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In mathematics and abstract algebra, a Boolean domain is a set consisting of exactly two elements whose interpretations include false and true. In logic, mathematics andtheoretical computer science, a Boolean domain is usually written as {0, 1},[1][2][3] {false, true}, {F, T},[4] or .[5]

The algebraic structure that naturally builds on a Boolean domain is the Boolean algebra with two elements. The initial object in the category of bounded lattices is a Boolean domain.

In computer science, a Boolean variable is a variable that takes values in some Boolean domain. Some programming languages feature reserved words or symbols for the elements of the Boolean domain, for example false and true. However, many programming languages do not have a Boolean datatype in the strict sense. In C or BASIC, for example, falsity is represented by the number 0 and truth is represented by the number 1 or −1 respectively, and all variables that can take these values can also take any other numerical values.

Boolean function

From Wikipedia, the free encyclopedia

Not to be confused with Binary function.

This article includes a list of references, related reading or external links, but its sources remain unclear because it lacksinline citations. Please improve this article by introducing more precise citations. (October 2012)

In mathematics, a (finitary) Boolean function (or switching function) is a function of the form ƒ : Bk → B, where B = {0, 1} is a Boolean domain and k is a non-negative integer called the arity of the function. In the case where k = 0, the "function" is essentially a constant element of B.

Every k-ary Boolean function can be expressed as a propositional formula in k variables x1, …, xk, and two propositional formulas are logically equivalent if and only if they express the same Boolean function. There are 22k k-ary functions for every k.

Boolean functions in applications[edit]

A Boolean function describes how to determine a Boolean value output based on some logical calculation from Boolean inputs. Such functions play a basic role in questions ofcomplexity theory as well as the design of circuits and chips for digital computers. The properties of Boolean functions play a critical role in cryptography, particularly in the design of symmetric key algorithms (see substitution box).

Boolean functions are often represented by sentences in propositional logic, and sometimes as multivariate polynomials over GF(2), but more efficient representations are binary decision diagrams (BDD), negation normal forms, and propositional directed acyclic graphs (PDAG).

In cooperative game theory, monotone Boolean functions are called simple games (voting games); this notion is applied to solve problems in social choice theory.

See also[edit]

Noise (electronics)

From Wikipedia, the free encyclopedia

This article is about fundamental noise processes. For noise arising from outside sources, see electromagnetic compatibility and electromagnetic interference.

Analog display of random fluctuations in voltage: e.g., pink noise.

In electronics, noise is a random fluctuation in an electrical signal, a characteristic of all electronic circuits.[1] Noise generated by electronic devices varies greatly, as it can be produced by several different effects. Thermal noise is unavoidable at non-zero temperature (seefluctuation-dissipation theorem), while other types depend mostly on device type (such as shot noise,[1][2] which needs steep potential barrier) or manufacturing quality and semiconductor defects, such as conductance fluctuations, including 1/f noise.

In communication systems, noise is an error or undesired random disturbance of a useful information signal in a communication channel. The noise is a summation of unwanted or disturbing energy from natural and sometimes man-made sources. Noise is, however, typically distinguished from interference, (e.g. cross-talk, deliberate jamming or other unwanted electromagnetic interference from specific transmitters), for example in the signal-to-noise ratio (SNR), signal-to-interference ratio (SIR) and signal-to-noise plus interference ratio(SNIR) measures. Noise is also typically distinguished from distortion, which is an unwanted systematic alteration of the signal waveform by the communication equipment, for example in the signal-to-noise and distortion ratio (SINAD). In a carrier-modulated passband analog communication system, a certain carrier-to-noise ratio (CNR) at the radio receiver input would result in a certain signal-to-noise ratio in the detected message signal. In a digital c

Signal chain

From Wikipedia, the free encyclopedia

Signal chain, or signal-processing chain is a term used in signal processing[1] and mixed-signal[2] system design to describe a series of signal-conditioning electronic components that receive input (data acquired from sampling either real-time phenomena or from stored data) in tandem, with the output of one portion of the chain supplying input to the next. Signal chains are often used in signal processing applications to gather and process data or to apply system controls based on analysis of real-time phenomena.

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linearity

Part of the Computing fundamentals glossary:

Linearity is the behavior of a circuit, particularly an amplifier , in which the output signalstrength varies in direct proportion to the input signal strength. In a linear device, the output-to-input signal amplitude ratio is always the same, no matter what the strength of the input signal (as long it is not too strong).

Heat sink

From Wikipedia, the free encyclopedia

This article is about components used to cool semiconductors. For other uses, see Heat sink (disambiguation).

A fan-cooled heat sink on the processor of a personal computer.

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