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A truth table is a structured representation that presents all possible combinations of truth values for the input variables of a Boolean function and their corresponding output values. A function f from A to F is a special relation, a subset of A×F, which simply means that f can be listed as a list of input-output pairs.
In the image, E () signifies a sum of minterms, denoted in the article as . The Karnaugh (/ˈkɑːnɔː/) map ( KM or K-map) is a method of simplifying Boolean algebra expressions. Maurice Karnaugh introduced it in 1953 [1] [2] as a refinement of Edward W. Veitch 's 1952 Veitch chart, [3] [4] which itself was a rediscovery of Allan Marquand 's ...
With Logic Friday users can enter a logic function as a truth table, equation, or gate diagram, minimize the function, and then view the results in both of the other two representations. The last release was version 1.1.4 dated 2012. Minilog. Minilog is a free Windows program that provides logic minimization exploiting this Espresso algorithm
The column-11 operator (IF/THEN), shows Modus ponens rule: when p→q=T and p=T only one line of the truth table (the first) satisfies these two conditions. On this line, q is also true. Therefore, whenever p → q is true and p is true, q must also be true.
Binary decision diagram. In computer science, a binary decision diagram ( BDD) or branching program is a data structure that is used to represent a Boolean function. On a more abstract level, BDDs can be considered as a compressed representation of sets or relations. Unlike other compressed representations, operations are performed directly on ...
In computability theory a truth-table reduction is a type of reduction from a decision problem to a decision problem . To solve a problem in , the reduction describes the answer to as a boolean formula or truth table of some finite number of queries to . Truth-table reductions are related to Turing reductions, and strictly weaker.
In digital logic, a don't-care term (abbreviated DC, historically also known as redundancies, irrelevancies, optional entries, invalid combinations, vacuous combinations, forbidden combinations, unused states or logical remainders) for a function is an input-sequence (a series of bits) for which the function output does not matter.
Universal generalization / instantiation. Existential generalization / instantiation. In propositional logic, material implication [1] [2] is a valid rule of replacement that allows a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that P implies Q is logically equivalent to not- or and ...