The increasing speed and complexity of today’s designs implies a significant increase in the power consumption of very-large-scale integration (VLSI) chips. To meet this challenge, researchers have developed many different design techniques to reduce power. The complexity of today’s ICs, with over 100 million transistors, clocked at over 1 GHz, means manual power optimization would be hopelessly slow all too likely to contain errors. ...

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Power optimization EDA, Power optimization EDA - Introduction and history, Power optimization EDA - Power Analysis of CMOS circuits, Power optimization EDA - Circuit-Level Power Optimization, Power optimization EDA - Logic Synthesis for Low Power

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The power consumption of digital CMOS circuits is generally considered in terms of three components: The dynamic power component, related to the charging and discharging of the load capacitance at the gate output. The short-circuit power component. During the transition of the input line from one voltage level to the other, there is a period of time when both the PMOS and the NMOS transistors are on, thus creating a path from VDD to ground. The static power component, due ...

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Power optimization EDA, Power optimization EDA - Introduction and history, Power optimization EDA - Power Analysis of CMOS circuits, Power optimization EDA - Circuit-Level Power Optimization, Power optimization EDA - Logic Synthesis for Low Power

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Peirce's law can be very confusing, especially if you're new to logic, so let's make it a little more concrete with an example. Unfortunately for us, we have been drafted into the navy. Life at sea is no fun, but at least the lunch line serves pears. We like pears, so we're glad that they're served often. The navy has a very odd custom. Sometimes when we go through a line, every pear is glued to a kiwi. We call these "glue lines". The custom says that every glue line must have pears. Customs often have the force of laws, and this cust ...

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Peirce's law, Peirce's law - History, Peirce's law - Proof of Peirce's law, Peirce's law - Peirce's law explained for non-mathematicians

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Popular perceptions of randomness are frequently wrong, based on logical fallacies. Following is an attempt to identify the source of such fallacies and correct the logical errors. For a more detailed discussion, see Gambler's Fallacy. Randomness - A number is due. This argument says that "since all numbers will eventually come up in a random selection, those that have not come up yet are 'due' and thus more likely to come up soon". This logic is only correct if applied to a system where numbers that come ...

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Randomness, Randomness - History, Randomness - Randomness versus unpredictability, Randomness - Misconceptions/logical fallacies, Randomness - A number is due, Randomness - A number is cursed, Randomness - Study of randomness, Randomness - In philosophy, Randomness - In biology, Randomness - In the natural sciences, Randomness - Source of randomness, Randomness - In mathematics, Randomness - In communication theory, Randomness - In finance, Randomness - Applications and use of randomness, Randomness - Generating randomness, Randomness - Quotations, Randomness - Books

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History of computer science - The theoretical groundwork. The mathematical foundations of modern computer science began to be laid by Kurt Gödel with his incompleteness theorem (1931). In this theorem, he showed that there were limits to what could be proved and disproved within a formal system. This led to work by Gödel and others to define and describe these formal systems, introdu ...

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History of computer science, History of computer science - Early history, History of computer science - Early computing, History of computer science - Binary logic, History of computer science - The Analytical Engine, History of computer science - Emergence of a discipline, History of computer science - The theoretical groundwork, History of computer science - Shannon and Information Theory

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Logical conditional statements are not statements of causality. Since logical conditional statements and causal statements are both presented using "If...then..." in English they are commonly confused; they are distinct, however. The standard conditional statement expresses a fact about the actual world, while causal statements imply something more. For example all of the following statements are true (interpreting "If... then..." as the logical conditional): If George Bush was president of the United States in 2004, t ...

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Causality, Causality - Causation in the history of philosophy, Causality - Aristotle, Causality - Hume, Causality - Spinoza, Causality - Causality determinism and existentialism, Causality - Necessary and sufficient causes, Causality - Causality contrasted with logical implication, Causality - Counterfactual theories of causation, Causality - Probabilistic causation, Causality - Derivation theories, Causality - Manipulation theories, Causality - Process theories, Causality - Causality in psychology, Causality - Attribution, Causality - Causation and salience, Causality - Symbolism and causality, Causality - Causation in religion and theology, Causality - Cosmological argument, Causality - Karma, Causality - Reversed causality, Causality - Causality in science and the humanities, Causality - Physics, Causality - Engineering, Causality - History, Causality - Causality in law

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However, computer memories were very small by current standards because they were expensive, being made of iron ferrite cores at that time. So Planner adopted the then common expedient of using backtracking control structures to economize on the use of computer memory. In this way, the computer only had to store one possibility at a time in exploring alternatives. One implementation decision in Micro Planner had unfortunate consequences. Lisp had adopted the programming pun of identifying NIL, the empty list with logical ...

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Planner programming language, Planner programming language - Early History of Planner, Planner programming language - Control Structure Controversy, Planner programming language - Control structure characterizations, Planner programming language - Hairy control structure, Planner programming language - Control structures are patterns of passing messages, Planner programming language - Limitation of mathematical logic, Planner programming language - Reference, Planner programming language - External link

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History of computer science - Early computing. The earliest computers were, in fact, people, clerks who performed calculations. Computers would make astronomical calculations for calendars and also worked in commerce, government, and research. These computers often made use of calculating machines, which have a very long history. The earliest of these devices is the abacus, and it was thought to have been invented in Babylon circa 2400 BCE. Its original style of usage was by lines drawn in sand with pebbles. Abaci, of a m ...

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History of computer science, History of computer science - Early history, History of computer science - Early computing, History of computer science - Binary logic, History of computer science - The Analytical Engine, History of computer science - Emergence of a discipline, History of computer science - The theoretical groundwork, History of computer science - Shannon and Information Theory

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Consider the following function: f(A, B, C, D) = E(4, 8, 9, 10, 11, 12, 14, 15) The values inside E tell us which rows have output 1. This function has this truth table: A B C D f 0. 0 0 0 0 0 1. 0 0 0 1 0 2. 0 0 1 0 0 3. 0 0 1 1 0 4. 0 1 0 0 1 5. 0 1 0 1 0 6. 0 1 1 0 0 7. 0 1 1 1 0 8. 1 0 0 0 1 9. 1 0 0 1 1 10. 1 0 1 0 1 11. 1 0 1 1 1 12. 1 1 0 0 1 13. 1 1 0 1 ...

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Karnaugh map, Karnaugh map - History and nomenclature, Karnaugh map - Usage in boolean logic, Karnaugh map - Example, Karnaugh map - Race hazards, Karnaugh map - When not to use K-maps

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So-called descriptive relativists (for example, Ralph Barton Perry), accept that there are fundamental disagreements about the right course of action even when the same facts obtain and the same consequences are likely to arise. However, the descriptive relativist does not necessarily deny that there is one correct moral appraisal, given the same set of circumstances. Other descriptivists believe that opposing moral beliefs can both be true, though critics point out that this leads to obvious logical problems. The latter descriptivists, for ...

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Moral relativism, Moral relativism - History, Moral relativism - Some philosophical considerations, Moral relativism - Critics of relativism, Moral relativism - References and sources

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Bertrand Russell - Analytic philosophy. Russell is generally recognised as one of the founders of analytic philosophy, indeed, even of its several branches. At the beginning of the 20th century, alongside G. E. Moore, Russell was largely responsible for the British "revolt against Idealism", a philosophy greatly influenced by Georg Hegel and his British apostle, F. H. Bradley. This revolt was echoed 30 years later in Vienna by the logical positivists' "revolt against metaphysics". Russell was particularly appalle ...

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Bertrand Russell, Bertrand Russell - Biography, Bertrand Russell - Russell's philosophical work, Bertrand Russell - Analytic philosophy, Bertrand Russell - Epistemology, Bertrand Russell - Ethics, Bertrand Russell - Logical atomism, Bertrand Russell - Logic and mathematics, Bertrand Russell - Philosophy of language, Bertrand Russell - Philosophy of science, Bertrand Russell - Religion and theology, Bertrand Russell - Influence on philosophy, Bertrand Russell - Russell's activism, Bertrand Russell - Pacifism war and nuclear weapons, Bertrand Russell - Communism and socialism, Bertrand Russell - Women's suffrage, Bertrand Russell - Sexuality, Bertrand Russell - Eugenics and race, Bertrand Russell - Russell summing up his life, Bertrand Russell - Comments about Russell, Bertrand Russell - As a man, Bertrand Russell - As a philosopher, Bertrand Russell - As a writer and his place in history, Bertrand Russell - As a mathematician and logician, Bertrand Russell - As an activist, Bertrand Russell - As a recipient of the Nobel Prize for Literature, Bertrand Russell - From a daughter, Bertrand Russell - Quotes, Bertrand Russell - Asides, Bertrand Russell - Succession

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It would be difficult to overstate Russell's influence on modern philosophy, especially in the English-speaking world. While others were also influential, notably, Frege, Moore, and Wittgenstein, more than any other person, Russell made analysis the dominant approach to philosophy. Moreover, he is the founder or, at the very least, the prime mover of its major branches and themes, including several versions of the philosophy of language, formal logical analysis, and the philosophy of science. The various analytic movements throughout th ...

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Bertrand Russell, Bertrand Russell - Biography, Bertrand Russell - Russell's philosophical work, Bertrand Russell - Analytic philosophy, Bertrand Russell - Epistemology, Bertrand Russell - Ethics, Bertrand Russell - Logical atomism, Bertrand Russell - Logic and mathematics, Bertrand Russell - Philosophy of language, Bertrand Russell - Philosophy of science, Bertrand Russell - Religion and theology, Bertrand Russell - Influence on philosophy, Bertrand Russell - Russell's activism, Bertrand Russell - Pacifism war and nuclear weapons, Bertrand Russell - Communism and socialism, Bertrand Russell - Women's suffrage, Bertrand Russell - Sexuality, Bertrand Russell - Eugenics and race, Bertrand Russell - Russell summing up his life, Bertrand Russell - Comments about Russell, Bertrand Russell - As a man, Bertrand Russell - As a philosopher, Bertrand Russell - As a writer and his place in history, Bertrand Russell - As a mathematician and logician, Bertrand Russell - As an activist, Bertrand Russell - As a recipient of the Nobel Prize for Literature, Bertrand Russell - From a daughter, Bertrand Russell - Quotes, Bertrand Russell - Asides, Bertrand Russell - Succession

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In the 1980s programmable integrated circuits were developed. These devices contain circuits whose logical function and connectivity can be programmed by the user, rather than being fixed by the integrated circuit manufacturer. This allows a single chip to be programmed to implement different LSI-type functions such as logic gates, adders and registers. Current devices named FPGAs (Field Programmable Gate Arrays) can now implement tens of thousan ...

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Integrated circuit, Integrated circuit - Introduction, Integrated circuit - Advances in integrated circuits, Integrated circuit - Popularity of ICs, Integrated circuit - Classification and complexity, Integrated circuit - Manufacture, Integrated circuit - Fabrication, Integrated circuit - Packaging, Integrated circuit - History origins and generations, Integrated circuit - The birth of the IC, Integrated circuit - SSI MSI LSI, Integrated circuit - VLSI, Integrated circuit - ULSI WSI SOC, Integrated circuit - Other developments, Integrated circuit - Key industrial and academic data, Integrated circuit - Notable ICs, Integrated circuit - Manufacturers, Integrated circuit - VLSI conferences, Integrated circuit - VLSI journals

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Actor Michael Wisher based the voice of Davros in the 1975 Doctor Who story Genesis of the Daleks on Russell. ...

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Bertrand Russell, Bertrand Russell - Biography, Bertrand Russell - Russell's philosophical work, Bertrand Russell - Analytic philosophy, Bertrand Russell - Epistemology, Bertrand Russell - Ethics, Bertrand Russell - Logical atomism, Bertrand Russell - Logic and mathematics, Bertrand Russell - Philosophy of language, Bertrand Russell - Philosophy of science, Bertrand Russell - Religion and theology, Bertrand Russell - Influence on philosophy, Bertrand Russell - Russell's activism, Bertrand Russell - Pacifism war and nuclear weapons, Bertrand Russell - Communism and socialism, Bertrand Russell - Women's suffrage, Bertrand Russell - Sexuality, Bertrand Russell - Eugenics and race, Bertrand Russell - Russell summing up his life, Bertrand Russell - Comments about Russell, Bertrand Russell - As a man, Bertrand Russell - As a philosopher, Bertrand Russell - As a writer and his place in history, Bertrand Russell - As a mathematician and logician, Bertrand Russell - As an activist, Bertrand Russell - As a recipient of the Nobel Prize for Literature, Bertrand Russell - From a daughter, Bertrand Russell - Quotes, Bertrand Russell - Asides, Bertrand Russell - Succession

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Fuzzy logic was first proposed by Lotfi A. Zadeh of the University of California at Berkeley in a 1965 paper. He elaborated on his ideas in a 1973 paper that introduced the concept of "linguistic variables", which in this article equates to a variable defined as a fuzzy set. Other research followed, with the first industrial application, a cement kiln built in Denmark, coming on line in 1975. Fuzzy systems were largely ignored in the U.S. because they were associated with artificial intelligence, a field that periodically oversells itself and which did so in a big way in the mid-1980 ...

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Fuzzy control system, Fuzzy control system - Antilock brakes, Fuzzy control system - Fuzzy sets, Fuzzy control system - Fuzzy control in detail, Fuzzy control system - Building a fuzzy controller, Fuzzy control system - History & applications, Fuzzy control system - Reference

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Planner was the first language to feature procedural plans that were called by pattern-directed invocation using goals and assertions. A subset called Micro-Planner was implemented by Gerry Sussman, Eugene Charniak and Terry Winograd and was used in Winograd's natural-language understanding program SHRDLU, Eugene Charniak's story understanding work, and some other projects. This generated a great deal of excitement in the field of AI. It also generated controversy because it proposed an alternative ...

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Planner programming language, Planner programming language - Early History of Planner, Planner programming language - Control Structure Controversy, Planner programming language - Control structure characterizations, Planner programming language - Hairy control structure, Planner programming language - Control structures are patterns of passing messages, Planner programming language - Limitation of mathematical logic, Planner programming language - Reference, Planner programming language - External link

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The binary (or dyadic) positional notation for the first half is 1, and the second half is 2. The improper digit 0 plays the role of a wildcard character, pronounced both. So the ordinal fraction for the whole pizza is 0, both halves. 10 means the first half, both quarters. 100 means the first half, both quarters, both eighths. Obviously 1 = 10 = 100. Pad with zeroes to the right. This is like decimal fractions where 1 = 1.0 = 1.00. The second half is 2 or 20. The first quarter is 11. The second quarter is 12. The t ...

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Ordinal fraction, Ordinal fraction - Positional notation, Ordinal fraction - Logical conditions, Ordinal fraction - Ordinal fraction arithmetic, Ordinal fraction - Addition, Ordinal fraction - Comparison, Ordinal fraction - Subtraction, Ordinal fraction - Multiplication, Ordinal fraction - Division, Ordinal fraction - Algebraic rules, Ordinal fraction - Data modelling, Ordinal fraction - History, Ordinal fraction - Reference

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Finding all solutions to the eight queens puzzle is a good example of a simple but nontrivial problem. For this reason, it is often used as an example problem for various programming techniques, including nontraditional approaches such as constraint programming, logic programming or genetic algorithms. Most often, it is used as an example of a problem which can be solved with a recursive algorithm, by phrasing the n queens problem inductively in terms of adding a single queen to any solution to the n−1 queens problem. ...

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Eight queens puzzle, Eight queens puzzle - History, Eight queens puzzle - Constructing a solution, Eight queens puzzle - Counting all solutions, Eight queens puzzle - Related problems, Eight queens puzzle - The eight queens puzzle as an exercise in algorithm design, Eight queens puzzle - A standard recursive solution, Eight queens puzzle - A constraint logic programming solution, Eight queens puzzle - An iterative solution

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Prolog was an early programming language that was billed by its designers as being based on mathematical logic. The basis for the claim that Prolog was that it used backward chaining from goal to subgoal (as in Planner). Schematically, the process is: goal :- subgoal1, ..., subgoaln. which states that in order to prove goal, it is sufficient to prove subgoal1See also:

Logic programming, Logic programming - Basis in mathematical logic, Logic programming - Prolog, Logic programming - Limitations of Prolog as logic programming, Logic programming - Inductive logic, Logic programming - Application domains, Logic programming - History

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Bertrand Russell was born on 18 May 1872 at Trellech, Monmouthshire, Wales, into an aristocratic English family. His paternal grandfather, John Russell, the 1st Earl Russell, had been Prime Minister in the 1840s and 1860s, and was the second son of the 6th Duke of Bedford. The Russells had been prominent for several centuries in Britain, and were one of Britain's leading Whig (Liberal) families. Russell's mother Kate (nee Stanley) was also from an aristocratic family, and was the sister of Rosalind Howard, Countess of Carlisle. Russell's par ...

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Bertrand Russell, Bertrand Russell - Biography, Bertrand Russell - Russell's philosophical work, Bertrand Russell - Analytic philosophy, Bertrand Russell - Epistemology, Bertrand Russell - Ethics, Bertrand Russell - Logical atomism, Bertrand Russell - Logic and mathematics, Bertrand Russell - Philosophy of language, Bertrand Russell - Philosophy of science, Bertrand Russell - Religion and theology, Bertrand Russell - Influence on philosophy, Bertrand Russell - Russell's activism, Bertrand Russell - Pacifism war and nuclear weapons, Bertrand Russell - Communism and socialism, Bertrand Russell - Women's suffrage, Bertrand Russell - Sexuality, Bertrand Russell - Eugenics and race, Bertrand Russell - Russell summing up his life, Bertrand Russell - Comments about Russell, Bertrand Russell - As a man, Bertrand Russell - As a philosopher, Bertrand Russell - As a writer and his place in history, Bertrand Russell - As a mathematician and logician, Bertrand Russell - As an activist, Bertrand Russell - As a recipient of the Nobel Prize for Literature, Bertrand Russell - From a daughter, Bertrand Russell - Quotes, Bertrand Russell - Asides, Bertrand Russell - Succession

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Political and social activism occupied much of Russell's time for most of his long life, which makes his prodigious and seminal writing on a wide range of technical and non-technical subjects all the more remarkable. Russell remained politically active to the end, writing and exhorting world leaders and lending his name to various causes. Some maintain that during his last few years he gave his youthful followers too much license and that they used his name for some outlandish purposes that a more attentive Russell would not have appr ...

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Bertrand Russell, Bertrand Russell - Biography, Bertrand Russell - Russell's philosophical work, Bertrand Russell - Analytic philosophy, Bertrand Russell - Epistemology, Bertrand Russell - Ethics, Bertrand Russell - Logical atomism, Bertrand Russell - Logic and mathematics, Bertrand Russell - Philosophy of language, Bertrand Russell - Philosophy of science, Bertrand Russell - Religion and theology, Bertrand Russell - Influence on philosophy, Bertrand Russell - Russell's activism, Bertrand Russell - Pacifism war and nuclear weapons, Bertrand Russell - Communism and socialism, Bertrand Russell - Women's suffrage, Bertrand Russell - Sexuality, Bertrand Russell - Eugenics and race, Bertrand Russell - Russell summing up his life, Bertrand Russell - Comments about Russell, Bertrand Russell - As a man, Bertrand Russell - As a philosopher, Bertrand Russell - As a writer and his place in history, Bertrand Russell - As a mathematician and logician, Bertrand Russell - As an activist, Bertrand Russell - As a recipient of the Nobel Prize for Literature, Bertrand Russell - From a daughter, Bertrand Russell - Quotes, Bertrand Russell - Asides, Bertrand Russell - Succession

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Admitting to failure in helping the world to conquer war and in winning his perpetual intellectual battle for eternal truths, Russell wrote this in "Reflections on My Eightieth Birthday", which also served as the last entry in the last volume of his autobiography, published in his 98th year: "I have lived in the pursuit of a vision, both personal and social. Personal: to care for what is noble, for what is beautiful, for what is gentle; to allow moments of insight to give wisdom at more mundane times. Social: to see in im ...

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Bertrand Russell, Bertrand Russell - Biography, Bertrand Russell - Russell's philosophical work, Bertrand Russell - Analytic philosophy, Bertrand Russell - Epistemology, Bertrand Russell - Ethics, Bertrand Russell - Logical atomism, Bertrand Russell - Logic and mathematics, Bertrand Russell - Philosophy of language, Bertrand Russell - Philosophy of science, Bertrand Russell - Religion and theology, Bertrand Russell - Influence on philosophy, Bertrand Russell - Russell's activism, Bertrand Russell - Pacifism war and nuclear weapons, Bertrand Russell - Communism and socialism, Bertrand Russell - Women's suffrage, Bertrand Russell - Sexuality, Bertrand Russell - Eugenics and race, Bertrand Russell - Russell summing up his life, Bertrand Russell - Comments about Russell, Bertrand Russell - As a man, Bertrand Russell - As a philosopher, Bertrand Russell - As a writer and his place in history, Bertrand Russell - As a mathematician and logician, Bertrand Russell - As an activist, Bertrand Russell - As a recipient of the Nobel Prize for Literature, Bertrand Russell - From a daughter, Bertrand Russell - Quotes, Bertrand Russell - Asides, Bertrand Russell - Succession

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