Nonblocking Minimal Spanning Switch
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Nonblocking Minimal Spanning Switch
A nonblocking minimal spanning switch is a device that can connect N inputs to N outputs in any combination. The most familiar use of switches of this type is in a telephone exchange. The term "non-blocking" means that if it is not defective, it can always make the connection. The term "minimal" means that it has the fewest possible components, and therefore the minimal expense. Historically, in telephone switches, connections between callers were arranged with large, expensive banks of electromechanical relays, Strowger switches. The basic mathematical property of Strowger switches is that for each input to the switch, there is exactly one output. Much of the mathematical switching circuit theory attempts to use this property to reduce the total number of switches needed to connect a combination of inputs to a combination of outputs. In the 1940s and 1950s, engineers in Bell Lab began an extended series of mathematical investigations into methods for reducing the size and e ...
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Minimal Spanning Switch 4 4 4
Minimal may refer to: * Minimal (music genre), art music that employs limited or minimal musical materials * "Minimal" (song), 2006 song by Pet Shop Boys * Minimal (supermarket) or miniMAL, a former supermarket chain in Germany and Poland * Minimal (''Dungeons & Dragons''), a creature of magically reduced size in the game ''Dungeons & Dragons'' * Minimal (chocolate), a bean to bar chocolate store in Japan, featured in '' Kantaro: The Sweet Tooth Salaryman'' * Minimal (clothing), an Indonesia clothing-retail company that worked with fashion model Ayu Gani See also * *Minimalism (other) *Maximal (other) *Minimisation (other) *Minimal prime (other) In mathematics, the term minimal prime may refer to *Minimal prime ideal In mathematics, especially in commutative algebra, certain prime ideals called minimal prime ideals play an important role in understanding rings and modules. The notion of ...
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Lockstep (computing)
Lockstep systems are fault-tolerant computer systems that run the same set of operations at the same time in parallel. The redundancy (duplication) allows error detection and error correction: the output from lockstep operations can be compared to determine if there has been a fault if there are at least two systems (dual modular redundancy), and the error can be automatically corrected if there are at least three systems (triple modular redundancy), via majority vote. The term "lockstep" originates from army usage, where it refers to synchronized walking, in which marchers walk as closely together as physically practical. To run in lockstep, each system is set up to progress from one well-defined state to the next well-defined state. When a new set of inputs reaches the system, it processes them, generates new outputs and updates its state. This set of changes (new inputs, new outputs, new state) is considered to define that step, and must be treated as an atomic transaction; in ...
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Recursion
Recursion (adjective: ''recursive'') occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics and computer science, where a function being defined is applied within its own definition. While this apparently defines an infinite number of instances (function values), it is often done in such a way that no infinite loop or infinite chain of references ("crock recursion") can occur. Formal definitions In mathematics and computer science, a class of objects or methods exhibits recursive behavior when it can be defined by two properties: * A simple ''base case'' (or cases) — a terminating scenario that does not use recursion to produce an answer * A ''recursive step'' — a set of rules that reduces all successive cases toward the base case. For example, the following is a recursive definition of a person's ''ancestor''. One's ances ...
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Control Logic
Control logic is a key part of a software program that controls the operations of the program. The control logic responds to commands from the user, and it also acts on its own to perform automated tasks that have been structured into the program. Control logic can be modeled using a state diagram, which is a form of hierarchical state machine. These state diagrams can also be combined with flow charts to provide a set of computational semantics for describing complex control logic. This mix of state diagrams and flow charts A flowchart is a type of diagram that represents a workflow or process. A flowchart can also be defined as a diagrammatic representation of an algorithm, a step-by-step approach to solving a task. The flowchart shows the steps as boxes of v ... is illustrated in the figure on the right, which shows the control logic for a simple stopwatch. The control logic takes in commands from the user, as represented by the event named “START”, but also has a ...
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Telephone Switch
telephone exchange, telephone switch, or central office is a telecommunications system used in the public switched telephone network (PSTN) or in large enterprises. It interconnects telephone subscriber lines or virtual circuits of digital systems to establish telephone calls between subscribers. In historical perspective, telecommunication terms have been used with different semantics over time. The term ''telephone exchange'' is often used synonymously with ''central office'', a Bell System term. Often, a ''central office'' is defined as a building used to house the inside plant equipment of potentially several telephone exchanges, each serving a certain geographical area. Such an area has also been referred to as the exchange or exchange area. In North America, a central office location may also be identified as a ''wire center'', designating a facility to which a telephone is connected and obtains dial tone. For business and billing purposes, telecommunication carriers defin ...
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E-carrier
The E-carrier is a member of the series of carrier systems developed for digital transmission of many simultaneous telephone calls by time-division multiplexing. The European Conference of Postal and Telecommunications Administrations (CEPT) originally standardized the E-carrier system, which revised and improved the earlier American T-carrier technology, and this has now been adopted by the International Telecommunication Union Telecommunication Standardization Sector (ITU-T). It was widely used in almost all countries outside the US, Canada, and Japan. E-carrier deployments have steadily been replaced by Ethernet as telecommunication networks transition towards all IP. E1 frame structure An E1 link operates over two separate sets of wires, usually unshielded twisted pair (balanced cable) or using coaxial (unbalanced cable). A nominal 3 volt peak signal is encoded with pulses using a method avoiding long periods without polarity changes. The line data rate is 2.048 Mbit/s ( ...
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T-carrier
The T-carrier is a member of the series of carrier systems developed by AT&T Bell Laboratories for digital transmission of multiplexed telephone calls. The first version, the Transmission System 1 (T1), was introduced in 1962 in the Bell System, and could transmit up to 24 telephone calls simultaneously over a single transmission line of copper wire. Subsequent specifications carried multiples of the basic T1 (1.544 Mbit/s) data rates, such as T2 (6.312 Mbit/s) with 96 channels, T3 (44.736 Mbit/s) with 672 channels, and others. Although a ''T2'' was defined as part of AT&T's T-carrier system, which defined five levels, T1 through T5, only the T1 and T3 were commonly in use.1999 ad: On the left, in an aisle seat, a man who very much "filled" his airline seat while on the right side of the aisle is a height-challenged man whose shoe toes barely reach the floor Transmission System 1 The T-carrier is a hardware specification for carrying multiple time-division mul ...
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Time-slot Interchange
{{Short description, Network switch storing data in RAM in one sequence A time-slot interchange (TSI) switch is a network switch that stores data in RAM in one sequence, and reads it out in a different sequence. It uses RAM, a small routing memory and a counter. Like any switch, it has input and output ports. The RAM stores the packets or other data that arrive via its input terminal. Mechanism In a pure time-slot interchange switch, there is only one physical input, and one physical output. Each physical connection is an opportunity for a switching fabric to fail. The limited number of connections of this switch is therefore valuable in a large switching fabric, because it makes this type of switching very reliable. The disadvantage of this type of switch is that it introduces delay into the signals. When a packet (or byte, on telephone switches) comes to the input, the switch stores the data in RAM in one sequence, and reads it out in a different sequence. Switch designs ...
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Time-division Multiplexing
Time-division multiplexing (TDM) is a method of transmitting and receiving independent signals over a common signal path by means of synchronized switches at each end of the transmission line so that each signal appears on the line only a fraction of time in an alternating pattern. This method transmits two or more digital signals or analog signals over a common channel. It can be used when the bit rate of the transmission medium exceeds that of the signal to be transmitted. This form of signal multiplexing was developed in telecommunications for telegraphy systems in the late 19th century, but found its most common application in digital telephony in the second half of the 20th century. History Time-division multiplexing was first developed for applications in telegraphy to route multiple transmissions simultaneously over a single transmission line. In the 1870s, Émile Baudot developed a time-multiplexing system of multiple Hughes telegraph machines. In 1944, the Britis ...
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AND Gate
The 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. Symbols 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. Additional inputs can be added as needed. For more information see Logic gate symbols article. It can also be denoted as symbol "^" or "&". The AND gate with inputs ''A'' and ''B'' and output ''C'' implements the logical expression C = A \cdot B. This expression also may be denoted as C=A \wedge B or C=A \And B. Implementations An AND gate can be designed using only N-channel (pictured) or P-channel MOSFETs, but is usually implemented with both (CMOS). ...
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Banyan Switch
In electronics, a banyan switch is a complex crossover switch used in electrical or optical switches. It is named for its resemblance to the roots of the banyan tree which cross over in complex patterns. Logical banyan switches are used in logic or signal pathways to crossover switching of signals onto new pathways. They can be mechanical microelectromechanical systems, electrical or nonlinear optics. Their complexity depends on the topology of the individual switches in a switch matrix (how wide it is by how many 'plies' or layers of switches it takes), to implement a desired crossover logic. Design Typical crossover matrices follow this formula: an N×N banyan switch uses (N/2) log2 N elements. Other formulas are used for differing number of crossover layers, and scaling is possible, but becomes very large and complex with large N×N arrays. CAD can be used to take the drudgery out of creating these designs. A banyan network is implemented by interconnecting 2×2 switching ...
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Crossover Switch
In electronics, a crossover switch or matrix switch is a switch connecting multiple inputs to multiple outputs using complex array matrices designed to switch any one input path to any one (or more) output path(s). There are blocking and non-blocking types of cross-over switches. These switches can be microelectromechanical systems, electrical, or optical non-linear optics, and are used in electronics and fiber optic circuits, as well as some optical computers. A banyan switch is one type of cross-over switch. Their complexity depends on the topology of the individual switches in a switch matrix (how wide it is by how many 'plies' or layers of switches it takes), to implement the desired crossover logic. Formula Typical crossover matrices follow the formula: an N×N Banyan switch uses (N/2) log N elements. Other formulas are used for differing number of cross-over layers, and scaling is possible, but becomes very large and complex with large N×N arrays. CAD and AI can be used to ...
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