1. Boolean Algebra - Wikipedia, The Free Encyclopedia Retrieved from http//en.wikipedia.org/wiki/boolean_algebra . Categories Disambiguation Mathematical disambiguation http://en.wikipedia.org/wiki/Boolean_algebra

Boolean algebra From Wikipedia, the free encyclopedia Jump to: navigation search Boolean algebra may mean: Boolean algebra (structure) , a class of algebras (mathematical structures satisfying particular laws) Boolean algebra (logic) , the algebra of truth values and operations on them For introductory articles, see: Boolean algebra (introduction) , a general overview Boolean logic , including applications such as computer science Boolean algebras canonically defined edit See also Boolean (disambiguation) This disambiguation page lists articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " http://en.wikipedia.org/wiki/Boolean_algebra Categories Disambiguation Mathematical disambiguation Views Article Discussion Edit this page History Personal tools Log in / create account Navigation Main Page Contents Featured content Current events ... Random article Interaction About Wikipedia Community portal Recent changes Contact Wikipedia ... Help Search Toolbox What links here Related changes Upload file Special pages ... Cite this page Languages Fran§ais This page was last modified on 21 March 2008, at 00:20.

2. CiteULike: Tag Boolean_algebra [1 Article] Recent papers classified by the tag boolean_algebra. posted to boolean_algebra history_of_logic kripke_semantics modal_logic by CLLC on 200603-27 http://www.citeulike.org/tag/boolean_algebra

Register Log in FAQ Sponsored link CiteULike News CiteGeist Discussion Journals Browse current issues Groups Search groups Tag boolean_algebra [1 article] Recent papers classified by the tag boolean_algebra. Mathematical modal logic: a view of its evolution Journal of Applied Logic , Vol. 1, No. 5-6. (2003), pp. 309-392. by Robert Goldblatt posted to by CLLC on 2006-03-27 10:38:18 as Note: You may cite this page as: http://www.citeulike.org/tag/boolean_algebra RIS BibTeX RSS Related Tags Tags related to: boolean_algebra Filter: CiteULike organises scholarly (or academic) papers or literature and provides bibliographic (which means it makes bibliographies) for universities and higher education establishments. It helps undergraduates and postgraduates. People studying for PhDs or in postdoctoral (postdoc) positions. The service is similar in scope to EndNote or RefWorks or any other reference manager like BibTeX, but it is a social bookmarking service for scientists and humanities researchers.

3. MATHS: Algebras With Two Associative Operators if complete then we almost have a boolean_algebra(0= *Set, 1= +Set) except there is no subsets=Net{ For XSets, boolean_algebra (V=(@^X), ). http://www.csci.csusb.edu/dick/maths/math_41_Two_Operators.html

Skip Navigation CSUSB CNS Comp Sci Dept ... Contact ] [Search Tue Sep 18 15:18:26 PDT 2007 Contents Algebras with two associative operators : Distributive laws : High School Identities for sum and product : Hoare's Axiom System ... Glossary Algebras with two associative operators This a set of rough notes on what happens when you have a set of elements with two different associative operators. Algebras like these are very common. The background is the standard notations and the rules that relate the two operations together. STANDARD ::= See http://csci.csusb.edu/dick/maths/math.11.STANDARD.html STANDARD Distributive laws For S:Set, For S:Set, For S:Set, distributive o has a higher priority than * For S:Set, absorbitive High School Identities for sum and product Burris & Lee 93, Stanley Burris and Simon Lee, "Tarski's High School Identities", American Math Monthly V100n3(Mar 93) pp231-236. HSd (*) distributive(A) (+). For x,y,z:A. def x+y = y+x, def x+(y+z) = (x+y)+z, def x*1 = x, def x*y = y*x, def x*(y*z) =(x*y)*z, def x*(y+z) =(x*y)+(x*z).

4. Theory Boolean_Algebra (Isabelle2007: November 2007) (* ID $Id boolean_algebra.thy,v 1.4 2007/11/05 164804 ballarin Exp $ Author header {* Boolean Algebras *} theory boolean_algebra imports Main begin http://www.cl.cam.ac.uk/~lp15/Isabelle/dist/library/HOL/HOL-Word/Boolean_Algebra

Theory Boolean_Algebra Up to index of Isabelle/HOL/HOL-Word theory imports Main begin lemma x y z x y z x y y x x y z y x z lemma x y z x y z x y y x x y z y x z lemma dual: boolean compl Complement lemma a x a x a y a y x y lemma x y x y x y lemma x x lemma x y x y Conjunction lemma x x x lemma x lemma lemma x lemma x x lemma x x lemma x x y x y lemma y z x y x z x lemma x y z x y x z y z x y x z x Disjunction lemma x x x lemma x lemma lemma x x lemma x lemma x x lemma x x y x y lemma y z x y x z x lemma x y z x y x z y z x y x z x De Morgan's Laws lemma x y x y lemma x y x y Symmetric Difference lemma x y x y x y lemma x y y x lemma x y z x y z lemma x y z x y z x y y x x y z y x z lemma x x lemma x x lemma x x lemma x x lemma x x lemma x x y y lemma x y x y lemma x y x y lemma x x lemma x x lemma x y z x y x z lemma y z x y x z x lemma x y z x y x z y z x y x z x

5. ProgrammingToolBox Comp_orgI Boolean_algebra.htm -- : Open Source Web Directory web programming, perl sample code, php sample code, sql server administration, postgres configuration, mysql configuration, server side programming, http://www.sirfsup.com/programmingToolBox/comp_orgI/boolean_algebra.htm

The Open Source Swiss Army Knife /programmingToolBox/comp_orgI/ /programmingToolBox/comp_orgI/ sub-categories http://www.sirfsup.com/ web directory content Not logged in Chat Register Login unix ... windows return to: http:/www.sirfsup.com programmingToolBox Permalink: boolean_algebra.htm Title: add article options : please login print view (some) theorems commutative, distr. assoc. laws de-morgan's laws I won't reproduce all the laws of boolean algebra here, my fingers got too tired. As luke was told, "use the force" meaning "google". (some) theorems X + = x x + 1 = 1 x + x = x x * x = x X * 1 = x x * = (x')' = x laws of complementarity x + x' = 1 x * x' = commutative, distr. assoc. laws xy = yx c + b = b + c the distributive law not applicable to normal algebra is: x + yz = (x + y)(x + z). this is very useful in manipulating expressions. de-morgan's laws do not confuse with dual; in dual, change and to or, or to and, to 1, 1 to but do not complement variables. In contrast, to apply deMorgan's laws do what's done for a dual and also complement the variables. DeMorgan's laws are : (x + y)' = x'y' (xy)' = x' + y' In other words

6. E-Tutor - Dictionary - 'boolean_algebra' Definition of boolean algebra . You searched for Boolean algebra. Noun. a system of symbolic logic devised by George Boole; used in computers http://www.e-tutor.com/et3/dictionary/define/Boolean_algebra

@import "/themes/shared/thickbox.css"; Home Enroll Tour Contact Us ... About Definition of 'boolean algebra' You searched for Boolean algebra Noun a system of symbolic logic devised by George Boole; used in computers Synonyms: Boolean logic Search: Dictionary Google Get this dictionary without ads as part of the e-Tutor Virtual Learning Program

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8. Boolean Algebra Home, www.playhookey.com, Mon, 03-10-2008. Digital Logic Families Digital Experiments Analog Analog Experiments DC Theory AC Theory Optics http://www.play-hookey.com/digital/boolean_algebra.html

Home www.play-hookey.com Sun, 03-30-2008 Digital Logic Families Digital Experiments Analog ... Test HTML Direct Links to Other Digital Pages: Combinational Logic: Basic Gates Derived Gates The XOR Function Binary Addition ... Boolean Algebra Sequential Logic: RS NAND Latch RS NOR Latch Clocked RS Latch RS Flip-Flop ... Converting Flip-Flop Inputs Alternate Flip-Flop Circuits: D Flip-Flop Using NOR Latches CMOS Flip-Flop Construction Counters: Basic 4-Bit Counter Synchronous Binary Counter Synchronous Decimal Counter Frequency Dividers ... The Johnson Counter Registers: Shift Register (S to P) Shift Register (P to S) The 555 Timer: 555 Internals and Basic Operation 555 Application: Pulse Sequencer Boolean Algebra One of the primary requirements when dealing with digital circuits is to find ways to make them as simple as possible. This constantly requires that complex logical expressions be reduced to simpler expressions that nevertheless produce the same results under all possible conditions. The simpler expression can then be implemented with a smaller, simpler circuit, which in turn saves the price of the unnecessary gates, reduces the number of gates needed, and reduces the power and the amount of space required by those gates. One tool to reduce logical expressions is the mathematics of logical expressions, introduced by George Boole in 1854 and known today as

9. Boolean Algebra - Wikiversity Retrieved from http//en.wikiversity.org/wiki/boolean_algebra . Categories Electronic engineering Mathematics Algebra http://en.wikiversity.org/wiki/Boolean_algebra

Boolean algebra From Wikiversity Jump to: navigation search Contents Introduction Symbols Truth Tables: Rules and Syntax ... edit Introduction Boolean algebra is a specialized algebraic system which deals with boolean values, i.e. values that are either true or false. It forms part of a system called w:Boolean_logic , but we will discuss it here as part of a course on digital electronics. Boolean algebra describes logical and set operations. A logical operation might be for example: "I have flour and water, I can make dough". In a case where I have flour and water, this statement is true. If one of the elements is not true then it is clearly false. Another might be: "I have eggs or bacon, I have food" In a case where I had eggs but not bacon, or if I had only bacon, or if I had eggs and bacon, the statement I have food would be true. Only if I did not have eggs nor bacon would "I have food" be false. Boolean Algebra works like this. One creates statements which are true only if all their component statements are true. Now, taking the first example, lets replace flour with a letter representative of it: F, water with W, and dough with D. In order to write it out we need a symbol for "and". The symbol for "and" in boolean algebra is

10. Boolean Algebra http//encarta.msn.com/encyclopedia_761558504/boolean_algebra.html . http//www.essentialresults.com/article/boolean_algebra http://www.scienceoxygen.com/electrical/18.html

Science Oxygen Home Science Projects Study Reference Notes ... Boolean Algebra... http://134.193.15.25/vu/course/cs281/lectures/boolean-algebra/boolean-algeb ADAM: Boolean search tips... http://adam.ac.uk/info/boolean.html Howstuffworks "How Boolean Logic Works"... http://computer.howstuffworks.com/boolean.htm Null03 1/7/03 4:35 PM Page 93 ... http://computerscience.jbpub.com/ecoa/Null03.pdf Boolean Algebra... http://cs-people.bu.edu/jconsidi/teaching/notes/cs210/node6.html boolean algebra - definition by dict.die.net... http://dict.die.net/boolean%20algebra/ Boolean Algebra... http://ecen3233.okstate.edu/Boolean%20Algebra.htm Logic Gates and Boolean Algebra... http://educ.queensu.ca/~compsci/resources/BoolLogic/titlepage.html MSN Encarta - Dictionary - Boolean algebra... http://encarta.msn.com/encnet/features/dictionary/DictionaryResults.aspx?re MSN Encarta - Boolean Algebra... http://encarta.msn.com/encyclopedia_761558504/Boolean_Algebra.html MSN Encarta - Related Items - Algebra... http://encarta.msn.com/related_761552816_2/Boolean_Algebra.html Boolean algebra - definition of Boolean algebra in Encyclopedia...

11. Boolean Algebra - Simple English Wikipedia, The Free Encyclopedia Retrieved from http//simple.wikipedia.org/wiki/boolean_algebra . Category Algebra. Views. Page Talk Change this page History. Personal tools http://simple.wikipedia.org/wiki/Boolean_algebra

Boolean algebra From the Simple English Wikipedia, the free encyclopedia that anyone can change Jump to: navigation search Boolean algebra is algebra with variables (things which can be changed) that have only two states (or two numbers ). To make things easy, in this article they will be called TRUE or 1, and FALSE or 0. Boolean algebra is named after its creator, George Boole change Rules of Boolean algebra In Digital Electronics the signals of computer i.e given here true and false are denoted by 1 and respectively. TRUE + TRUE = TRUE TRUE + FALSE = TRUE FALSE + TRUE = TRUE FALSE + FALSE = FALSE Hence the T.T. will be This is the equivalent of an OR gate, which is why + is considered a binary OR operator TRUE - TRUE = FALSE TRUE - FALSE = TRUE FALSE - TRUE = TRUE FALSE - FALSE = FALSE This is the equivalent of an XOR gate, which is why - is considered a binary XOR operator. TRUE * TRUE = TRUE TRUE * FALSE = FALSE FALSE * TRUE = FALSE FALSE * FALSE = FALSE This is the equivalent of an AND gate, which is why * is considered a binary AND gate. NOT (FALSE) = TRUE NOT (TRUE) = FALSE Division is best thought of as the reverse of multiplication, for now.

12. 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 http://www.daviddarling.info/encyclopedia/B/Boolean_algebra.html

MATHEMATICS A B C ... CONTACT 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. Related category MATHEMATICS Also on this site: Encyclopedia of History BACK TO TOP var site="s13space1234"

13. Boolean Algebra - English To Russian Dictionary english to russian dictionary containing references. http://www.online-dictionary.biz/english/russian/vocabulary/reference/boolean_al

var language=22; var from='english'; var to='russian'; Online Dictionary Chinese to English English to Chinese ... French to English German to English to Japanese Italian to English Japanese to English to German Latin to English Russian to English ... Swedish to English If you can't find the translation you need, try our free translation Boolean Algebra - English To Russian Dictionary boolean algebra A B C D ... Z All content on this website is property of LocalTranslation unless stated otherwise. document.getElementById("generationTime").innerHTML='('+(0.55)+' seconds)'; document.getElementById("generationTime").innerHTML='('+(0.55)+' seconds)';

14. Boolean Algebra - Indopedia, The Indological Knowledgebase Retrieved from http//www.indopedia.org/boolean_algebra.html . This page has been accessed 4836 times. This page was last modified 0004, 30 Nov 2004 by http://www.indopedia.org/Boolean_algebra.html

Indopedia Main Page FORUM Help ... Log in The Indology CMS In other languages: Deutsch Categories Boolean algebra Order theory ... Wikipedia Article Boolean algebra ज्ञानकोश: - The Indological Knowledgebase 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.

15. Boolean Algebra - Wikipedia Boolean algebra. In mathematics and computer science, Boolean algebras are algebraic structures which capture the essence of the logical operations AND, http://facetroughgemstones.com/wikipedia/bo/Boolean_algebra.html

Office Supplies Buy Posters A-Z Products Website Advertising ... Boolean algebra In mathematics and computer science Boolean algebras are algebraic structures which "capture the essence" of the logical operations AND OR and NOT as well as the set theoretic operations union intersection and complement 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 defined by George Boole in the middle of the 19th century and first applied to switching by Claude Shannon in the 20th century The operators of Boolean algebra may be repesented 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. Table of contents showTocToggle("show","hide")

16. 2006-05-18 Wikipedia/ Elistrzewo_(PKP_station) Mrzezino Never boolean_algebra. name. Proposition. name. Structure_(mathematical_logic) Categoryboolean_algebra. cat 1.0 1.079480 5.393287 3.568724 7.083505 20.174561 http://www.alvis.info/alvis_docs/wp_18052006/2025.xml.gz

17. Boolean Algebra - Wikipedia Retrieved from http//nostalgia.wikipedia.org/wiki/boolean_algebra . This page was last modified 0440, 15 January 2005. Content is available under GNU http://nostalgia.wikipedia.org/wiki/Boolean_algebra

Boolean algebra From Wikipedia HomePage Recent changes View source Page history ... Log in Special pages Double redirects Broken redirects Disambiguation pages Log in Preferences My watchlist Recent changes Upload file File list Gallery of new files User list Statistics Random page Orphaned pages Uncategorized pages Uncategorized categories Uncategorized files Uncategorized templates Unused categories Unused files Wanted pages Wanted categories Most linked to pages Most linked to categories Most linked-to templates Pages with the most categories Most linked to files Pages with the most revisions Pages with the fewest revisions Short pages Long pages New pages Oldest pages Dead-end pages Protected pages Protected titles All pages Prefix index List of blocked IP addresses and usernames User contributions What links here Book sources Categories Export pages Version System messages Logs MIME search Search for duplicate files List redirects Unused templates Random redirect Pages without language links File path Search List of Wikimedia wikis Expand templates CategoryTree Gadgets Parser diff test Cross-namespace links Wikimedia Board of Trustees election Search web links Printable version A Boolean algebra is a lattice A , ^, v) which has the following properties: There exists an element 0, such that a v = a for all a in A (bounded below) There exists an element 1, such that a ^ 1 = a for all a in A (bounded above) For all a, b, c in A: (a v b) ^ c = (a ^ c) v (b ^ c) (distributive law) For every a in A there exists an element ~a in A such that a v ~a = 1 and a ^ ~a = (existence of complements)

18. Boolean Algebra - CoreOntoWiki Translate this page boolean_algebra Inspec A type of algebra that deals with Retrieved from http//korterm.kaist.ac.kr/ontowiki/index.php/boolean_algebra http://korterm.kaist.ac.kr/ontowiki/index.php/Boolean_algebra

var skin = 'monobook';var stylepath = '/ontowiki/skins'; Boolean algebra From CoreOntoWiki Jump to: navigation search boolean_algebra ë ¼ë¦¬ 대수 Inspec A type of algebra that deals with logical rather than numerical relationship. [ìž‘ì— ìž]KAIST : TERMIUM 형식 ë ¼ë¦¬í•™ì— 기호법을 ë„ìž í•˜ì—¬ ë ¼ë¦¬ë¥¼ 해석하려고 한불(Boole)의 착상(1847ë „)을 바탕으로 ê·¸ 후 수학자나 ë ¼ë¦¬í•™ìžê°€ 개량을 가하여 발전시킨 추상적인 대수계. [ìž‘ì— ìž]KAIST : 컴퓨터용어사전_성안당 edit Taxonomic relation is subclass of: is superclass of: edit Non-taxonomic Relation has relations of: edit See also at wikiPedia Retrieved from " http://korterm.kaist.ac.kr/ontowiki/index.php/Boolean_algebra Views Article Discussion Edit History Personal tools Log in / create account CoreOnto ITDeviceOntology -byKAIST -byYU -byPosTech ... ITPersonOntology Navigation Main Page Community portal Current events Recent changes ... Donations Search Toolbox What links here Related changes Special pages Printable version ... Permanent link This page was last modified 13:00, 8 April 2007. This page has been accessed 60 times.

19. Boolean Algebra - Wiktionary Retrieved from http//en.wiktionary.org/wiki/boolean_algebra . Categories English nouns Computing Logic Algebra http://en.wiktionary.org/wiki/Boolean_algebra

Boolean algebra From Wiktionary Jump to: navigation search edit English edit Noun Wikipedia has an article on: Boolean algebra Wikipedia Singular Boolean algebra Plural uncountable Boolean algebra uncountable algebra logic computing An algebra in which all elements can take only one of two values (typically and 1, or "true" and "false") and are subject to operations based on AND OR and NOT edit Translations Croatian: Booleova algebra (hr) f Czech: Booleova algebra (cs) f booleovsk¡ algebra (cs) f Japanese: (bÅ«ru-daisÅ«) Swedish: Boolesk algebra (sv) Retrieved from " http://en.wiktionary.org/wiki/Boolean_algebra Categories English nouns Computing ... Algebra Views Entry Discussion Edit History Personal tools Log in / create account Navigation Main Page Community portal Requested entries Recent changes ... Contact us Search Toolbox What links here Related changes Upload file Special pages ... Permanent link In other languages This page was last modified 00:03, 23 January 2008. Content is available under GNU Free Documentation License About Wiktionary

20. Talk:Electronics/Boolean Algebra - Wikibooks, Collection Of Open-content Textboo unsigned comment was added by 198.104.64.238 (talk • contribs) . Retrieved from http//en.wikibooks.org/wiki/TalkElectronics/boolean_algebra http://en.wikibooks.org/wiki/Talk:Electronics/Boolean_Algebra

Talk:Electronics/Boolean Algebra From Wikibooks, the open-content textbooks collection Talk:Electronics Jump to: navigation search The section on De Morgan's law is confusing. "De Morgan's Law is a consequence of the fact that the not or negation operator is not distributive." yet the examples shown are the opposite and there is nothing to say the examples are what cannot be done. —The preceding unsigned comment was added by talk contribs Retrieved from " http://en.wikibooks.org/wiki/Talk:Electronics/Boolean_Algebra Views Module Discussion Edit this page History Personal tools Log in / create account Navigation Main Page Help Cookbook Wikijunior ... Donations Community Bulletin Board Community portal Reading room Help cleanup ... Contact us Search Toolbox What links here Related changes Upload file Special pages ... Permanent link This page was last modified 05:19, 10 January 2008. All text is available under the terms of the GNU Free Documentation License (see for details). Wikibooks® is a registered trademark of the Wikimedia Foundation, Inc. About Wikibooks

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