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**Unformatted text preview: **1 7/29/07 Melvin A. Breuer 1 Boolean switching functions Melvin A. Breuer University of Southern California Viterbi School of Engineering Ming Hsieh Department of Electrical Engineering Fill-in Answer Animation only 7/29/07 Melvin A. Breuer 2 Background material Boolean George Boole--an English mathematician and logician; 1815-1864 Boolean algebra--a deductive logic system usually applied to classes, in which under the operations of intersection and symmetric difference, classes are treated as algebraic quantities (Webster) Switching Elect. A device for turning on or off or directing an electric current Switchboard Elect. A structural unit containing mounting switches and instruments necessary to complete telephone circuits manually (Webster) 2 7/29/07 Melvin A. Breuer 3 Background material Functions Math- A relation between two sets in which one (or one or more) element of the second set is assigned to each element in the first set (Webster) 7/29/07 Melvin A. Breuer 4 Boolean algebra (booleen) Boolean Algebra, 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, the author of Alices Adventures in Wonderland) -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. Partial only 3 7/29/07 Melvin A. Breuer 5 "Claude E. Shannon, the founder of what is often called Information Theory, in his master's thesis showed in a masterful way how the analysis of complicated circuits for switching could be affected by the use of Boolean algebra. This surely must be one of the most important master's theses ever written... The paper was a landmark in that it helped to change digital circuit design from an art to a science." Hermann Goldstine Shannon Only partial 7/29/07 Melvin A. Breuer 6 More people Irving Reed (USC)-- know for the Reed-Solomon code, and the Reed-Muller code. We will mention the Reed expansion later in this module 4...

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