Accession Number : AD0717205

Title :   Galois Logic Design.

Descriptive Note : Final rept. 1 Oct 69-31 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 two-element 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 single-primitive systems are considered, capable of utilizing a single LSI chip-type throughout any network to be designed. One especially natural primitive offers the additional potential of maximizing effective LSI-yield. Methods are suggested for the design of general and universal Galois functions in two-primitive and one-primitive 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