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Reconvergent Fan-out
Reconvergent fan-out is a technique to make VLSI logic simulation less pessimistic. Static timing analysis tries to figure out the best and worst case time estimate for each signal as they pass through an electronic device. Whenever a signal passes through a node, a bit of uncertainty must be added to the time required for the signal to transit that device. These uncertain delays add up so, after passing through many devices, the worst-case timing for a signal could be unreasonably pessimistic. It is common for two signals to share an identical path, branch and follow different paths for a while, then converge back to the same point to produce a result. When this happens, you can remove a fair amount of uncertainty from the total delay because you know that they shared a common path for a while. Even though each signal has an uncertain delay, because their delays were identical for part of the journey the total uncertainty can be reduced. This tightens up the worst-case estimat ...
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Very-large-scale Integration
Very large-scale integration (VLSI) is the process of creating an integrated circuit (IC) by combining millions or billions of MOS transistors onto a single chip. VLSI began in the 1970s when MOS integrated circuit (Metal Oxide Semiconductor) chips were developed and then widely adopted, enabling complex semiconductor and telecommunication technologies. The microprocessor and memory chips are VLSI devices. Before the introduction of VLSI technology, most ICs had a limited set of functions they could perform. An electronic circuit might consist of a CPU, ROM, RAM and other glue logic. VLSI enables IC designers to add all of these into one chip. History Background The history of the transistor dates to the 1920s when several inventors attempted devices that were intended to control current in solid-state diodes and convert them into triodes. Success came after World War II, when the use of silicon and germanium crystals as radar detectors led to improvements in fabrication ...
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Logic Simulation
Logic simulation is the use of simulation software to predict the behavior of digital circuits and hardware description languages. Simulation can be performed at varying degrees of physical abstraction, such as at the transistor level, gate level, register-transfer level (RTL), electronic system-level (ESL), or behavioral level. Use in verification Logic simulation may be used as part of the verification process in designing hardware. Simulations have the advantage of providing a familiar look and feel to the user in that it is constructed from the same language and symbols used in design. By allowing the user to interact directly with the design, simulation is a natural way for the designer to get feedback on their design. Length of simulation The level of effort required to debug and then verify the design is proportional to the maturity of the design. That is, early in the design's life, bugs and incorrect behavior are usually found quickly. As the design matures, the simul ...
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Static Timing Analysis
Static timing analysis (STA) is a simulation method of computing the expected timing of a Synchronous circuit, synchronous digital circuit without requiring a simulation of the full circuit. High-performance integrated circuits have traditionally been characterized by the clock frequency at which they operate. Measuring the ability of a circuit to operate at the specified speed requires an ability to measure, during the design process, its delay at numerous steps. Moreover, delay calculation must be incorporated into the inner loop of timing optimizers at various phases of design, such as logic synthesis, layout (Placement (EDA), placement and Routing (EDA), routing), and in in-place optimizations performed late in the design cycle. While such timing measurements can theoretically be performed using a rigorous SPICE, circuit simulation, such an approach is liable to be too slow to be practical. Static timing analysis plays a vital role in facilitating the fast and reasonably ac ...
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Worst Case
In computer science, best, worst, and average cases of a given algorithm express what the resource usage is ''at least'', ''at most'' and ''on average'', respectively. Usually the resource being considered is running time, i.e. time complexity, but could also be memory or some other resource. Best case is the function which performs the minimum number of steps on input data of n elements. Worst case is the function which performs the maximum number of steps on input data of size n. Average case is the function which performs an average number of steps on input data of n elements. In real-time computing, the worst-case execution time is often of particular concern since it is important to know how much time might be needed ''in the worst case'' to guarantee that the algorithm will always finish on time. Average performance and worst-case performance are the most used in algorithm analysis. Less widely found is best-case performance, but it does have uses: for example, where the ...
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Graph Theory
In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are connected by '' edges'' (also called ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a set of vertices (also called nodes or points); * E \subseteq \, a set of edges (also called links or lines), which are unordered pairs of vertices (that is, an edge is associated with t ...
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Static Code Analysis
In computer science, static program analysis (or static analysis) is the analysis of computer programs performed without executing them, in contrast with dynamic program analysis, which is performed on programs during their execution. The term is usually applied to analysis performed by an automated tool, with human analysis typically being called "program understanding", program comprehension, or code review. In the last of these, software inspection and software walkthroughs are also used. In most cases the analysis is performed on some version of a program's source code, and, in other cases, on some form of its object code. Rationale The sophistication of the analysis performed by tools varies from those that only consider the behaviour of individual statements and declarations, to those that include the complete source code of a program in their analysis. The uses of the information obtained from the analysis vary from highlighting possible coding errors (e.g., the lint t ...
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Fan-out
In digital electronics, the fan-out is the number of gate inputs driven by the output of another single logic gate. In most designs, logic gates are connected to form more complex circuits. While no logic gate input can be fed by more than one output at a time without causing contention, it is common for one output to be connected to several inputs. The technology used to implement logic gates usually allows a certain number of gate inputs to be wired directly together without additional interfacing circuitry. The maximum fan-out of an output measures its load-driving capability: it is the greatest number of inputs of gates of the same type to which the output can be safely connected. Logical practice Maximum limits on fan-out are usually stated for a given logic family or device in the manufacturer's datasheets. These limits assume that the driven devices are members of the same family. More complex analysis than fan-in and fan-out is required when two different logic fami ...
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Fan-in
Fan-in is the number of inputs a logic gate can handle. For instance the fan-in for the AND gate shown in the figure is 3. Physical logic gates with a large fan-in tend to be slower than those with a small fan-in. This is because the complexity of the input circuitry increases the input capacitance of the device. Using logic gates with higher fan-in will help in reducing the depth of a logic circuit; this is because circuit design is realized by the target logic family at a digital level, meaning any large fan-in logic gates are simply the smaller fan-in gates chained together in series at a given depth to widen the circuit instead. Fan-in tree of a node refers to a collection of signals that contribute to the input signal of that node. In quantum logic gates the fan-in always has to be equal to the number of outputs, the Fan-out. Gates for which the numbers of inputs and outputs differ would not be reversible (unitary) and are therefore not allowed. See also * Fan-out In d ...
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