
Accession Number : AD0717205
Title : Galois Logic Design.
Descriptive Note : Final rept. 1 Oct 6931 Aug 70,
Corporate Author : SPERRY RAND CORP ST PAUL MINN UNIVAC DEFENSE SYSTEMS DIV
Personal Author(s) : Ellison,James T. ; Kolman,Bernard
Report Date : OCT 1970
Pagination or Media Count : 162
Abstract : The report discusses the problems of logic design by means of finite field theory, their interrelationship and some approaches to their solution, with emphasis on logic networks whose function is externally determined. Galois theory is the study of finite fields and can be viewed as a generalization of the twoelement Boolean algebra traditionally used in logic design. This report attempts to give an introduction to those topics of Galois field theory most relevant to hardware vendor and logic designer and develops the theory of universal Galois functions and its categorical implications. There is a detailed discussion of Boolean encoding procedures which lead to highly efficient Galois multiplication gates and optimal Galois addition gates. Various singleprimitive systems are considered, capable of utilizing a single LSI chiptype throughout any network to be designed. One especially natural primitive offers the additional potential of maximizing effective LSIyield. Methods are suggested for the design of general and universal Galois functions in twoprimitive and oneprimitive systems. In conclusion, a variety of areas is identified for further research in Galois logic design. (Author)
Descriptors : (*LOGIC CIRCUITS, DESIGN), (*ALGEBRA, *COMPUTER LOGIC), SWITCHING CIRCUITS, GATES(CIRCUITS), CODING, POLYNOMIALS, THEOREMS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE