Boolean logic in the context of "George Boole"

Digital electronics is a field of electronics involving the study of digital signals and the engineering of devices that use or produce them. It deals with the relationship between binary inputs and outputs by passing electrical signals through logical gates, resistors, capacitors, amplifiers, and other electronic components. The field of digital electronics is in contrast to analog electronics, which work primarily with analog signals (signals with varying degrees of intensity as opposed to on/off two-state binary signals). Despite the name, digital electronics designs include important analog design considerations.

Large assemblies of logic gates, used to represent more complex ideas, are often packaged into integrated circuits. Complex devices may have simple electronic representations of Boolean logic functions.

In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) asks whether there exists an interpretation that satisfies a given Boolean formula. In other words, it asks whether the formula's variables can be consistently replaced by the values TRUE or FALSE to make the formula evaluate to TRUE. If this is the case, the formula is called satisfiable, else unsatisfiable. For example, the formula "a AND NOT b" is satisfiable because one can find the values a = TRUE and b = FALSE, which make (a AND NOT b) = TRUE. In contrast, "a AND NOT a" is unsatisfiable.

SAT is the first problem that was proven to be NP-complete—this is the Cook–Levin theorem. This means that all problems in the complexity class NP, which includes a wide range of natural decision and optimization problems, are at most as difficult to solve as SAT. There is no known algorithm that efficiently solves each SAT problem (where "efficiently" means "deterministically in polynomial time"). Although such an algorithm is generally believed not to exist, this belief has not been proven or disproven mathematically. Resolving the question of whether SAT has a polynomial-time algorithm would settle the P versus NP problem - one of the most important open problems in the theory of computing.

A union catalog is a combined library catalog describing the collections of a number of libraries. Union catalogs have been created in a range of media, including book format, microform, cards and more recently, networked electronic databases. Print union catalogs are typically arranged by title, author or subject (often employing a controlled vocabulary); electronic versions typically support keyword and Boolean queries. Union catalogs are useful to librarians, as they assist in locating and requesting materials from other libraries through interlibrary loan service. They also allow researchers to search through collections to which they would not otherwise have access, such as manuscript collections.

The largest union catalog ever printed is the American National Union Catalog Pre-1956 Imprints (NUC), completed in 1981. This achievement has since been superseded by the creation of union catalogs in the form of electronic databases, of which the largest is OCLC's WorldCat. Other examples include K10plus in Germany, Library Hub Discover (formerly COPAC) provided by Research Libraries UK and AMICUS, provided by Library and Archives Canada.

In 3D computer graphics and solid modeling, a polygon mesh is a collection of vertices, edges and faces that defines the shape of a polyhedral object's surface. It simplifies rendering, as in a wire-frame model. The faces usually consist of triangles (triangle mesh), quadrilaterals (quads), or other simple convex polygons (n-gons). A polygonal mesh may also be more generally composed of concave polygons, or even polygons with holes.

The study of polygon meshes is a large sub-field of computer graphics (specifically 3D computer graphics) and geometric modeling. Different representations of polygon meshes are used for different applications and goals. The variety of operations performed on meshes includes Boolean logic (Constructive solid geometry), smoothing, and simplification. Algorithms also exist for ray tracing, collision detection, and rigid-body dynamics with polygon meshes. If the mesh's edges are rendered instead of the faces, then the model becomes a wireframe model.

Integrated circuit design, semiconductor design, chip design or IC design, is a sub-field of electronics engineering, encompassing the particular logic and circuit design techniques required to design integrated circuits (ICs). An IC consists of miniaturized electronic components built into an electrical network on a monolithic semiconductor substrate by photolithography.

IC design can be divided into the broad categories of digital and analog IC design. Digital IC design is to produce components such as microprocessors, FPGAs, memories (RAM, ROM, and flash) and digital ASICs. Digital design focuses on logical correctness, maximizing circuit density, and placing circuits so that clock and timing signals are routed efficiently. Analog IC design also has specializations in power IC design and RF IC design. Analog IC design is used in the design of op-amps, linear regulators, phase locked loops, oscillators and active filters. Analog design is more concerned with the physics of the semiconductor devices such as gain, matching, power dissipation, and resistance. Fidelity of analog signal amplification and filtering is usually critical, and as a result analog ICs use larger area active devices than digital designs and are usually less dense in circuitry.