Truth functionIn logic, a truth function is a function that accepts truth values as input and produces a unique truth value as output. In other words: The input and output of a truth function are all truth values; a truth function will always output exactly one truth value; and inputting the same truth value(s) will always output the same truth value.
Canonical normal formIn Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form (CDNF) or minterm canonical form, and its dual, the canonical conjunctive normal form (CCNF) or maxterm canonical form. Other canonical forms include the complete sum of prime implicants or Blake canonical form (and its dual), and the algebraic normal form (also called Zhegalkin or Reed–Muller). Minterms are called products because they are the logical AND of a set of variables, and maxterms are called sums because they are the logical OR of a set of variables.
Logic optimizationLogic optimization is a process of finding an equivalent representation of the specified logic circuit under one or more specified constraints. This process is a part of a logic synthesis applied in digital electronics and integrated circuit design. Generally, the circuit is constrained to a minimum chip area meeting a predefined response delay. The goal of logic optimization of a given circuit is to obtain the smallest logic circuit that evaluates to the same values as the original one.
XNOR gateThe XNOR gate (sometimes ENOR, EXNOR or NXOR and pronounced as Exclusive NOR) is a digital logic gate whose function is the logical complement of the Exclusive OR (XOR) gate. It is equivalent to the logical connective () from mathematical logic, also known as the material biconditional. The two-input version implements logical equality, behaving according to the truth table to the right, and hence the gate is sometimes called an "equivalence gate". A high output (1) results if both of the inputs to the gate are the same.
Karnaugh mapThe Karnaugh map (KM or K-map) is a method of simplifying Boolean algebra expressions. Maurice Karnaugh introduced it in 1953 as a refinement of Edward W. Veitch's 1952 Veitch chart, which was a rediscovery of Allan Marquand's 1881 logical diagram aka Marquand diagram but with a focus now set on its utility for switching circuits. Veitch charts are also known as Marquand–Veitch diagrams or, rarely, as Svoboda charts, and Karnaugh maps as Karnaugh–Veitch maps (KV maps).
NAND gateIn digital electronics, a NAND gate (NOT-AND) is a logic gate which produces an output which is false only if all its inputs are true; thus its output is complement to that of an AND gate. A LOW (0) output results only if all the inputs to the gate are HIGH (1); if any input is LOW (0), a HIGH (1) output results. A NAND gate is made using transistors and junction diodes. By De Morgan's laws, a two-input NAND gate's logic may be expressed as =+, making a NAND gate equivalent to inverters followed by an OR gate.
XOR gateXOR gate (sometimes EOR, or EXOR and pronounced as Exclusive OR) is a digital logic gate that gives a true (1 or HIGH) output when the number of true inputs is odd. An XOR gate implements an exclusive or () from mathematical logic; that is, a true output results if one, and only one, of the inputs to the gate is true. If both inputs are false (0/LOW) or both are true, a false output results. XOR represents the inequality function, i.e., the output is true if the inputs are not alike otherwise the output is false.
Logic gateA logic gate is an idealized or physical 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 logic gate, one that has, for instance, zero rise time and unlimited fan-out, or it may refer to a non-ideal physical device (see ideal and real op-amps for comparison). In the real world, the primary way of building logic gates uses diodes or transistors acting as electronic switches.
TruthTruth is the property of being in accord with fact or reality. In everyday language, truth is typically ascribed to things that aim to represent reality or otherwise correspond to it, such as beliefs, propositions, and declarative sentences. Truth is usually held to be the opposite of falsehood. The concept of truth is discussed and debated in various contexts, including philosophy, art, theology, law, and science. Most human activities depend upon the concept, where its nature as a concept is assumed rather than being a subject of discussion, including journalism and everyday life.
AND gateThe AND gate is a basic digital logic gate that implements logical conjunction (∧) from mathematical logic - AND gate behaves according to the truth table. A HIGH output (1) results only if all the inputs to the AND gate are HIGH (1). If not all inputs to the AND gate are HIGH, LOW output results. The function can be extended to any number of inputs. There are three symbols for AND gates: the American (ANSI or 'military') symbol and the IEC ('European' or 'rectangular') symbol, as well as the deprecated DIN symbol.
NOR gateThe NOR gate is a digital logic gate that implements logical NOR - it behaves according to the truth table to the right. A HIGH output (1) results if both the inputs to the gate are LOW (0); if one or both input is HIGH (1), a LOW output (0) results. NOR is the result of the negation of the OR operator. It can also in some senses be seen as the inverse of an AND gate. 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.
OR gateThe OR gate is a digital logic gate that implements logical disjunction. The OR gate returns true if any of its inputs are true; otherwise it returns false. The input and output states are normally represented by different voltage levels. Any OR gate can be constructed with two or more inputs. It outputs a 1 if any of these inputs are 1, or outputs a 0 only if all inputs are 0. The inputs and outputs are binary digits ("bits") which have two possible logical states.
Logical truthLogical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. In other words, a logical truth is a statement which is not only true, but one which is true under all interpretations of its logical components (other than its logical constants). Thus, logical truths such as "if p, then p" can be considered tautologies.
Espresso heuristic logic minimizerThe ESPRESSO logic minimizer is a computer program using heuristic and specific algorithms for efficiently reducing the complexity of digital logic gate circuits. ESPRESSO-I was originally developed at IBM by Robert K. Brayton et al. in 1982. and improved as ESPRESSO-II in 1984. Richard L. Rudell later published the variant ESPRESSO-MV in 1986 and ESPRESSO-EXACT in 1987. Espresso has inspired many derivatives. Electronic devices are composed of numerous blocks of digital circuits, the combination of which performs the required task.
Boolean circuitIn computational complexity theory and circuit complexity, a Boolean circuit is a mathematical model for combinational digital logic circuits. A formal language can be decided by a family of Boolean circuits, one circuit for each possible input length. Boolean circuits are defined in terms of the logic gates they contain. For example, a circuit might contain binary AND and OR gates and unary NOT gates, or be entirely described by binary NAND gates. Each gate corresponds to some Boolean function that takes a fixed number of bits as input and outputs a single bit.
Boolean algebraIn mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (and) denoted as ∧, disjunction (or) denoted as ∨, and the negation (not) denoted as ¬.
Circuit designThe process of circuit design can cover systems ranging from complex electronic systems down to the individual transistors within an integrated circuit. One person can often do the design process without needing a planned or structured design process for simple circuits. Still, teams of designers following a systematic approach with intelligently guided computer simulation are becoming increasingly common for more complex designs.
Integrated circuitAn integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set of electronic circuits on one small flat piece (or "chip") of semiconductor material, usually silicon. Large numbers of miniaturized transistors and other electronic components are integrated together on the chip. This results in circuits that are orders of magnitude smaller, faster, and less expensive than those constructed of discrete components, allowing a large transistor count.
Fuzzy logicFuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1. The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by Iranian Azerbaijani mathematician Lotfi Zadeh.
Electronic circuitAn electronic circuit is composed of individual electronic components, such as resistors, transistors, capacitors, inductors and diodes, connected by conductive wires or traces through which electric current can flow. It is a type of electrical circuit and to be referred to as electronic, rather than electrical, generally at least one active component must be present. The combination of components and wires allows various simple and complex operations to be performed: signals can be amplified, computations can be performed, and data can be moved from one place to another.
