Binary Decoder
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Binary Decoder
In digital electronics, a binary decoder is a combinational logic circuit that converts binary information from the n coded inputs to a maximum of 2n unique outputs. They are used in a wide variety of applications, including instruction decoding, data multiplexing and data demultiplexing, seven segment displays, and as address decoders for memory and port-mapped I/O. There are several types of binary decoders, but in all cases a decoder is an electronic circuit with multiple input and multiple output signals, which converts every unique combination of input states to a specific combination of output states. In addition to integer data inputs, some decoders also have one or more "enable" inputs. When the enable input is negated (disabled), all decoder outputs are forced to their inactive states. Depending on its function, a binary decoder will convert binary information from n input signals to as many as 2n unique output signals. Some decoders have less than 2n output lines; in ...
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Digital Electronics
Digital electronics is a field of electronics involving the study of digital signals and the engineering of devices that use or produce them. This is in contrast to analog electronics and analog signals. Digital electronic circuits are usually made from large assemblies of logic gates, often packaged in integrated circuits. Complex devices may have simple electronic representations of Boolean logic functions. History The binary number system was refined by Gottfried Wilhelm Leibniz (published in 1705) and he also established that by using the binary system, the principles of arithmetic and logic could be joined. Digital logic as we know it was the brain-child of George Boole in the mid 19th century. In an 1886 letter, Charles Sanders Peirce described how logical operations could be carried out by electrical switching circuits.Peirce, C. S., "Letter, Peirce to A. Marquand", dated 1886, '' Writings of Charles S. Peirce'', v. 5, 1993, pp. 541–3. GooglPreview See Burks, ...
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Demultiplexer
In electronics, a multiplexer (or mux; spelled sometimes as multiplexor), also known as a data selector, is a device that selects between several analog or digital input signals and forwards the selected input to a single output line. The selection is directed by a separate set of digital inputs known as select lines. A multiplexer of 2^n inputs has n select lines, which are used to select which input line to send to the output. A multiplexer makes it possible for several input signals to share one device or resource, for example, one analog-to-digital converter or one communications transmission medium, instead of having one device per input signal. Multiplexers can also be used to implement Boolean functions of multiple variables. Conversely, a demultiplexer (or demux) is a device taking a single input and selecting signals of the output of the compatible mux, which is connected to the single input, and a shared selection line. A multiplexer is often used with a complementa ...
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Priority Encoder
A priority encoder is a circuit or algorithm that compresses multiple binary inputs into a smaller number of outputs. The output of a priority encoder is the binary representation of the index of the most significant activated line, starting from zero. They are often used to control interrupt requests by acting on the highest priority interrupt input. If two or more inputs are given at the same time, the input having the highest priority will take precedence. An example of a single bit 4 to 2 encoder is shown, where highest-priority inputs are to the left and "x" indicates an irrelevant value - i.e. any input value there yields the same output since it is superseded by higher-priority input. The output V indicates if the input is valid. Priority encoders can be easily connected in arrays to make larger encoders, such as one 16-to-4 encoder made from six 4-to-2 priority encoders - four 4-to-2 encoders having the signal source connected to their inputs, and the two remaining enco ...
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One-hot
In digital circuits and machine learning, a one-hot is a group of bits among which the legal combinations of values are only those with a single high (1) bit and all the others low (0). A similar implementation in which all bits are '1' except one '0' is sometimes called one-cold. In statistics, dummy variables represent a similar technique for representing categorical data. Applications Digital circuitry One-hot encoding is often used for indicating the state of a state machine. When using binary, a decoder is needed to determine the state. A one-hot state machine, however, does not need a decoder as the state machine is in the ''n''th state if, and only if, the ''n''th bit is high. A ring counter with 15 sequentially ordered states is an example of a state machine. A 'one-hot' implementation would have 15 flip flops chained in series with the Q output of each flip flop connected to the D input of the next and the D input of the first flip flop connected to the Q output of t ...
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Multiplexer
In electronics, a multiplexer (or mux; spelled sometimes as multiplexor), also known as a data selector, is a device that selects between several analog or digital input signals and forwards the selected input to a single output line. The selection is directed by a separate set of digital inputs known as select lines. A multiplexer of 2^n inputs has n select lines, which are used to select which input line to send to the output. A multiplexer makes it possible for several input signals to share one device or resource, for example, one analog-to-digital converter or one communications transmission medium, instead of having one device per input signal. Multiplexers can also be used to implement Boolean functions of multiple variables. Conversely, a demultiplexer (or demux) is a device taking a single input and selecting signals of the output of the compatible mux, which is connected to the single input, and a shared selection line. A multiplexer is often used with a complement ...
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Mask (computing)
In computer science, a mask or bitmask is data that is used for bitwise operations, particularly in a bit field. Using a mask, multiple bits in a byte, nibble, word, etc. can be set either on or off, or inverted from on to off (or vice versa) in a single bitwise operation. An additional use of masking involves predication in vector processing, where the bitmask is used to select which element operations in the vector are to be executed (mask bit is enabled) and which are not (mask bit is clear). Common bitmask functions Masking bits to 1 To turn certain bits on, the bitwise OR operation can be used, following the principle that Y OR 1 = 1 and Y OR 0 = Y. Therefore, to make sure a bit is on, OR can be used with a 1. To leave a bit unchanged, OR is used with a 0. Example: Masking ''on'' the higher nibble (bits 4, 5, 6, 7) while leaving the lower nibble (bits 0, 1, 2, 3) unchanged. 10010101 10100101 OR 11110000 11110000 = 11110101 11110101 Masking bits to 0 Mo ...
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Digital-to-analog Converter
In electronics, a digital-to-analog converter (DAC, D/A, D2A, or D-to-A) is a system that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function. There are several DAC architectures; the suitability of a DAC for a particular application is determined by figures of merit including: resolution, maximum sampling frequency and others. Digital-to-analog conversion can degrade a signal, so a DAC should be specified that has insignificant errors in terms of the application. DACs are commonly used in music players to convert digital data streams into analog audio signals. They are also used in televisions and mobile phones to convert digital video data into analog video signals. These two applications use DACs at opposite ends of the frequency/resolution trade-off. The audio DAC is a low-frequency, high-resolution type while the video DAC is a high-frequency low- to medium-resolution type. Due to the complexity a ...
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Unary Coding
Unary coding, or the unary numeral system and also sometimes called thermometer code, is an entropy encoding that represents a natural number, ''n'', with a code of length ''n'' + 1 ( or ''n'' ), usually ''n'' ones followed by a zero (if ''natural number'' is understood as ''non-negative integer'') or with ''n'' − 1 ones followed by a zero (if ''natural number'' is understood as ''strictly positive integer''). For example 5 is represented as 111110 or 11110. Some representations use ''n'' or ''n'' − 1 zeros followed by a one. The ones and zeros are interchangeable without loss of generality. Unary coding is both a prefix-free code and a self-synchronizing code. Unary coding is an optimally efficient encoding for the following discrete probability distribution :\operatorname(n) = 2^\, for n=1,2,3,.... In symbol-by-symbol coding, it is optimal for any geometric distribution :\operatorname(n) = (k-1)k^\, for which ''k'' ≥ φ = 1.6 ...
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4511
The 4000 series is a CMOS logic family of integrated circuits (ICs) first introduced in 1968 by RCA. It had a supply voltage range of 5V to 20V, which is much wider than any contemporary logic family. Almost all IC manufacturers active during this initial era fabricated models for this series. Its naming convention is still in use today. History The 4000 series was introduced as the ''CD4000 COS/MOS'' series in 1968 by RCA as a lower power and more versatile alternative to the 7400 series of transistor-transistor logic (TTL) chips. The logic functions were implemented with the newly introduced Complementary Metal–Oxide–Semiconductor (CMOS) technology. While initially marketed with "COS/MOS" labeling by RCA (which stood for Complementary Symmetry Metal-Oxide Semiconductor), the shorter ''CMOS'' terminology emerged as the industry preference to refer to the technology. The first chips in the series were designed by a group led by Albert Medwin. Wide adoption was initially hi ...
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Seven-segment Display
A seven-segment display is a form of electronic display device for displaying decimal numerals that is an alternative to the more complex dot matrix displays. Seven-segment displays are widely used in digital clocks, electronic meters, basic calculators, and other electronic devices that display numerical information. History Seven-segment representation of figures can be found in patents as early as 1903 (in ), when Carl Kinsley invented a method of telegraphically transmitting letters and numbers and having them printed on tape in a segmented format. In 1908, F. W. Wood invented an 8-segment display, which displayed the number 4 using a diagonal bar (). In 1910, a seven-segment display illuminated by incandescent bulbs was used on a power-plant boiler room signal panel. They were also used to show the dialed telephone number to operators during the transition from manual to automatic telephone dialing. They did not achieve widespread use until the advent of LEDs in the 1970 ...
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Binary-coded Decimal
In computing and electronic systems, binary-coded decimal (BCD) is a class of binary encodings of decimal numbers where each digit is represented by a fixed number of bits, usually four or eight. Sometimes, special bit patterns are used for a sign or other indications (e.g. error or overflow). In byte-oriented systems (i.e. most modern computers), the term ''unpacked'' BCD usually implies a full byte for each digit (often including a sign), whereas ''packed'' BCD typically encodes two digits within a single byte by taking advantage of the fact that four bits are enough to represent the range 0 to 9. The precise 4-bit encoding, however, may vary for technical reasons (e.g. Excess-3). The ten states representing a BCD digit are sometimes called '' tetrades'' (for the nibble typically needed to hold them is also known as a tetrade) while the unused, don't care-states are named , ''pseudo-decimals'' or ''pseudo-decimal digits''. BCD's main virtue, in comparison to binary posit ...
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Combinational Logic
In automata theory, combinational logic (also referred to as time-independent logic or combinatorial logic) is a type of digital logic which is implemented by Boolean circuits, where the output is a pure function of the present input only. This is in contrast to sequential logic, in which the output depends not only on the present input but also on the history of the input. In other words, sequential logic has ''memory'' while combinational logic does not. Combinational logic is used in computer circuits to perform Boolean algebra on input signals and on stored data. Practical computer circuits normally contain a mixture of combinational and sequential logic. For example, the part of an arithmetic logic unit, or ALU, that does mathematical calculations is constructed using combinational logic. Other circuits used in computers, such as half adders, full adders, half subtractors, full subtractors, multiplexers, demultiplexers, encoders and decoders are also made by using combin ...
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