Logical equality is a logical operator that corresponds to equality in Boolean algebra and to the logical biconditional in propositional calculus. It gives the functional value true if both functional arguments have the same logical value, and false if they are different.
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- Logical equality is a logical operator that corresponds to equality in Boolean algebra and to the logical biconditional in propositional calculus. It gives the functional value true if both functional arguments have the same logical value, and false if they are different. It is customary practice in various applications, if not always technically precise, to indicate the operation of logical equality on the logical operands x and y by any of the following forms: <math>\begin{matrix} x \leftrightarrow y & \quad & \quad & x \Leftrightarrow y \\ x \ \mbox{EQ} \ y & \quad & \quad & x = y \end{matrix}</math> Some logicians, however, draw a firm distinction between a functional form, like those in the lefthand column, which they interpret as an application of a function to a pair of arguments — and thus a mere indication that the value of the compound expression depends on the values of the component expressions — and an equational form, like those in the righthand column, which they interpret as an assertion that the arguments have equal values, in other words, that the functional value of the compound expression is true. In mathematics, the plus sign "+" almost invariably indicates an operation that satisfies the axioms assigned to addition in the type of algebraic structure that is known as a field. For boolean algebra, this means that the logical operation signified by "+" is not the same as the inclusive disjunction signified by "∨" but is actually equivalent to the logical inequality operator signified by "≠", or what amounts to the same thing, the exclusive disjunction signified by "XOR". Naturally, these variations in usage have caused some failures to communicate between mathematicians and switching engineers over the years. At any rate, one has the following array of corresponding forms for the symbols associated with logical inequality: <math>\begin{matrix} x + y & \quad & \quad & x \not\equiv y \\ x \ \mbox{XOR} \ y & \quad & \quad & x \ne y \end{matrix}</math> This explains why "EQ" is often called "XNOR" in the combinational logic of circuit engineers, since it is the Negation of the XOR operation. Another rationalization of the admittedly circuitous name "XNOR" is that one begins with the "both false" operator NOR and then adds the eXception, "or both true".
- Ein XNOR-Gatter (engl. eXclusive NOT OR) ist ein Gatter, bei dem am Ausgang genau dann eine logische "1" anliegt, wenn an einer geraden Anzahl von Eingängen "1" anliegt und an den restlichen "0". Im Fall von zwei Eingängen liegt am Ausgang also genau dann "1" an, wenn an beiden Eingängen "1" oder an beiden Eingängen "0" anliegt (im zweiten Fall liegt an null Eingängen "1" an, und 0 zählt als gerade Zahl). Die XNOR-Verknüpfung wird auch als Äquivalenz, Biimplikation oder Bikonditional bezeichnet.
- De XNOR-poort is een digitale elektronische schakeling. De poort bezit twee of meer ingangen en 1 uitgang. De logische toestand van de uitgang is uitsluitend 0, als precies één ingang 1 is. De bepaling exclusief heeft betrekking op het wederzijds uitsluitende karakter van de ingangen voor de functie.
- Bramka XNOR - bramka logiczna realizująca funkcję negacji alternatywy wykluczającej (tzw. Bramka Równoważności). Bramka ta neguje wynik bramki XOR czyli zwraca fałsz (0), jeśli dokładnie jedno z wejść: A lub B jest prawdą (1), a w przeciwnym wypadku zwraca prawdę. Innymi słowy bramka XNOR dopuszcza pojawienie się dwóch takich samych sygnałów na wejściu.
- XNOR-grind är en inverterad xor-grind. Det betyder att den gör precis tvärtom mot en xor-grind. <math>Y=\overline{A\oplus B}</math>
- XNOR / NXOR Kapısı, XOR kapısının sonucunun tersini üretir. Sadece bir girişi 1 olduğunda 0 cevabı verir; diğer tüm durumlarda ise 1 cevabını verir. XNOR Kapısının doğruluk tablosu:
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- XNOR gate
- the corresponding concept in combinational logic
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- Logical equality is a logical operator that corresponds to equality in Boolean algebra and to the logical biconditional in propositional calculus. It gives the functional value true if both functional arguments have the same logical value, and false if they are different.
- Ein XNOR-Gatter (engl. eXclusive NOT OR) ist ein Gatter, bei dem am Ausgang genau dann eine logische "1" anliegt, wenn an einer geraden Anzahl von Eingängen "1" anliegt und an den restlichen "0". Im Fall von zwei Eingängen liegt am Ausgang also genau dann "1" an, wenn an beiden Eingängen "1" oder an beiden Eingängen "0" anliegt (im zweiten Fall liegt an null Eingängen "1" an, und 0 zählt als gerade Zahl).
- De XNOR-poort is een digitale elektronische schakeling. De poort bezit twee of meer ingangen en 1 uitgang. De logische toestand van de uitgang is uitsluitend 0, als precies één ingang 1 is. De bepaling exclusief heeft betrekking op het wederzijds uitsluitende karakter van de ingangen voor de functie.
- Bramka XNOR - bramka logiczna realizująca funkcję negacji alternatywy wykluczającej (tzw. Bramka Równoważności). Bramka ta neguje wynik bramki XOR czyli zwraca fałsz (0), jeśli dokładnie jedno z wejść: A lub B jest prawdą (1), a w przeciwnym wypadku zwraca prawdę. Innymi słowy bramka XNOR dopuszcza pojawienie się dwóch takich samych sygnałów na wejściu.
- XNOR-grind är en inverterad xor-grind. Det betyder att den gör precis tvärtom mot en xor-grind. <math>Y=\overline{A\oplus B}</math>
- XNOR / NXOR Kapısı, XOR kapısının sonucunun tersini üretir. Sadece bir girişi 1 olduğunda 0 cevabı verir; diğer tüm durumlarda ise 1 cevabını verir. XNOR Kapısının doğruluk tablosu:
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- Logical equality
- XNOR-Gatter
- XNOR-poort
- XNOR
- XNOR
- XNOR kapısı
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