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Generalized Signed-Digit Number Systems: A Unifying Framework for Redundant Number Representations
January 1990 (vol. 39 no. 1)
pp. 89-98

Signed-digit (SD) number representation systems have been defined for any radix r≤3 with digit values ranging over the set (- alpha , . . ., -1, 0, 1, . . ., alpha ), where alpha is an arbitrary integer in the range 1/2r> alpha >r. Such number representation systems possess sufficient redundancy to allow for the annihilation of carry or borrow chains and hence result in fast propagation-free addition and subtraction. The author refers to the above as ordinary SD number systems and defines generalized SD number systems which contain them as a special symmetric subclass. It is shown that the generalization not only provides a unified view of all redundant number systems which have proven useful in practice (including stored-carry and stored-borrowed systems), but also leads to new number systems not examined before. Examples of such new number systems are stored-carry-or-borrow systems, stored-double-carry systems, and certain redundant decimal representations.

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Index Terms:
generalised signed-digit number systems; unifying framework; redundant number representations; carry; borrow; fast propagation-free addition; subtraction; digital arithmetic.
B. Parhami, "Generalized Signed-Digit Number Systems: A Unifying Framework for Redundant Number Representations," IEEE Transactions on Computers, vol. 39, no. 1, pp. 89-98, Jan. 1990, doi:10.1109/12.46283
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