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Tseytin Transformation
The Tseytin transformation, alternatively written Tseitin transformation, takes as input an arbitrary combinatorial logic circuit and produces an equisatisfiable boolean formula in conjunctive normal form (CNF). The length of the formula is linear in the size of the circuit. Input vectors that make the circuit output "true" are in 1-to-1 correspondence with assignments that satisfy the formula. This reduces the problem of circuit satisfiability on any circuit (including any formula) to the satisfiability problem on 3-CNF formulas. It was discovered by the Russian scientist Grigori Tseitin. Motivation The naive approach is to write the circuit as a Boolean expression, and use De Morgan's law and the distributive property to convert it to CNF. However, this can result in an exponential increase in equation size. The Tseytin transformation outputs a formula whose size grows linearly relative to the input circuit's. Approach The output equation is the constant 1 set equal to an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinational Logic
In automata theory, combinational logic (also referred to as time-independent logic) is a type of digital logic that 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 combinational logic. Prac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OR ANSI
Or or OR may refer to: Arts and entertainment Film and television * "O.R.", a 1974 episode of ''M*A*S*H'' * ''Or (My Treasure)'', a 2004 movie from Israel (''Or'' means "light" in Hebrew) Music * ''Or'' (album), a 2002 album by Golden Boy with Miss Kittin * ''*O*R'', the original title of Olivia Rodrigo's album ''Sour'', 2021 * "Or", a song by Israeli singer Chen Aharoni in Kdam Eurovision 2011 * Or Records, a record label * Organized Rhyme, a Canadian hip-hop group featuring Tom Green Businesses and organizations * Or (political party) (), Israel * OR Books, an American publisher * Owasco River Railway, Auburn, New York, U.S. (by reporting mark) * TUI fly Netherlands, formerly ''Arke'', a Dutch charter airline (by IATA designator) Language and linguistics * Or (digraph), in the Uzbek alphabet * Or (letter) (or ''forfeda''), in Ogham, the Celtic tree alphabet * Odia language, a language spoken in East India (ISO 639) * Or, an English grammatical conjunction * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Comb Logic Tseitin
A comb is a tool consisting of a shaft that holds a row of teeth for pulling through the hair to clean, untangle, or style it. Combs have been used since prehistoric times, having been discovered in very refined forms from settlements dating back to 5,000 years ago in Persia. Weaving combs made of whalebone dating to the middle and late Iron Age have been found on archaeological digs in Orkney and Somerset. Description Combs are made of a shaft and teeth that are placed at a perpendicular angle to the shaft. Combs can be made out of a number of materials, most commonly plastic, metal, or wood. In antiquity, horn and whalebone was sometimes used. Combs made from ivory and tortoiseshell were once common but concerns for the animals that produce them have reduced their usage. Wooden combs are largely made of boxwood, cherry wood, or other fine-grained wood. Good quality wooden combs are usually handmade and polished. Combs come in various shapes and sizes depending on what they ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
XNOR Gate
The XNOR gate (sometimes ENOR, EXNOR, NXOR, XAND and pronounced as exclusive NOR) is a digital logic gate whose function is the logical complement of the exclusive OR ( XOR) gate. It is equivalent to the logical connective (\leftrightarrow) from mathematical logic, also known as the material biconditional. The two-input version implements logical equality, behaving according to the truth table to the right, and hence the gate is sometimes called an "equivalence gate". A high output (1) results if both of the inputs to the gate are the same. If one but not both inputs are high (1), a low output (0) results. The algebraic notation used to represent the XNOR operation is S = A \odot B. The algebraic expressions (A + \overline) \cdot (\overline + B) and A \cdot B + \overline A \cdot \overline B both represent the XNOR gate with inputs ''A'' and ''B''. Symbols There are two symbols for XNOR gates: one with distinctive shape and one with rectangular shape and label. Both symbols ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
XNOR ANSI
The XNOR gate (sometimes ENOR, EXNOR, NXOR, XAND and pronounced as exclusive NOR) is a digital logic gate whose function is the logical complement of the exclusive OR (XOR) gate. It is equivalent to the logical connective (\leftrightarrow) from mathematical logic, also known as the material biconditional. The two-input version implements logical equality, behaving according to the truth table to the right, and hence the gate is sometimes called an "equivalence gate". A high output (1) results if both of the inputs to the gate are the same. If one but not both inputs are high (1), a low output (0) results. The algebraic notation used to represent the XNOR operation is S = A \odot B. The algebraic expressions (A + \overline) \cdot (\overline + B) and A \cdot B + \overline A \cdot \overline B both represent the XNOR gate with inputs ''A'' and ''B''. Symbols There are two symbols for XNOR gates: one with distinctive shape and one with rectangular shape and label. Both symbols fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
XOR Gate
XOR gate (sometimes EOR, or EXOR and pronounced as Exclusive OR) is a digital logic gate that gives a true (1 or HIGH) output when the number of true inputs is odd. An XOR gate implements an exclusive disjunction, exclusive or (\nleftrightarrow) from mathematical logic; that is, a true output results if one, and only one, of the inputs to the gate is true. If both inputs are false (0/LOW) or both are true, a false output results. XOR represents the inequality function, i.e., the output is true if the inputs are not alike otherwise the output is false. A way to remember XOR is "must have one or the other but not both". An XOR gate may serve as a "programmable inverter" in which one input determines whether to invert the other input, or to simply pass it along with no change. Hence it functions as a Inverter (logic gate), inverter (a NOT gate) which may be activated or deactivated by a switch. XOR can also be viewed as addition Modular arithmetic, modulo 2. As a result, XOR gates ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
XOR ANSI
Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs, XOR is true if and only if the inputs differ (one is true, one is false). With multiple inputs, XOR is true if and only if the number of true inputs is odd. It gains the name "exclusive or" because the meaning of "or" is ambiguous when both operands are true. XOR ''excludes'' that case. Some informal ways of describing XOR are "one or the other but not both", "either one or the other", and "A or B, but not A and B". It is symbolized by the prefix operator J Translated as and by the infix operators XOR (, , or ), EOR, EXOR, \dot, \overline, \underline, , \oplus, \nleftrightarrow, and \not\equiv. Definition The truth table of A\nleftrightarrow B shows that it outputs true whenever the inputs differ: Equivalences, elimination, and introduction Exclusive disjunction essentially mea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NOT Gate
Not or NOT may also refer to: Language * Not, the general declarative form of "no", indicating a negation of a related statement that usually precedes * ... Not!, a grammatical construction used as a contradiction, popularized in the early 1990s Science and technology * Negation, a unary operator in logic depicted as ~, ¬, or ! * Bitwise NOT In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral (considered as a bit string) at the level of its individual bits. It is a fast and simple action, basic to the higher-level arithmetic operatio ..., an operator used in computer programming * NOT gate, a digital logic gate (commonly called an inverter) * Nordic Optical Telescope, an astronomical telescope at Roque de los Muchachos Observatory, La Palma, Canary Islands Other uses * Nottingham railway station (station code NOT) * Polish Federation of Engineering Associations (''Naczelna Organizacja Techniczna'') * Not, Missouri, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NOR Gate
The NOR (NOT OR) gate is a digital logic gate that implements logical NOR - it behaves according to the truth table to the right. A HIGH output (1) results if both the inputs to the gate are LOW (0); if one or both input is HIGH (1), a LOW output (0) results. NOR is the result of the negation of the OR gate, OR operator. It can also in some senses be seen as the inverse of an AND gate. NOR is a functionally complete operation—NOR gates can be combined to generate any other logical function. It shares this property with the NAND gate. By contrast, the Logical disjunction, OR operator is ''monotonic'' as it can only change LOW to HIGH but not vice versa. In most, but not all, circuit implementations, the negation comes for free—including CMOS and Transistor–transistor logic, TTL. In such logic families, OR is the more complicated operation; it may use a NOR followed by a NOT. A significant exception is some forms of the domino logic family. Symbols There are three symbol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OR Gate
The OR gate is a digital logic gate that implements logical disjunction. The OR gate outputs "true" if any of its inputs is "true"; otherwise it outputs "false". The input and output states are normally represented by different voltage levels. Description Any OR gate can be constructed with two or more inputs. It outputs a 1 if any of these inputs are 1, or outputs a 0 only if all inputs are 0. The inputs and outputs are binary digits ("bits") which have two possible truth value, logical states. In addition to 1 and 0, these states may be called true and false, high and low, active and inactive, or other such pairs of symbols. Thus it performs a logical disjunction (∨) from mathematical logic. The gate can be represented with the plus sign (+) because it can be used for Disjunction introduction, logical addition. Equivalently, an OR gate finds the ''maximum'' between two binary digits, just as the AND gate finds the ''minimum''. Together with the AND gate and the NOT gate, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
