Multiplexer

In electronics, a multiplexer (or mux) is a device that selects one of several analog or digital input signals and forwards the selected input into a single line. A multiplexer of 2ⁿ inputs has n select lines, which are used to select which input line to send to the output. Multiplexers are mainly used to increase the amount of data that can be sent over the network within a certain amount of time and bandwidth. A multiplexer is also called a data selector.

An electronic multiplexer makes it possible for several signals to share one device or resource, for example one A/D converter or one communication line, instead of having one device per input signal.

Conversely, a demultiplexer (or demux) is a device taking a single input signal and selecting one of many data-output-lines, which is connected to the single input. A multiplexer is often used with a complementary demultiplexer on the receiving end.

An electronic multiplexer can be considered as a multiple-input, single-output switch, and a demultiplexer as a single-input, multiple-output switch. The schematic symbol for a multiplexer is an isosceles trapezoid with the longer parallel side containing the input pins and the short parallel side containing the output pin. The schematic on the right shows a 2-to-1 multiplexer on the left and an equivalent switch on the right. The wire connects the desired input to the output.

4+1 architectural view model

4+1 is a view model designed by Philippe Kruchten for "describing the architecture of software-intensive systems, based on the use of multiple, concurrent views". The views are used to describe the system from the viewpoint of different stakeholders, such as end-users, developers and project managers. The four views of the model are logical, development, process and physical view. In addition selected use cases or scenarios are used to illustrate the architecture serving as the 'plus one' view. Hence the model contains 4+1 views:

Mathematical fallacy

In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept of mathematical fallacy. There is a distinction between a simple mistake and a mathematical fallacy in a proof: a mistake in a proof leads to an invalid proof just in the same way, but in the best-known examples of mathematical fallacies, there is some concealment in the presentation of the proof. For example, the reason validity fails may be a division by zero that is hidden by algebraic notation. There is a striking quality of the mathematical fallacy: as typically presented, it leads not only to an absurd result, but does so in a crafty or clever way. Therefore, these fallacies, for pedagogic reasons, usually take the form of spurious proofs of obvious contradictions. Although the proofs are flawed, the errors, usually by design, are comparatively subtle, or designed to show that certain steps are conditional, and should not be applied in the cases that are the exceptions to the rules.

Digital electronics

Digital electronics or digital (electronic) circuits are electronics that handle digital signals - discrete bands of analog levels - rather than by continuous ranges (as used in analogue electronics). All levels within a band of values represent the same numeric value. Because of this discretization, relatively small changes to the analog signal levels due to manufacturing tolerance, signal attenuation or parasitic noise do not leave the discrete envelope, and as a result are ignored by signal state sensing circuitry.

In most cases, the number of these states is two, and they are represented by two voltage bands: one near a reference value (typically termed as "ground" or zero volts), and the other a value near the supply voltage. These correspond to the "false" ("0") and "true" ("1") values of the Boolean domain respectively, named after its inventor, George Boole, yielding binary code.

Digital techniques are useful because it is easier to get an electronic device to switch into one of a number of known states than to accurately reproduce a continuous range of values.

Quadraphonic sound

Quadraphonic (or Quadrophonic and sometimes Quadrasonic) sound – similar to what is now called 4.0 surround sound – uses four channels in which speakers are positioned at the four corners of the listening space, reproducing signals that are (wholly or in part) independent of one another. Quadraphonic audio was the earliest consumer product in surround sound and thousands of quadraphonic recordings were made during the 1970s.

It was a commercial failure due to many technical problems and format incompatibilities. Quadraphonic audio formats were more expensive to produce than standard two-channel stereo. Playback required additional speakers and specially designed decoders and amplifiers.

Operation

Quadraphonic audio reproduction on vinyl records was problematic, because some systems were based on discrete sound channels (allowing for full separation of the four original recorded channels, albeit with restricted high-frequency response and reduced record life), while others were matrix encoded into two tracks that would also play back in standard, two-channel, stereo on normal audio equipment (so-called 'compatible' quadraphonic). Also, there were inexpensive "derived" solutions that only provided back ambiance channels, not a defined placement of individual instruments.