Title :
Theory of Computer Addition and Overflows
Author :
Garner, Harvey L.
Author_Institution :
Moore School of Electrical Engineering, University of Pennsylvania
fDate :
4/1/1978 12:00:00 AM
Abstract :
Computer addition is a groupoid. If an additive identity exists it is unique. If(and only if) addition is defined with the compute through the overflow (CTO) property, then a finite ring of integers is the homomorphic image of the computer number system and addition. Stated another way, the necessary and sufficient condition for CTO is a congruence relation on the integers. Also, if the number system has CTO capabilities for addition, it also has extended CTO properties for addition. A technique is presented for determining the correct sum in the extended compute through overflow (ECTO) mode of computation.
Keywords :
Additive identity; compute through overflow (CTO); computer arithmetic; models of computer arithmetic; number systems; overflow behavior; Additives; Computational modeling; Digital arithmetic; Digital systems; Hardware; Sufficient conditions; Additive identity; compute through overflow (CTO); computer arithmetic; models of computer arithmetic; number systems; overflow behavior;
Journal_Title :
Computers, IEEE Transactions on
DOI :
10.1109/TC.1978.1675101
