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Boolean Circuit
In computational complexity theory and circuit complexity, a Boolean circuit is a mathematical model for combinational digital logic circuits. A formal language can be decided by a family of Boolean circuits, one circuit for each possible input length. Boolean circuits are defined in terms of the logic gates they contain. For example, a circuit might contain binary AND and OR gates and unary NOT gates, or be entirely described by binary NAND gates. Each gate corresponds to some Boolean function that takes a fixed number of bits as input and outputs a single bit. Boolean circuits provide a model for many digital components used in computer engineering, including multiplexers, adders, and arithmetic logic units, but they exclude sequential logic. They are an abstraction that omits many aspects relevant to designing real digital logic circuits, such as metastability, fanout, glitches, power consumption, and propagation delay variability. Formal definition In givi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Three Input Boolean Circuit
3 (three) is a number, numeral and digit. It is the natural number following 2 and preceding 4, and is the smallest odd prime number and the only prime preceding a square number. It has religious and cultural significance in many societies. Evolution of the Arabic digit The use of three lines to denote the number 3 occurred in many writing systems, including some (like Roman and Chinese numerals) that are still in use. That was also the original representation of 3 in the Brahmic (Indian) numerical notation, its earliest forms aligned vertically. However, during the Gupta Empire the sign was modified by the addition of a curve on each line. The Nāgarī script rotated the lines clockwise, so they appeared horizontally, and ended each line with a short downward stroke on the right. In cursive script, the three strokes were eventually connected to form a glyph resembling a with an additional stroke at the bottom: ३. The Indian digits spread to the Caliphate in the 9th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adder (electronics)
An adder, or summer, is a digital circuit that performs addition of numbers. In many computers and other kinds of microprocessor, processors, adders are used in the arithmetic logic units (ALUs). They are also used in other parts of the processor, where they are used to calculate address space, addresses, database index, table indices, increment and decrement operators and similar operations. Although adders can be constructed for many number representations, such as binary-coded decimal or excess-3, the most common adders operate on binary numbers. In cases where two's complement or ones' complement is being used to represent negative numbers, it is trivial to modify an adder into an adder–subtractor. Other signed number representations require more logic around the basic adder. History George Stibitz invented the 2-bit binary adder (the Model K (calculator), Model K) in 1937. Binary adders Half adder The half adder adds two single binary digits A and B. It has two outputs, s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Completeness
In Mathematical logic, logic, a functionally complete set of logical connectives or Boolean function, Boolean operators is one that can be used to express all possible truth tables by combining members of the Set (mathematics), set into a Boolean expression.. ("Complete set of logical connectives").. ("[F]unctional completeness of [a] set of logical operators"). A well-known complete set of connectives is . Each of the singleton (mathematics), singleton sets and is functionally complete. However, the set is incomplete, due to its inability to express NOT. A gate (or set of gates) that is functionally complete can also be called a universal gate (or a universal set of gates). In a context of propositional logic, functionally complete sets of connectives are also called (''expressively'') ''adequate''.. (Defines "expressively adequate", shortened to "adequate set of connectives" in a section heading.) From the point of view of digital electronics, functional completeness means t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fan-out
In digital electronics, the fan-out is the number of gate inputs driven by the output of another single logic gate. In most designs, logic gates are connected to form more complex circuits. While no logic gate input can be fed by more than one output at a time without causing contention, it is common for one output to be connected to several inputs. The technology used to implement logic gates usually allows a certain number of gate inputs to be wired directly together without additional interfacing circuitry. The maximum fan-out of an output measures its load-driving capability: it is the greatest number of inputs of gates of the same type to which the output can be safely connected. Logical practice Maximum limits on fan-out are usually stated for a given logic family or device in the manufacturer's datasheets. These limits assume that the driven devices are members of the same family. More complex analysis than fan-in and fan-out is required when two different logic fami ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Expression
In computer science, a Boolean expression (also known as logical expression) is an expression used in programming languages that produces a Boolean value when evaluated. A Boolean value is either true or false. A Boolean expression may be composed of a combination of the Boolean constants True/False or Yes/No, Boolean-typed variables, Boolean-valued operators, and Boolean-valued functions. Boolean expressions correspond to propositional formulas in logic and are associated to Boolean circuits. Boolean operators Most programming languages have the Boolean operators OR, AND and NOT; in C and some languages inspired by it, these are represented by ", , " (double pipe character), "&&" (double ampersand) and "!" ( exclamation point) respectively, while the corresponding bitwise operations are represented by ", ", "&" and "~" (tilde).E.g. for Java see . In the mathematical literature the symbols used are often "+" ( plus), "·" ( dot) and overbar, or "∨" ( vel), "∧" ( et ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Propositional Formula
In propositional logic, a propositional formula is a type of syntactic formula which is well formed. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional formula may also be called a propositional expression, a sentence, or a sentential formula. A propositional formula is constructed from simple propositions, such as "five is greater than three" or propositional variables such as ''p'' and ''q'', using connectives or logical operators such as NOT, AND, OR, or IMPLIES; for example: : (''p'' AND NOT ''q'') IMPLIES (''p'' OR ''q''). In mathematics, a propositional formula is often more briefly referred to as a "proposition", but, more precisely, a propositional formula is not a proposition but a formal expression that ''denotes'' a proposition, a formal object under discussion, just like an expression such as "" is not a value, but denotes a value. In some contexts, maintaining the distinction may be of importanc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Directed Acyclic Graph
In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists of vertices and edges (also called ''arcs''), with each edge directed from one vertex to another, such that following those directions will never form a closed loop. A directed graph is a DAG if and only if it can be topologically ordered, by arranging the vertices as a linear ordering that is consistent with all edge directions. DAGs have numerous scientific and computational applications, ranging from biology (evolution, family trees, epidemiology) to information science (citation networks) to computation (scheduling). Directed acyclic graphs are also called acyclic directed graphs or acyclic digraphs. Definitions A graph is formed by vertices and by edges connecting pairs of vertices, where the vertices can be any kind of object that is connected in pairs by edges. In the case of a directed graph, each edg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heribert Vollmer
Heribert is a Germanic given name, derived from ''hari'' ("host") and '' beraht'' ("bright"). See also Herbert, another given name with the same roots. *Charibert of Laon (died before 762), also spelled Heribert, Count of Laon and maternal grandfather of Charlemagne *Heribert of Cologne (c. 970-1021), saint, Archbishop of Cologne and Chancellor of Holy Roman Emperor Otto III *Heribert Aribert (archbishop of Milan) (died 1045) * Heribert Adam (born 1936), German-born Canadian political scientist and sociologist * Heribert Barrera (1917–2011), Catalan chemist and politician * Heribert Beissel (1933–2021), German orchestra conductor * Heribert Bruchhagen (born 1948), German football player, manager and executive * Heribert Faßbender (born 1941), German sports journalist *Heribert Hirte (born 1958) German legal scholar and politician * Heribert Illig (born 1947), German germanist and author *Herbert von Karajan (1908-1989), Austrian orchestra and opera conductor born Heribert, Ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Propagation Delay
Propagation delay is the time duration taken for a signal to reach its destination, for example in the electromagnetic field, a wire, speed of sound, gas, fluid or seismic wave, solid body. Physics * An electromagnetic wave travelling through a medium has a propagation delay determined by the speed of light in that particular medium, or ca. 1 nanosecond per in a vacuum. * An electric signal travelling through a wire has an propagation delay of ca. 1 nanosecond per . See also radio propagation, velocity factor, signal velocity and mechanical wave. Electronics Logic gates can have a gate delay ranging from picoseconds to more than 10 nanoseconds, depending on the technology being used. It is the time between the gate input becoming stable and the gate output becoming stable. Manufacturers often refer to the time from the input changing to 50% of its final input level, to the output reaching 50% of its final output level; this may depend on the direction of the level cha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Optimization (EDA)
Power optimization is the use of electronic design automation tools to optimize (reduce) the power consumption of a digital design, such as that of an integrated circuit, while preserving the functionality. Introduction and history The increasing speed and complexity of today’s designs implies a significant increase in the power consumption of very-large-scale integration (VLSI) chips. To meet this challenge, researchers have developed many different design techniques to reduce power. The complexity of today’s ICs, with over 100 million transistors, clocked at over 1 GHz, means manual power optimization would be hopelessly slow and all too likely to contain errors. Computer-aided design (CAD) tools and methodologies are mandatory. One of the key features that led to the success of complementary metal-oxide semiconductor, or CMOS, technology was its intrinsic low-power consumption. This meant that circuit designers and electronic design automation (EDA) tools could affo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hazard (logic)
In digital logic, a hazard is an undesirable effect caused by either a deficiency in the system or external influences in both synchronous circuit, synchronous and asynchronous circuits. Logic hazards are manifestations of a problem in which changes in the input variables do not change the output correctly due to some form of delay caused by logic elements (NOT gate, NOT, AND gate, AND, OR gates, etc.) This results in the logic not performing its function properly. The three different most common kinds of hazards are usually referred to as static, dynamic and function hazards. Hazards are a temporary problem, as the logic circuit will eventually settle to the desired function. Therefore, in synchronous designs, it is standard practice to flip-flop (electronics), register the output of a circuit before it is being used in a different clock domain or routed out of the system, so that hazards do not cause any problems. If that is not the case, however, it is imperative that hazard ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fanout
In digital electronics, the fan-out is the number of gate inputs driven by the output of another single logic gate. In most designs, logic gates are connected to form more complex circuits. While no logic gate input can be fed by more than one output at a time without causing contention, it is common for one output to be connected to several inputs. The technology used to implement logic gates usually allows a certain number of gate inputs to be wired directly together without additional interfacing circuitry. The maximum fan-out of an output measures its load-driving capability: it is the greatest number of inputs of gates of the same type to which the output can be safely connected. Logical practice Maximum limits on fan-out are usually stated for a given logic family or device in the manufacturer's datasheets. These limits assume that the driven devices are members of the same family. More complex analysis than fan-in and fan-out is required when two different logic fami ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
