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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
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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