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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 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 ...
A digital circuit is typically constructed from small electronic circuits called logic gates that can be used to create combinational logic. Each logic gate is designed to perform a function of Boolean logic when acting on logic signals.
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). [1] [2] Alternative names are switching function, used especially in older computer science literature, [3] [4] and truth function (or logical function), used in logic.
In a context of propositional logic, functionally complete sets of connectives are also called (expressively) adequate. [ 3 ] From the point of view of digital electronics , functional completeness means that every possible logic gate can be realized as a network of gates of the types prescribed by the set.
Circuits of this kind provide a generalization of Boolean circuits and a mathematical model for digital logic circuits. Circuits are defined by the gates they contain and the values the gates can produce. For example, the values in a Boolean circuit are Boolean values, and the circuit includes conjunction, disjunction, and negation gates.
Direct-coupled transistor logic (DCTL) is similar to resistor–transistor logic (RTL), but the input transistor bases are connected directly to the collector outputs without any base resistors. Consequently, DCTL gates have fewer components, are more economical, and are simpler to fabricate onto integrated circuits than RTL gates.
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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.