Logic Gates

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Logic Gates. Informatics INFO I101 February 3, 2003 John C. Paolillo, Instructor. Items for Today. Last week Digitization Graphic, audio and video data sizes This time Digital logic, Boolean algebra, and circuits Logic gates and truth tables. Set Theory &Logic. Boolean Algebra. - PowerPoint PPT Presentation

Text of Logic Gates

  • Logic GatesInformatics INFO I101February 3, 2003John C. Paolillo, Instructor

  • Items for TodayLast weekDigitizationGraphic, audio and video data sizesThis timeDigital logic, Boolean algebra, and circuitsLogic gates and truth tables

  • A Fundamental Unity

  • Binary ArithmeticMeans zero, carry 1 (two distinct outputs)

  • Boolean AlgebraORANDBinary addition: ExOR (for ones place)plus AND (for carry)

  • Electric CircuitsParallelSeries

  • A Fundamental UnityAny logical or mathematical problem may be formulated in set theoretic termsBoolean logic may be used to represent any set-theoretic operationThe fundamental elements of Boolean logic may be implemented in electric circuitsTherefore, any logical or mathematical problem may be implemented in electrical circuits!

  • Logic Gates

  • What are Logic Gates?Logic gates are conventional arrangements of switches that are treated as unitsThey abstract away from the details of individual switchesThey may be implemented in any number of waysOnly their function is important

  • Symbols for Logic Gates

  • Functions of Logic Gates

  • Boolean Logic HintsAND: if you know that one input is 0, it doesnt matter what the other input is, the output will be 0OR: if you know that one input is 1, it doesnt matter what the other input is, the output will always be 1XOR: if you know that the inputs are the same, then the output will always be 0

  • Some Example Circuits

  • Synthesizing XOR

  • Synthesizing OR from NAND

  • Encoding Position in a 2-by-2 Board

  • Decoding Position to a 2-by-2 Board

  • 4-line multiplexer

  • 4-line demultiplexer

  • Synthesizing AND from NOR

  • Other Applications of Boolean Logic

  • Graphic Paint/Copy ModesCOPYORXOR

  • Database Search QueriesA keyword represents the set of documents containing itBoolean AND represents the intersection of the sets corresponding to two (or more) search termsBoolean OR represents the union of the sets corresponding to two (or more) search terms