41. Dictionary Of Computers - Boolean Algebra boolean algebra. Set of algebraic rules, named after mathematician George Boole, boolean algebra includes a series of operators (AND, OR, NOT, http://www.tiscali.co.uk/reference/dictionaries/computers/data/m0044414.html

// Show bread crumbs navigation path. breadcrumbs('four'); //> From: www.tiscali.co.uk/reference/ DICTIONARIES Animals Computers Difficult Words ... Plants Frames not supported Frames not supported Index A B C D ... Z Boolean algebra Set of algebraic rules, named after mathematician George Boole, in which TRUE and FALSE are equated to and 1. Boolean algebra includes a series of operators (AND, OR, NOT, NAND (NOT AND), NOR, and XOR (exclusive OR)), which can be used to manipulate TRUE and FALSE values (see truth table ). It is the basis of computer logic because the truth values can be directly associated with bits These rules are used in searching databases either locally or across the Internet via services like Altavista to limit the number of hits to those which most closely match a user's requirements. A search instruction such as 'tennis NOT table' would retrieve articles about tennis and reject those about ping-pong. Helicon Publishing LTD 2000. Dictionary search Search for: Jamaica Flag Black, yellow, and green are colours found in many African flags and reflect the islanders' heritage. Effective date 6 August 1962. Print now Send to a friend Related articles Related products var st_pg=""; var st_ai=""; var st_v=1.0; var st_ci="762"; var st_di="d001"; var st_dd="st.sageanalyst.net"; var st_tai="v:1.2.3";

42. Boolean Algebra Logic - Expert Web Search Engine Tips, Query boolean algebra Logic Expert Web Search Engine Tips, Query. http://www.livinginternet.com/w/wu_expert_bool.htm

Home Contents ^ Up <- Previous ... Lists The Logic of Boolean Algebra The logical simplicity of boolean algebra enables the construction of powerful, efficient search queries. The concept of boolean algebra is embedded in human psychology, in our very biological understanding of how the world works. It is the foundation for all of mathematics , most of science, and much of philosophy. But more importantly, it is useful for the construction of advanced Internet search queries, and is used throughout the examples in the following pages. The subsections below provide information on boolean expressions , the boolean operators AND OR , and NOT , some boolean tricks , and and a list of boolean capable search sites Expressions . It is easier to understand boolean algebra when we compare it to the familiar arithmetic algebra we learned in school, with the operators +, , x, / combined with operands in expressions like the following: ( a + b ) x c When we know the values of the operands of an algebraic expression, then we can figure out the overall value. For example, if a=2, b =3, and c=4, then the overall value of the above expression is 20.

43. What's So Logical About Boolean Algebra? What s so logical about boolean algebra? George Boole believed in what he called the ‘process of analysis’, that is, the process by which combinations of http://www.home.gil.com.au/~bredshaw/boolean.htm

What's so logical about boolean algebra? George Boole believed in what he called the ‘process of analysis’, that is, the process by which combinations of interpretable symbols are obtained. It is the use of these symbols according to well-determined methods of combination that he believed presented ‘true calculus’. Today, all our computers employ Boole's logic system - using microchips that contain thousands of tiny electronic switches arranged into logical ‘gates’ that produce predictable and reliable conclusions. The basic logic gates comprise of AND OR and NOT . It is these gates, used in differing combinations, that allow the computer to execute its operations using binary language. Each gate assesses various information (consisting of high or low voltages) in accordance with predetermined rules, and produces a single high or low voltage logical conclusion. The voltage itself represents the binary yes-no, true-false, zero-one concept. AND gates will only yield a TRUE result (that is, a binary 1) if all input is TRUE. Therefore, the top two gates will produce a FALSE (binary 0) result.

44. Boolean Algebra - Definition Of Boolean Algebra In Encyclopedia In mathematics and computer science, boolean algebras, or Boolean lattices, are algebraic structures which capture the essence of the logical operations http://encyclopedia.laborlawtalk.com/Boolean_algebra

Add to Favorites General Encyclopedia Legal ... Law forum Search Word: Visit our Law forums Labor Law Accidents Law Bankruptcy Law Business Law ... Tax Law In mathematics and computer science Boolean algebras , or Boolean lattices , are algebraic structures which "capture the essence" of the logical operations AND OR and NOT as well as the corresponding set theoretic operations intersection union and complement They are named after George Boole , an English mathematician at University College Cork, who first defined them as part of a system of logic in the mid 19th century . Specifically, Boolean algebra was an attempt to use algebraic techniques to deal with expressions in the propositional calculus . Today, Boolean algebras find many applications in electronic design. They were first applied to switching by Claude Shannon in the 20th century The operators of Boolean algebra may be represented in various ways. Often they are simply written as AND, OR and NOT. In describing circuits, NAND (NOT AND), NOR (NOT OR) and XOR (eXclusive OR) may also be used. Mathematicians often use + for OR and . for AND (since in some ways those operations are analogous to addition and multiplication in other algebraic structures ) and represent NOT by a line drawn above the expression being negated.

45. Boolean Algebra boolean algebra is both a formalization of the algebraic aspects of logic, An important aspect of the axioms and properties of boolean algebra (and http://www.rwc.uc.edu/koehler/comath/24.html

Boolean Algebra Boolean Algebra is both a formalization of the algebraic aspects of logic , and the customary language of logic used by the designers of computers. A Boolean Algebra is defined as: a set, with two special elements (0 and 1), and three operations: sum ("+"), product ("*") and complement (" ' " or "prime") which obey the Commutative Distributive Identity (not including the boundedness identities) and Complement axioms These axioms are the same as the properties with those names which we discussed earlier; here we call them axioms because they are assumptions: from them, all of the remaining properties can be formally derived. Logic is a Boolean Algebra: the set is the set of all propositions the special elements are T (1) and F (0) the three operations are AND (product), OR (sum) and NOT (complement). All of properties of the logical operators which we have previously discussed can be represented using the symbols of Boolean Algebra. For example, the first DeMorgan's Law is written as (a + b)' = a' * b' instead of and the (non-boundedness) Identities are written as a + = a and a * 1 = a instead of For the record, the complete list of axioms and properties in both logical and Boolean symbols is:

46. AllRefer.com - Boolean Algebra (Mathematics) - Encyclopedia AllRefer.com reference and encyclopedia resource provides complete information on boolean algebra, Mathematics. Includes related research links. http://reference.allrefer.com/encyclopedia/B/Booleanal.html

AllRefer Channels :: Health Yellow Pages Reference Weather September 16, 2005 Medicine People Places History ... Maps Web AllRefer.com You are here : AllRefer.com Reference Encyclopedia Mathematics ... Boolean algebra By Alphabet : Encyclopedia A-Z B Boolean algebra, Mathematics Related Category: Mathematics Boolean algebra [b OO E u n] Pronunciation Key , an abstract mathematical system primarily used in computer science and in expressing the relationships between sets (groups of objects or concepts). The notational system was developed by the English mathematician George Boole c.1850 to permit an algebraic manipulation of logical statements. Such manipulation can demonstrate whether or not a statement is true and show how a complicated statement can be rephrased in a simpler, more convenient form without changing its meaning. In his 1881 treatise, Symbolic Logic, the English logician and mathematician John Venn interpreted Boole's work and introduced a new method of diagramming Boole's notation; this was later refined by the English mathematician Charles Dodgson (better known as Lewis Carroll : this method is now know as the Venn diagram. When used in set theory, Boolean notation can demonstrate the relationship between groups, indicating what is in each set alone, what is jointly contained in both, and what is contained in neither. Boolean algebra is of significance in the study of information theory, the theory of probability, and the geometry of sets. The expression of electrical networks in Boolean notation has aided the development of switching theory and the design of computers.

47. Boolean Algebra - Quick Reference boolean algebra, also known as the algebra of logic , is a branch of boolean algebra has become the main cornerstone of digital electronics, http://www.semiconfareast.com/boolean.htm

See Also: Logic Gates What is a Semiconductor? Boolean Algebra - Quick Reference Boolean Algebra , also known as the 'algebra of logic' , is a branch of mathematics that is similar in form to algebra, but dealing with logical instead of numerical relationships. It was invented by George Boole , after whom this system was named. Thus, instead of variables that represent numerical quantities as in conventional algebra, Boolean algebra handles variables that represent two types of logic propositions: 'true' and 'false'. Boolean algebra has become the main cornerstone of digital electronics, since the latter also operates with two logic states, '1' and '0', represented by two distinct voltage levels. Boolean algebra's formal interpretation of logical operators AND, OR, and NOT has allowed the systematic development of complex digital systems from simple logic gates, that now not only include circuits that perform mathematical operations, but intricate data processing as well. Tables 1 to 4 summarize the definitions of logical operators and their basic mathematical properties as represented in Boolean algebra.

48. HAKMEM -- BOOLEAN ALGEBRA -- DRAFT, NOT YET PROOFED boolean algebra. Previous Up Next The hope is that the best Boolean networks for functions might lead to the best algorithms. http://www.inwap.com/pdp10/hbaker/hakmem/boolean.html

Beeler, M., Gosper, R.W., and Schroeppel, R. HAKMEM . MIT AI Memo 239, Feb. 29, 1972. Retyped and converted to html ('Web browser format) by Henry Baker, April, 1995. BOOLEAN ALGEBRA Previous Up Next ITEM 17 (Schroeppel): Problem: synthesize a given logic function or set of functions using the minimum number of two-input AND gates. NOT gates are assumed free. Feedback is not allowed. The given functions are allowed to have X (don't care) entries for some values of the variables. P XOR Q requires three AND gates. MAJORITY(P,Q,R) requires 4 AND gates. "PQRS is a prime number" seems to need seven gates. The hope is that the best Boolean networks for functions might lead to the best algorithms. ITEM 18 (Speciner): Number of monotonic increasing Boolean N functions of N variables - 2 (T, F) 1 3 (T, F, P) 2 6 (T, F, P, Q, P AND Q, P OR Q) 3 20 4 168 = 8 * 3 * 7 5 7581 = 3 * 7 * 19^2 6 7,828,354 = 2 * 359 * 10903 (Ouch!) N from to 4 suggest that a formula should exist, but 5 and 6 are discouraging. A difficult generalization: Given two partial orderings, find the number of maps from one to the other that are compatible with the ordering. A related puzzle: A partition of N is a finite string of non-increasing integers that add up to N. Thus 7 3 3 2 1 1 1 is a partition of 18. Sometimes an infinite string of zeros is extended to the right, filling a half-line. The number of partitions of N, P(N), is a fairly well understood function.

49. Boolean Algebra then we have the equations of boolean algebra. Before 1900 boolean algebra really meant the juggling of equations (and negequations) to reflect valid http://www.math.uwaterloo.ca/~snburris/htdocs/scav/boolean/boolean.html

Previous: Comparing the expressive power ... Next: Second proof of compactness for propositional logic Up: Supplementary Text Topics Boolean algebra If we take the equations that are true in the the calculus of classes and replace the symbols using the following table then we have the equations of Boolean algebra . Before 1900 Boolean algebra really meant the juggling of equations (and neg-equations) to reflect valid arguments. In 1904 E.V. Huntington wrote a paper [1] in which he viewed Boolean algebras as algebraic structures satisfying the equations obtained from the calculus of classes. This viewpoint became dominant in the 1920's under the influence of M.H. Stone and A. Tarski. Stone was initially interested in Boolean algebras in order to gain insight into the structure of rings of functions which were being investigated in functional analysis. He wrote two massive papers, one on the equivalence of Boolean algebras and Boolean rings, and the other on the duality between Boolean algebras and Boolean spaces [= totally disconnected compact Hausdorff spaces]. Tarski studied Boolean algebras while working on the abstract notion of `closure under deductive consequence'. In the 1930's Stone proved that every Boolean algebra is isomorphic to a field of sets, and that the equations true of the two-element Boolean algebra are the same as the equations true of all Boolean algebras; and these equations were consequences of a small initial set of defining equations. What has the modern subject of Boolean algebra got to do with propositional logic? Not very much. Boolean algebra became a deep and fascinating subject in its own right, with much more to offer than a convenient notation to analyze simple chains of reasoning. Nonetheless on the level of equivalence and equations the subjects of propositional logic, calculus of classes, and Boolean algebras are essentially the same, as illustrated by the following table:

50. Boole It began the algebra of logic called boolean algebra which now finds boolean algebra has wide applications in telephone switching and the design of http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Boole.html

George Boole Born: 2 Nov 1815 in Lincoln, Lincolnshire, England Died: 8 Dec 1864 in Ballintemple, County Cork, Ireland Click the picture above to see three larger pictures Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing George Boole 's parents were Mary Ann Joyce and John Boole. John made shoes but he was interested in science and in particular the application of mathematics to scientific instruments. Mary Ann was a lady's maid and she married John on 14 September 1806. They moved to Lincoln where John opened a cobbler's shop at 34 Silver Street. The family were not well off, partly because John's love of science and mathematics meant that he did not devote the energy to developing his business in the way he might have done. George, their first child, was born after Mary Ann and John had been married for nine years. They had almost given up hope of having children after this time so it was an occasion for great rejoicing. George was christened the day after he was born, an indication that he was a weak child that his parents feared might not live. He was named after John's father who had died in April 1815. Over the next five years Mary Ann and John had three further children, Mary Ann, William and Charles. If George was a weak child after his birth, he certainly soon became strong and healthy. George first attended a school in Lincoln for children of tradesmen run by two Misses Clarke when he was less than two years old. After a year he went to a commercial school run by Mr Gibson, a friend of John Boole, where he remained until he was seven years old. His early instruction in mathematics, however, was from his father who also gave George a liking for constructing optical instruments. When he was seven George attended a primary school where he was taught by Mr Reeves. His interests turned to languages and his father arranged that he receive instruction in Latin from a local bookseller.

51. Boolean Algebra boolean algebra. A set with n elements has 2n different subsets, The boolean algebra Bn consists of these 2n subsets with the operations of union http://rkb.home.cern.ch/rkb/AN16pp/node21.html

Next: Bootstrap Up: No Title Previous: Bivariate Normal Distribution Boolean Algebra A set with n elements has 2 n different subsets, including the empty set and I itself ( each either belongs to the subset or does not belong). The Boolean algebra B n consists of these 2 n subsets with the operations of union , intersection , and complement - (the complement of X is also written ). Examples of rules that are valid for any X Y Z are Every Boolean equation is equivalent to its dual, in which the operations of union and intersection are interchanged and simultaneously all variables are complemented. For example, is equivalent to B is also called propositional calculus. It is the calculus of truth values (0 = false, I = 1 = true, = or, = and, - = not). Boolean variables and operations can be used in high-level programming languages (TRUE, FALSE, OR, AND, NOT, sometimes XOR). Sometimes the rules of Boolean algebra can also be used to simplify considerably the logic of a complicated sequence of tests. A much more complete discussion of Boolean algebra can be found by looking in The Free On-line Dictionary of Computing.

52. Boolean Algebra. The Columbia Encyclopedia, Sixth Edition. 2001-05 boolean algebra. The Columbia Encyclopedia, Sixth Edition. 200105. http://www.bartleby.com/65/bo/Booleanal.html

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53. Boolean Algebra boolean algebra, bOO leun Pronunciation Key. boolean algebra , an abstract mathematical system primarily used in computer science and in expressing the http://www.infoplease.com/ce6/sci/A0808301.html

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54. Laws Of Boolean Algebra - Computer Fundamentals - Free Computer Science Tutorial Tutorial of laws of boolean algebra by laynetworks. http://www.laynetworks.com/Boolean Algebra.htm

Web laynetworks.com CS 01 CS 02 CS 03 CS 04 ... CS 17 Laws of Boolean Algebra Boolean Algebra The most obvious way to simplify Boolean expressions is to manipulate them in the same way as normal algebraic expressions are manipulated. With regards to logic relations in digital forms, a set of rules for symbolic manipulation is needed in order to solve for the unknowns. P1: X = or X = 1 Laws of Boolean Algebra the basic Boolean laws. Note that every law has two expressions, (a) and (b). This is known as duality. These are obtained by changing every AND(.) to OR(+), every OR(+) to AND(.) and all 1's to 0's and vice-versa.

55. Wiley::Ones And Zeros: Understanding Boolean Algebra, Digital Circuits, And The Ones and Zeros Understanding boolean algebra, Digital Circuits, and the Logic of Sets John R. Gregg ISBN 07803-3426-4 Paperback 296 pages http://www.wiley.com/WileyCDA/WileyTitle/productCd-0780334264.html

Location: United States change location Shopping Cart My Account Help ... Contact Us By Keyword By Title By Author By ISBN By ISSN Wiley Engineering Ones and Zeros: Understanding Boolean Algebra, Digital Circuits, and the Logic of Sets Related Subjects Quantum Electronics VLSI Join an Engineering Mailing List Related Titles Low-Power CMOS Design (Hardcover) by Anantha Chandrakasan (Editor), Robert W. Brodersen (Editor) Low-Voltage/Low-Power Integrated Circuits and Systems: Low-Voltage Mixed-Signal Circuits (Hardcover) by Edgar Sanchez-Sinencio (Editor), Andreas G. Andreou (Editor) Integrated Circuit Manufacturability : The Art of Process and Design Integration (Hardcover) by Jose Pineda de Gyvez (Editor), Dhiraj Pradhan (Editor) High-Performance System Design: Circuits and Logic (Hardcover) by Vojin G. Oklobdzija (Editor) Hardware Description Languages : Concepts and Principles (Hardcover) by Sumit Ghosh Design of High-Performance Microprocessor Circuits (Hardcover) by Anantha Chandrakasan (Editor), William J. Bowhill (Editor), Frank Fox (Editor) DRAM Circuit Design: A Tutorial (Hardcover) by Brent Keeth, R. Jacob Baker

56. Web Scripting And Logic, Or Boolean Algebra | Evolt.org A world community for web developers, evolt.org promotes the mutual free exchange of ideas, skills and experiences. http://www.evolt.org/article/Web_Scripting_and_Logic_or_Boolean_Algebra/17/49918

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57. Layout Design: Introduction To Boolean Algebra A free study guide in CMOS Layout Design. Covers digital logic, boolean algebra, transistor level schematics, and stick diagrams. http://www.geocities.com/cmoslayoutdesign/gmask/gmask03.html

Introduction to Boolean Algebra Boolean Algebra is a way of describing a circuit in the form of a mathematical formula. While this may sound difficult, it actually isn't difficult at all. The AND function is represented by a large dot (times sign), the OR function is represented by a plus sign, and the INVERTER function is represented by a line over top of the input. This equation states that output A is equal to input B AND input C. The above symbol is the schematic symbol for an AND gate. This equation states that output D is equal to input E OR input F. The above symbol is the schematic symbol for an OR gate. This equation states that output G is equal to INVERTED H. The above symbol is the schematic symbol for an INVERTER gate. Boolean Algebra formulas do become more complicated, and can be manipulated by following specific rules that will be discussed later. These three symbols will permit us to write equations for more complicated devices. The above is a two input AND (inputs A and B) and another two input AND (inputs C and D) both going into a two input OR gate who's output is E. The lines connecting the AND gates to the OR gate aren't required if the schematic is drawn so that their outputs are directly connected to the inputs of the OR gate. The equation for the first AND gate is A*B and the equation for the second AND gate is C*D. Both of these are going into an OR gate who's output is E. Since A*B is one input to this OR gate, and the other is C*D, the equation for E becomes...

58. Boolean Algebra Tech support, programming, web development, and internet marketing community. Forums to get free computer help and support. http://www.daniweb.com/techtalkforums/thread1733.html

entire site forums blogs code snippets link directory Whether you're a software developer, web developer, IT professional, or just a computer hobbiest, here you'll find everything Information Technology related all in one convenient place. To take advantage of everything our knowledgable and exciting online community of 49,379 members has to offer, please register . It's free! DaniWeb IT Community Software Development C and C++ C and C++ Tutorials Boolean Algebra Thread Tools Search this Thread Display Modes Nov 16th 2003, 11:07 AM cscgal vbmenu_register("postmenu_9514", true); Administrator Join Date: Feb 2002 Location: Lawn Guylen, NY Posts: 5,473 Boolean Algebra True and False The backbone of computer science is logic. Most often, those with logical minds make the best programmers. Hence, a very important programming concept is that of boolean algebra. A boolean expression is a true or false statement. In the world of computers, a true statement is represented by 1 while a false statement is represented by 0. Low level computer programming (the logic inside a computer) is actually a series of zeros and ones. The following chart diagrams the most common symbols of equality used in boolean algebra. Note that assignment statements use a single equals such as = while boolean algebra uses the double equals ==.

59. Questions About Assembly And Boolean Algebra x86 Assembly, MIPS Assembly, and other forms of machine language. Tech support, programming, web development, and internet marketing community. http://www.daniweb.com/techtalkforums/thread16453.html

entire site forums blogs code snippets link directory Whether you're a software developer, web developer, IT professional, or just a computer hobbiest, here you'll find everything Information Technology related all in one convenient place. To take advantage of everything our knowledgable and exciting online community of 49,379 members has to offer, please register . It's free! DaniWeb IT Community Software Development Legacy and Other Languages Assembly Questions about assembly and boolean algebra x86 Assembly, MIPS Assembly, and other forms of machine language. Thread Tools Search this Thread Display Modes Jan 3rd 2005, 11:01 PM Diode vbmenu_register("postmenu_81255", true); Junior Poster Join Date: Jan 2005 Posts: 1 Questions about assembly and boolean algebra I am determined to learn assembly. However, I have stumbled upon a little confusion regarding boolean algebra. It seems that the author of the very fine documentation I have been studying hasn't explained a whole lot on boolean algebra symbols. I am learning HLA, and I am studying it from their own documentation.

60. Boolean Algebra For any set A, the subsets of A form a boolean algebra under the operations of union, intersection, and complement. © David Darling. BACK TO TOP http://www.daviddarling.info/encyclopedia/B/Boolean_algebra.html

Return to The Worlds of David Darling INDEX LATEST NEWS ARCHIVE ... Z entire Web this site Boolean algebra An algebra in which the binary operations are chosen to model the union and intersection operations in set theory . For any set A , the subsets of A form a Boolean algebra under the operations of union, intersection, and complement. ALL MATHEMATICS ENTRIES BACK TO TOP var site="s13space1234"

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