ELEC220 - Fundamentals of Computer Engineering Collection...

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Unformatted text preview: Fundamentals of Computer Engineering Collection Editor: Katherine Fletcher Fundamentals of Computer Engineering Collection Editor: Katherine Fletcher Authors: Ian Barland Matthias Felleisen Katherine Fletcher John Greiner Phokion Kolaitis Moshe Vardi Online: < http://cnx.org/content/col10347/1.4/ > C O N N E X I O N S Rice University, Houston, Texas © 2008 Katherine Fletcher This selection and arrangement of content is licensed under the Creative Commons Attribution License: http://creativecommons.org/licenses/by/2.0/ Table of Contents An algorithm to implement a boolean function using only NAND's or only NOR's. . . . . . . . . . . . . . . . . . . . 1 DesignWorks Digital Simulation Software Tutorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 Appendices and References 1.1 Propositional Logic: normal forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.2 Propositional Equivalences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Attributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 iv An algorithm to implement a boolean function using only NAND's or only NOR's. 1 NAND's and NOR's are the most common basic logic circuit element in use because they are simpler to build than AND and OR gates, and because each is logically complete . Many logical functions are expressed using AND's, OR's, and Inverters (NOT), however, because an implementing circuit can be constructed straightforwardly from the truth table expression of a logical function and because Karnaugh Map's can be used to minimize AND, OR, INVERTER networks. This document is adapted, with permission, from algorithms and examples given in Dr. Jump's Elec326 course notes. [1] Below a simple algorithm is given for converting a network with AND gates, OR gates and INVERTERS to one with NAND gates or NOR gates exclusively. First the boolean function is represented using AND's, OR's, and NOT gates. Then, using DeMorgan's Law in various forms, the AND, OR, INVERTER networkOR's, and NOT gates....
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