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April 1978 (vol. 27 no. 4)
pp. 297-301
H.L. Garner, Moore School of Electrical Engineering, University of Pennsylvania
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.
Index Terms:
overflow behavior, Additive identity, computer arithmetic, compute through overflow (CTO), models of computer arithmetic, number systems
Citation:
H.L. Garner, "Theory of Computer Addition and Overflows," IEEE Transactions on Computers, vol. 27, no. 4, pp. 297-301, April 1978, doi:10.1109/TC.1978.1675101
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