are used.
</p><p>A symbol input device usually consists of a group of switches that are polled at regular intervals to see which switches are switched. Data will be lost if, within a single polling interval, two switches are pressed, or a switch is pressed, released, and pressed again. This polling can be done by a specialized processor in the device to prevent burdening the main <a href="Central_processing_unit" title="Central processing unit">CPU</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> When a new symbol has been entered, the device typically sends an <a href="Interrupt" title="Interrupt">interrupt</a>, in a specialized format, so that the CPU can read it.
</p><p>For devices with only a few switches (such as the buttons on a <a href="Joystick" title="Joystick">joystick</a>), the status of each can be encoded as bits (usually 0 for released and 1 for pressed) in a single word. 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.
</p><p>Devices with many switches (such as a <a href="Computer_keyboard" title="Computer keyboard">computer keyboard</a>) usually arrange these switches in a scan matrix, with the individual switches on the intersections of x and y lines. 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 <a href="Digital_signal" title="Digital signal">signal</a>, 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. The symbol is then <a href="Code" title="Code">encoded</a> or converted into a number based on the status of modifier keys and the desired <a href="Character_encoding" title="Character encoding">character encoding</a>.
</p><p>A custom <a href="Character_encoding" title="Character encoding">encoding</a> can be used for a specific application with no loss of data. However, using a standard encoding such as <a href="ASCII" title="ASCII">ASCII</a> is problematic if a symbol such as 'ß' needs to be converted but is not in the standard.
</p><p>It is estimated that in the year 1986, less than 1% of the world's technological capacity to store information was digital and in 2007 it was already 94%.<sup id="cite_ref-HilbertLopez2011_3-0" class="reference"><a href="#cite_note-HilbertLopez2011-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The year 2002 is assumed to be the year when humankind was able to store more information in digital than in analog format (the "beginning of the <a href="Digital_age" class="mw-redirect" title="Digital age">digital age</a>").<sup id="cite_ref-Hilbertvideo2011_4-0" class="reference"><a href="#cite_note-Hilbertvideo2011-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:0_5-0" class="reference"><a href="#cite_note-:0-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="States">States</h2></div>
<p>Digital data come in these three states: <a href="Data_at_rest" title="Data at rest">data at rest</a>, <a href="Data_in_transit" title="Data in transit">data in transit</a>, and <a href="Data_in_use" title="Data in use">data in use</a>. The <a href="CIA_Triad" class="mw-redirect" title="CIA Triad">confidentiality, integrity, and availability</a> have to be managed during the entire lifecycle from 'birth' to the destruction of the data.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>
</p>
<div class="mw-heading mw-heading2"><h2 id="Properties_of_digital_information">Properties of digital information</h2></div>
<p>All digital information possesses common properties that distinguish it from analog data with respect to communications:
</p>
<ul><li><b>Synchronization:</b> 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. In written or spoken human languages, synchronization is typically provided by <a href="Pausa" title="Pausa">pauses</a> (spaces), <a href="Capitalization" title="Capitalization">capitalization</a>, and <a href="Punctuation" title="Punctuation">punctuation</a>. Machine communications typically use special <a href="Synchronization_sequence" class="mw-redirect" title="Synchronization sequence">synchronization sequences</a>.</li>
<li><b>Language:</b> All digital communications require a <i><a href="Formal_language" title="Formal language">formal language</a></i>, which in this context consists of all the information that the sender and receiver of the digital communication must both possess, in advance, 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.</li>
<li><b>Errors:</b> Disturbances (<a href="Noise_(signal_processing)" title="Noise (signal processing)">noise</a>) in analog communications invariably introduce some, generally small deviation or error between the intended and actual communication. Disturbances in digital communication only result in errors when the disturbance is so large as to result in a symbol being misinterpreted as another symbol or disturbing the sequence of symbols. It is generally possible to have near-error-free digital communication. Further, techniques such as check codes may be used to <a href="Error_detection_and_correction" title="Error detection and correction">detect errors and correct them</a> through redundancy or re-transmission. Errors in digital communications can take the form of <i>substitution errors,</i> in which a symbol is replaced by another symbol, or <i>insertion/deletion</i> errors, in which an extra incorrect symbol is inserted into or deleted from a digital message. Uncorrected errors in digital communications have an unpredictable and generally large impact on the information content of the communication.</li>
<li><b><a href="Data_transmission" class="mw-redirect" title="Data transmission">Copying</a>:</b> 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.</li>
<li><b><a href="Granularity" title="Granularity">Granularity</a>:</b> The digital representation of a continuously variable analog value typically involves a selection of the number of symbols to be assigned to that value. The number of symbols determines the precision or resolution of the resulting datum. The difference between the actual analog value and the digital representation is known as <i><a href="Quantization_error" class="mw-redirect" title="Quantization error">quantization error</a></i>. For example, if the actual temperature is 23.234456544453 degrees, but only two digits (23) are assigned to this parameter in a particular digital representation, the quantizing error is 0.234456544453. This property of digital communication is known as <i>granularity</i>.</li>
<li><b><a href="Data_compression" title="Data compression">Compressible</a>:</b> According to Miller, "Uncompressed digital data is very large, and in its raw form, it would actually produce a larger signal (therefore be more difficult to transfer) than analog data. However, digital data can be compressed. Compression reduces the amount of bandwidth space needed to send information. Data can be compressed, sent, and then decompressed at the site of consumption. This makes it possible to send much more information and results in, for example, <a href="Digital_television" title="Digital television">digital television</a> signals offering more room on the airwave spectrum for more television channels."<sup id="cite_ref-:0_5-1" class="reference"><a href="#cite_note-:0-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></li></ul>
<div class="mw-heading mw-heading2"><h2 id="Historical_digital_systems">Historical digital systems</h2></div>
<p>Even though 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 or electronic.
</p>
<ul><li><a href="DNA" title="DNA">DNA</a> <a href="Genetic_code" title="Genetic code">genetic code</a> is a naturally occurring form of digital data storage.</li>
<li>Written text (due to the limited character set and the use of discrete symbols – the alphabet in most cases)</li>
<li>The <i><a href="Abacus" title="Abacus">abacus</a></i> was created sometime between 1000 BC and 500 BC, it later became 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. Beads only have meaning in discrete up and down states, not in analog in-between states.</li>
<li>A <i><a href="Beacon" title="Beacon">beacon</a></i> is perhaps the simplest non-electronic digital signal, with just two states (on and off). In particular, <i><a href="Smoke_signal" title="Smoke signal">smoke signals</a></i> are one of the oldest examples of a digital signal, where an analog "carrier" (smoke) is <a href="Modulated" class="mw-redirect" title="Modulated">modulated</a> with a blanket to generate a digital signal (puffs) that conveys information.</li>
<li><a href="Morse_code" title="Morse code">Morse code</a> 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 <a href="Electrical_telegraph" title="Electrical telegraph">electrical telegraph</a> or a flashing light.</li>
<li>The <a href="Braille" title="Braille">Braille</a> uses a six-bit code rendered as dot patterns.</li>
<li><a href="Flag_semaphore" title="Flag semaphore">Flag semaphore</a> uses rods or flags held in particular positions to send messages to the receiver watching them some distance away.</li>
<li><a href="International_maritime_signal_flags" title="International maritime signal flags">International maritime signal flags</a> have distinctive markings that represent letters of the alphabet to allow ships to send messages to each other.</li>
<li>More recently invented, a <a href="Modem" title="Modem">modem</a> modulates an analog "carrier" signal (such as sound) to encode binary electrical digital information, as a series of binary digital sound pulses. 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 <a href="Compact_audio_cassette" class="mw-redirect" title="Compact audio cassette">magnetic cassette tape</a> for use with early <a href="Home_computer" title="Home computer">home computers</a>.</li></ul>
<div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div>
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<ul><li><a href="Analog-to-digital_converter" title="Analog-to-digital converter">Analog-to-digital converter</a></li>
<li><a href="Barker_code" title="Barker code">Barker code</a></li>
<li><a href="Binary_number" title="Binary number">Binary number</a></li>
<li><a href="Comparison_of_analog_and_digital_recording" title="Comparison of analog and digital recording">Comparison of analog and digital recording</a></li>
<li><a href="Computer_data_storage" title="Computer data storage">Computer data storage</a></li>
<li><a href="Data_(computer_science)" title="Data (computer science)">Data (computer science)</a></li>
<li><a href="Data_remanence" title="Data remanence">Data remanence</a></li>
<li><a href="Digital_architecture" title="Digital architecture">Digital architecture</a></li>
<li><a href="Digital_art" title="Digital art">Digital art</a></li>
<li><a href="Digital_control" title="Digital control">Digital control</a></li>
<li><a href="Digital_divide" title="Digital divide">Digital divide</a></li>
<li><a href="Digital_electronics" title="Digital electronics">Digital electronics</a></li>
<li><a href="Digital_infinity" title="Digital infinity">Digital infinity</a></li>
<li><a href="Digital_native" title="Digital native">Digital native</a></li>
<li><a href="Digital_physics" title="Digital physics">Digital physics</a></li>
<li><a href="Digital_recording" title="Digital recording">Digital recording</a></li>
<li><a href="Digital_Revolution" class="mw-redirect" title="Digital Revolution">Digital Revolution</a></li>
<li><a href="Digital_video" title="Digital video">Digital video</a></li>
<li><a href="Digital-to-analog_converter" title="Digital-to-analog converter">Digital-to-analog converter</a></li>
<li><a href="Internet_forum" title="Internet forum">Internet forum</a></li></ul>
</div>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
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<li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">
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</style><cite id="CITEREFCeruzzi2012" class="citation book cs1">Ceruzzi, Paul E (29 June 2012). <i>Computing: A Concise History</i>. <a href="MIT_Press" title="MIT Press">MIT Press</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-262-51767-6</bdi>.</cite></span>
</li>
<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFHeinrichHeinzlRoithmayr2014" class="citation book cs1 cs1-prop-foreign-lang-source">Heinrich, Lutz J.; Heinzl, Armin; Roithmayr, Friedrich (29 August 2014). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Uq4FCgAAQBAJ&dq=Digitale+Daten+lexikon&pg=PA198"><i>Wirtschaftsinformatik-Lexikon</i></a> (in German). Walter de Gruyter GmbH & Co KG. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-486-81590-0</bdi>.</cite></span>
</li>
<li id="cite_note-HilbertLopez2011-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-HilbertLopez2011_3-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFMartin_HilbertPriscila_López2011" class="citation magazine cs1">Martin Hilbert; Priscila López (10 February 2011). <a rel="nofollow" class="external text" href="https://www.science.org/doi/10.1126/science.1200970">"The World's Technological Capacity to Store, Communicate, and Compute Information"</a>. <i><a href="Science_(journal)" title="Science (journal)">Science</a></i>. Vol. 332, no. 6025. pp. <span class="nowrap">60–</span>65. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.1200970">10.1126/science.1200970</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110531133712/http://www.sciencemag.org/content/suppl/2011/02/08/science.1200970.DC1/Hilbert-SOM.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 31 May 2011.</cite> Also <cite class="citation magazine cs1"><a rel="nofollow" class="external text" href="https://www.science.org/doi/suppl/10.1126/science.1200970/suppl_file/hilbert-som.pdf">"Supporting online material for The World's Technological Capacity to Store, Communicate, and Compute Information"</a> <span class="cs1-format">(PDF)</span>. <i><a href="Science_(journal)" title="Science (journal)">Science</a></i>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.1200970">10.1126/science.1200970</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110531133712/http://www.sciencemag.org/content/suppl/2011/02/08/science.1200970.DC1/Hilbert-SOM.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 31 May 2011.</cite> Free access to the article through here: <span class="url"><a rel="nofollow" class="external text" href="https://www.martinhilbert.net/WorldInfoCapacity.html/">www<wbr>.martinhilbert<wbr>.net<wbr>/WorldInfoCapacity<wbr>.html<wbr>/</a></span></span>
</li>
<li id="cite_note-Hilbertvideo2011-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hilbertvideo2011_4-0">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=iIKPjOuwqHo">"video animation on The World's Technological Capacity to Store, Communicate, and Compute Information from 1986 to 2010"</a>. 11 June 2011. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130221144621/https://www.youtube.com/watch?v=iIKPjOuwqHo">Archived</a> from the original on 21 February 2013<span class="reference-accessdate">. Retrieved <span class="nowrap">6 November</span> 2013</span> – via YouTube.</cite></span>
</li>
<li id="cite_note-:0-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFMiller2011" class="citation book cs1">Miller, Vincent (2011). <i>Understanding digital culture</i>. London: Sage Publications. sec. "Convergence and the contemporary media experience". <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-84787-497-9</bdi>.</cite></span>
</li>
<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20210414042237/https://www.ed.ac.uk/arts-humanities-soc-sci/about-us/information-security-and-governance/what-information-do-i-have-to-protect/the-three-states-of-information">"The three states of information"</a>. <i>The University of Edinburgh</i>. Archived from <a rel="nofollow" class="external text" href="https://www.ed.ac.uk/arts-humanities-soc-sci/about-us/information-security-and-governance/what-information-do-i-have-to-protect/the-three-states-of-information">the original</a> on 14 April 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">21 February</span> 2021</span>.</cite></span>
</li>
</ol></div></div>
<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>
<ul><li>Tocci, R. 2006. Digital Systems: Principles and Applications (10th Edition). Prentice Hall. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-13-172579-3</bdi></li></ul>
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</style><div id="Digital_electronics118" style="font-size:114%;margin:0 4em"><a href="Digital_electronics" title="Digital electronics">Digital electronics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="Electronic_component" title="Electronic component">Components</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Transistor" title="Transistor">Transistor</a></li>
<li><a href="Resistor" title="Resistor">Resistor</a></li>
<li><a href="Inductor" title="Inductor">Inductor</a></li>
<li><a href="Capacitor" title="Capacitor">Capacitor</a></li>
<li><a href="Printed_electronics" title="Printed electronics">Printed electronics</a></li>
<li><a href="Printed_circuit_board" title="Printed circuit board">Printed circuit board</a></li>
<li><a href="Electronic_circuit" title="Electronic circuit">Electronic circuit</a></li>
<li><a href="Flip-flop_(electronics)" title="Flip-flop (electronics)">Flip-flop</a></li>
<li><a href="Memory_cell_(computing)" title="Memory cell (computing)">Memory cell</a></li>
<li><a href="Combinational_logic" title="Combinational logic">Combinational logic</a></li>
<li><a href="Sequential_logic" title="Sequential logic">Sequential logic</a></li>
<li><a href="Logic_gate" title="Logic gate">Logic gate</a></li>
<li><a href="Boolean_circuit" title="Boolean circuit">Boolean circuit</a></li>
<li><a href="Integrated_circuit" title="Integrated circuit">Integrated circuit</a> (IC)</li>
<li><a href="Hybrid_integrated_circuit" title="Hybrid integrated circuit">Hybrid integrated circuit</a> (HIC)</li>
<li><a href="Mixed-signal_integrated_circuit" title="Mixed-signal integrated circuit">Mixed-signal integrated circuit</a></li>
<li><a href="Three-dimensional_integrated_circuit" title="Three-dimensional integrated circuit">Three-dimensional integrated circuit</a> (3D IC)</li>
<li><a href="Emitter-coupled_logic" title="Emitter-coupled logic">Emitter-coupled logic</a> (ECL)</li>
<li><a href="Erasable_programmable_logic_device" class="mw-redirect" title="Erasable programmable logic device">Erasable programmable logic device</a> (EPLD)</li>
<li><a href="Macrocell_array" title="Macrocell array">Macrocell array</a></li>
<li><a href="Programmable_logic_array" title="Programmable logic array">Programmable logic array</a> (PLA)</li>
<li><a href="Programmable_logic_device" title="Programmable logic device">Programmable logic device</a> (PLD)</li>
<li><a href="Programmable_Array_Logic" title="Programmable Array Logic">Programmable Array Logic</a> (PAL)</li>
<li><a href="Generic_Array_Logic" title="Generic Array Logic">Generic Array Logic</a> (GAL)</li>
<li><a href="Complex_programmable_logic_device" title="Complex programmable logic device">Complex programmable logic device</a> (CPLD)</li>
<li><a href="Field-programmable_gate_array" title="Field-programmable gate array">Field-programmable gate array</a> (FPGA)</li>
<li><a href="Field-programmable_object_array" title="Field-programmable object array">Field-programmable object array</a> (FPOA)</li>
<li><a href="Application-specific_integrated_circuit" title="Application-specific integrated circuit">Application-specific integrated circuit</a> (ASIC)</li>
<li><a href="Tensor_Processing_Unit" title="Tensor Processing Unit">Tensor Processing Unit</a> (TPU)</li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;">Theory</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Digital_signal" title="Digital signal">Digital signal</a></li>
<li><a href="Boolean_algebra" title="Boolean algebra">Boolean algebra</a></li>
<li><a href="Logic_synthesis" title="Logic synthesis">Logic synthesis</a></li>
<li><a href="Logic_in_computer_science" title="Logic in computer science">Logic in computer science</a></li>
<li><a href="Computer_architecture" title="Computer architecture">Computer architecture</a></li>
<li><a href="Digital_signal_(signal_processing)" title="Digital signal (signal processing)">Digital signal</a>
<ul><li><a href="Digital_signal_processing" title="Digital signal processing">Digital signal processing</a></li></ul></li>
<li><a href="Circuit_minimization_for_Boolean_functions" class="mw-redirect" title="Circuit minimization for Boolean functions">Circuit minimization</a></li>
<li><a href="Switching_circuit_theory" title="Switching circuit theory">Switching circuit theory</a></li>
<li><a href="Gate_equivalent" title="Gate equivalent">Gate equivalent</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;"><a href="Electronics_design" class="mw-redirect" title="Electronics design">Design</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Logic_synthesis" title="Logic synthesis">Logic synthesis</a></li>
<li><a href="Place_and_route" title="Place and route">Place and route</a>
<ul><li><a href="Placement_(electronic_design_automation)" title="Placement (electronic design automation)">Placement</a></li>
<li><a href="Routing_(electronic_design_automation)" title="Routing (electronic design automation)">Routing</a></li></ul></li>
<li><a href="Transaction-level_modeling" title="Transaction-level modeling">Transaction-level modeling</a></li>
<li><a href="Register-transfer_level" title="Register-transfer level">Register-transfer level</a>
<ul><li><a href="Hardware_description_language" title="Hardware description language">Hardware description language</a></li>
<li><a href="High-level_synthesis" title="High-level synthesis">High-level synthesis</a></li></ul></li>
<li><a href="Formal_equivalence_checking" title="Formal equivalence checking">Formal equivalence checking</a></li>
<li><a href="Synchronous_circuit" title="Synchronous circuit">Synchronous logic</a></li>
<li><a href="Asynchronous_circuit" title="Asynchronous circuit">Asynchronous logic</a></li>
<li><a href="Finite-state_machine" title="Finite-state machine">Finite-state machine</a>
<ul><li><a href="Hierarchical_state_machine" class="mw-redirect" title="Hierarchical state machine">Hierarchical state machine</a></li></ul></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;">Applications</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Computer_hardware" title="Computer hardware">Computer hardware</a>
<ul><li><a href="Hardware_acceleration" title="Hardware acceleration">Hardware acceleration</a></li></ul></li>
<li><a href="Digital_audio" title="Digital audio">Digital audio</a>
<ul><li><a href="Digital_radio" title="Digital radio">radio</a></li></ul></li>
<li><a href="Digital_photography" title="Digital photography">Digital photography</a></li>
<li><a href="Telephony#Digital_telephony" title="Telephony">Digital telephone</a></li>
<li><a href="Digital_video" title="Digital video">Digital video</a>
<ul><li><a href="Digital_cinematography" title="Digital cinematography">cinematography</a></li>
<li><a href="Digital_television" title="Digital television">television</a></li></ul></li>
<li><a href="Electronic_literature" title="Electronic literature">Electronic literature</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;text-align:center;">Design issues</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="Metastability_(electronics)" title="Metastability (electronics)">Metastability</a></li>
<li><a href="Runt_pulse" title="Runt pulse">Runt pulse</a></li></ul>
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