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In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. [1] Second-order logic is in turn extended by higher-order logic and type theory . First-order logic quantifies only variables that range over individuals (elements of the domain of discourse ); second-order ...
v. t. e. A truth table is a mathematical table used in logic —specifically in connection with Boolean algebra, Boolean functions, and propositional calculus —which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. [1]
De Morgan's Laws represented as a circuit with logic gates (International Electrotechnical Commission diagrams). In extensions of classical propositional logic, the duality still holds (that is, to any logical operator one can always find its dual), since in the presence of the identities governing negation, one may always introduce an operator ...
An example Karnaugh map. This image actually shows two Karnaugh maps: for the function ƒ, using minterms (colored rectangles) and for its complement, using maxterms (gray rectangles). In the image, E () signifies a sum of minterms, denoted in the article as . The Karnaugh map ( KM or K-map) is a method of simplifying Boolean algebra expressions.
Logic gate. A logic circuit diagram for a 4-bit carry lookahead binary adder design using only the AND, OR, and XOR logic gates. A logic gate is a device that performs a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal ...
For example, a set of reversible gates is called functionally complete, if it can express every reversible operator. The 3-input Fredkin gate is functionally complete reversible gate by itself – a sole sufficient operator. There are many other three-input universal logic gates, such as the Toffoli gate.
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. Connectives can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary connective can be used to join the two atomic formulas and , rendering the complex formula .
AND-OR-invert. AND-OR-Invert. AND-OR-invert (AOI) logic and AOI gates are two-level compound (or complex) logic functions constructed from the combination of one or more AND gates followed by a NOR gate (equivalent to an OR gate through an Inverter gate, which is the "OI" part of "AOI"). Construction of AOI cells is particularly efficient using ...