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Logic Redundancy
Logic redundancy occurs in a digital gate network containing circuitry that does not affect the static logic function. There are several reasons why logic redundancy may exist. One reason is that it may have been added deliberately to suppress transient glitches (thus causing a race condition) in the output signals by having two or more product terms overlap with a third one. Consider the following equation: : Y = A B + \overline C + B C. The third product term BC is a redundant consensus term. If A switches from 1 to 0 while B = 1 and C = 1, Y remains 1. During the transition of signal A in logic gates, both the first and second term may be 0 momentarily. The third term prevents a glitch since its value of 1 in this case is not affected by the transition of signal A. Another reason for logic redundancy is poor design practices which unintentionally result in logically redundant terms. This causes an unnecessary increase in network complexity, and possibly hampering the abili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic Gate
A logic gate is an idealized or physical device implementing a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, one that has for instance zero rise time and unlimited fan-out, or it may refer to a non-ideal physical device (see Ideal and real op-amps for comparison). Logic gates are primarily implemented using diodes or transistors acting as electronic switches, but can also be constructed using vacuum tubes, electromagnetic relays (relay logic), fluidic logic, pneumatic logic, optics, molecules, or even mechanical elements. Now, most logic gates are made from MOSFETs (metal–oxide–semiconductor field-effect transistors). With amplification, logic gates can be cascaded in the same way that Boolean functions can be composed, allowing the construction of a physical model of all of Boolean logic, and therefore, all of the algorithms and mathem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Race Condition
A race condition or race hazard is the condition of an electronics, software, or other system where the system's substantive behavior is dependent on the sequence or timing of other uncontrollable events. It becomes a bug when one or more of the possible behaviors is undesirable. The term ''race condition'' was already in use by 1954, for example in David A. Huffman's doctoral thesis "The synthesis of sequential switching circuits". Race conditions can occur especially in logic circuits, multithreaded, or distributed Distribution may refer to: Mathematics *Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations *Probability distribution, the probability of a particular value or value range of a varia ... software programs. In electronics A typical example of a race condition may occur when a logic gate combines signals that have traveled along different paths from the same source. The inputs to the gate can chan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Consensus Theorem
In Boolean algebra, the consensus theorem or rule of consensus is the identity: :xy \vee \barz \vee yz = xy \vee \barz The consensus or resolvent of the terms xy and \barz is yz. It is the conjunction of all the unique literals of the terms, excluding the literal that appears unnegated in one term and negated in the other. If y includes a term which is negated in z (or vice versa), the consensus term yz is false; in other words, there is no consensus term. The conjunctive dual of this equation is: :(x \vee y)(\bar \vee z)(y \vee z) = (x \vee y)(\bar \vee z) Proof : \begin xy \vee \barz \vee yz &= xy \vee \barz \vee (x \vee \bar)yz \\ &= xy \vee \barz \vee xyz \vee \baryz \\ &= (xy \vee xyz) \vee (\barz \vee \baryz) \\ &= xy(1\vee z)\vee\barz(1\vee y) \\ &= xy \vee \barz \end Consensus The consensus or consensus term of two conjunctive terms of a disjunction is defined when one term contains the literal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iddq Testing
Iddq testing is a method for testing CMOS integrated circuits for the presence of manufacturing faults. It relies on measuring the supply current (Idd) in the quiescent state (when the circuit is not switching and inputs are held at static values). The current consumed in the state is commonly called Iddq for Idd (quiescent) and hence the name. Iddq testing uses the principle that in a correctly operating quiescent CMOS digital circuit, there is no static current path between the power supply and ground, except for a small amount of leakage. Many common semiconductor manufacturing faults will cause the current to increase by orders of magnitude, which can be easily detected. This has the advantage of checking the chip for many possible faults with one measurement. Another advantage is that it may catch faults that are not found by conventional stuck-at fault test vectors. Iddq testing is somewhat more complex than just measuring the supply current. If a line is shorted to Vdd, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CPU Time
CPU time (or process time) is the amount of time for which a central processing unit (CPU) was used for processing instructions of a computer program or operating system, as opposed to elapsed time, which includes for example, waiting for input/output (I/O) operations or entering low-power (idle) mode. The CPU time is measured in clock ticks or seconds. Often, it is useful to measure CPU time as a percentage of the CPU's capacity, which is called the CPU usage. CPU time and CPU usage have two main uses. The CPU time is used to quantify the overall empirical efficiency of two functionally identical algorithms. For example any sorting algorithm takes an unsorted list and returns a sorted list, and will do so in a deterministic number of steps based for a given input list. However a bubble sort and a merge sort have different running time complexity such that merge sort tends to complete in fewer steps. Without any knowledge of the workings of either algorithm a greater CPU time ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karnaugh Map
The Karnaugh map (KM or K-map) is a method of simplifying Boolean algebra expressions. Maurice Karnaugh introduced it in 1953 as a refinement of Edward W. Veitch's 1952 Veitch chart, which was a rediscovery of Allan Marquand's 1881 ''logical diagram'' aka Marquand diagram but with a focus now set on its utility for switching circuits. Veitch charts are also known as Marquand–Veitch diagrams or, rarely, as Svoboda charts, and Karnaugh maps as Karnaugh–Veitch maps (KV maps). The Karnaugh map reduces the need for extensive calculations by taking advantage of humans' pattern-recognition capability. It also permits the rapid identification and elimination of potential race conditions. The required Boolean results are transferred from a truth table onto a two-dimensional grid where, in Karnaugh maps, the cells are ordered in Gray code, and each cell position represents one combination of input conditions. Cells are also known as minterms, while each cell value represents the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quine–McCluskey Algorithm
The Quine–McCluskey algorithm (QMC), also known as the method of prime implicants, is a method used for minimization of Boolean functions that was developed by Willard V. Quine in 1952 and extended by Edward J. McCluskey in 1956. As a general principle this approach had already been demonstrated by the logician Hugh McColl in 1878, was proved by Archie Blake in 1937, and was rediscovered by Edward W. Samson and Burton E. Mills in 1954 and by Raymond J. Nelson in 1955. Also in 1955, Paul W. Abrahams and John G. Nordahl as well as Albert A. Mullin and Wayne G. Kellner proposed a decimal variant of the method. The Quine–McCluskey algorithm is functionally identical to Karnaugh mapping, but the tabular form makes it more efficient for use in computer algorithms, and it also gives a deterministic way to check that the minimal form of a Boolean function has been reached. It is sometimes referred to as the tabulation method. The method involves two steps: # Finding all prime i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Espresso Heuristic Logic Minimizer
The ESPRESSO logic minimizer is a computer program using heuristic and specific algorithms for efficiently reducing the complexity of digital logic gate circuits. ESPRESSO-I was originally developed at IBM by Robert K. Brayton et al. in 1982. and improved as ESPRESSO-II in 1984. Richard L. Rudell later published the variant ESPRESSO-MV in 1986 and ESPRESSO-EXACT in 1987. Espresso has inspired many derivatives. Introduction Electronic devices are composed of numerous blocks of digital circuits, the combination of which performs the required task. The efficient implementation of logic functions in the form of logic gate circuits (such that no more logic gates are used than are necessary) is necessary to minimize production costs, and/or maximize a device's performance. Designing digital logic circuits All digital systems are composed of two elementary functions: memory elements for storing information, and combinational circuits that transform that information. State machine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-map 6,8,9,10,11,12,13,14 1only
The Karnaugh map (KM or K-map) is a method of simplifying Boolean algebra expressions. Maurice Karnaugh introduced it in 1953 as a refinement of Edward W. Veitch's 1952 Veitch chart, which was a rediscovery of Allan Marquand's 1881 ''logical diagram'' aka Marquand diagram but with a focus now set on its utility for switching circuits. Veitch charts are also known as Marquand–Veitch diagrams or, rarely, as Svoboda charts, and Karnaugh maps as Karnaugh–Veitch maps (KV maps). The Karnaugh map reduces the need for extensive calculations by taking advantage of humans' pattern-recognition capability. It also permits the rapid identification and elimination of potential race conditions. The required Boolean results are transferred from a truth table onto a two-dimensional grid where, in Karnaugh maps, the cells are ordered in Gray code, and each cell position represents one combination of input conditions. Cells are also known as minterms, while each cell value represents the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-map 6,8,9,10,11,12,13,14 Anti-race 1only
The Karnaugh map (KM or K-map) is a method of simplifying Boolean algebra expressions. Maurice Karnaugh introduced it in 1953 as a refinement of Edward W. Veitch's 1952 Veitch chart, which was a rediscovery of Allan Marquand's 1881 ''logical diagram'' aka Marquand diagram but with a focus now set on its utility for switching circuits. Veitch charts are also known as Marquand–Veitch diagrams or, rarely, as Svoboda charts, and Karnaugh maps as Karnaugh–Veitch maps (KV maps). The Karnaugh map reduces the need for extensive calculations by taking advantage of humans' pattern-recognition capability. It also permits the rapid identification and elimination of potential race conditions. The required Boolean results are transferred from a truth table onto a two-dimensional grid where, in Karnaugh maps, the cells are ordered in Gray code, and each cell position represents one combination of input conditions. Cells are also known as minterms, while each cell value represents the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Algebra
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (''and'') denoted as ∧, disjunction (''or'') denoted as ∨, and the negation (''not'') denoted as ¬. Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction and division. So Boolean algebra is a formal way of describing logical operations, in the same way that elementary algebra describes numerical operations. Boolean algebra was introduced by George Boole in his first book ''The Mathematical Analysis of Logic'' (1847), and set forth more fully in his '' An Investigation of the Laws of Thought'' (1854). According to Huntington, the term "Boolean algebra" wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronic Engineering
Electronics engineering is a sub-discipline of electrical engineering which emerged in the early 20th century and is distinguished by the additional use of active components such as semiconductor devices to amplify and control electric current flow. Previously electrical engineering only used passive devices such as mechanical switches, resistors, inductors and capacitors. It covers fields such as: analog electronics, digital electronics, consumer electronics, embedded systems and power electronics. It is also involved in many related fields, for example solid-state physics, radio engineering, telecommunications, control systems, signal processing, systems engineering, computer engineering, instrumentation engineering, electric power control, robotics. The Institute of Electrical and Electronics Engineers (IEEE) is one of the most important professional bodies for electronics engineers in the US; the equivalent body in the UK is the Institution of Engineering and Technology ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
