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The Application of Iterated Consensus to Multiple-Valued Logic Design.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OHIO SCHOOL OF ENGINEERING
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Present day switching theory deals with binary circuits. Inherently, however, some signals are not two-valued in nature. With recent advances in integrated circuit technology, multiple-output devices have become more feasible. Thus, all that is needed to make practical use of these devices as they are made available is a generalized mathematical model which can be manipulated and implemented relatively easily. In this report, a multi-valued algebra is introduced as a mathematical model for the study of switching circuits having two or more logic values and some of the techniques for manipulating switching functions are presented. In particular, a map method related to the Karnaugh map is presented. As in the two-valued case, the prime implicants of a function can be found directly from its map. Unfortunately, this map method is practical only for functions fo three or fewer variables. An operation which is applicable to functions of any number of variables is the generalized consensus operation. In the literature, Allen and Givone have developed an iterated consensus procedure for multi-valued, single-output functions. This thesis presents the extension to the multiple-output function case.
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