Theory of Computer Addition and Overflows

Theory of Computer Addition and Overflows

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 necessar...

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Veröffentlicht in:IEEE transactions on computers 1978-04, Vol.C-27 (4), p.297-301
1. Verfasser: Garner
Format: Artikel
Sprache:eng
Schlagworte:
Additive identity
compute through overflow (CTO)
computer arithmetic
models of computer arithmetic
number systems
overflow behavior
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description 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.
doi_str_mv 10.1109/TC.1978.1675101
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ispartof IEEE transactions on computers, 1978-04, Vol.C-27 (4), p.297-301
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1557-9956
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source IEEE Electronic Library (IEL)
subjects Additive identity
compute through overflow (CTO)
computer arithmetic
models of computer arithmetic
number systems
overflow behavior
title Theory of Computer Addition and Overflows
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