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De Morgan's laws represented with Venn diagrams.In each case, the resultant set is the set of all points in any shade of blue. In propositional logic and Boolean algebra, De Morgan's laws, [1] [2] [3] also known as De Morgan's theorem, [4] are a pair of transformation rules that are both valid rules of inference.
Digitale Schaltungstechnik/ Schaltalgebra/ De Morgan; Usage on es.wikipedia.org Leyes de De Morgan; Usage on fr.wikibooks.org Électronique numérique : logique/Fonctions logiques élémentaires; Usage on hi.wikipedia.org डिमॉर्गन नियम; Usage on hu.wikipedia.org De Morgan-azonosságok; Usage on ro.wikipedia.org Formulele ...
Boolean prime ideal theorem; Compactness theorem; Consensus theorem; De Morgan's laws; Duality (order theory) Laws of classical logic; Peirce's law; Stone's representation theorem for Boolean algebras
De Morgan algebras are important for the study of the mathematical aspects of fuzzy logic. The standard fuzzy algebra F = ([0, 1], max( x , y ), min( x , y ), 0, 1, 1 − x ) is an example of a De Morgan algebra where the laws of excluded middle and noncontradiction do not hold.
The term "Boolean algebra" honors George Boole (1815–1864), a self-educated English mathematician. He introduced the algebraic system initially in a small pamphlet, The Mathematical Analysis of Logic, published in 1847 in response to an ongoing public controversy between Augustus De Morgan and William Hamilton, and later as a more substantial book, The Laws of Thought, published in 1854.
Integrated injection logic (IIL, I 2 L, or I2L) is a class of digital circuits built with multiple collector bipolar junction transistors (BJT). [1] When introduced it had speed comparable to TTL yet was almost as low power as CMOS, making it ideal for use in VLSI (and larger) integrated circuits. The gates can be made smaller with this logic ...
The De Morgan dual is the canonical conjunctive normal form , maxterm canonical form, or Product of Sums (PoS or POS) which is a conjunction (AND) of maxterms. These forms can be useful for the simplification of Boolean functions, which is of great importance in the optimization of Boolean formulas in general and digital circuits in particular.
A CMOS transistor NAND element. V dd denotes positive voltage.. In CMOS logic, if both of the A and B inputs are high, then both the NMOS transistors (bottom half of the diagram) will conduct, neither of the PMOS transistors (top half) will conduct, and a conductive path will be established between the output and Vss (ground), bringing the output low.