Issue No. 03 - March (1993 vol. 42)

ISSN: 0018-9340

pp: 379-384

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.210182

ABSTRACT

<p>Ordinary signed-digit (OSD) number representation systems have been defined for any radix r<or=3 with digit values ranging over the set (- alpha . . .,-1,0,1. . ., alpha ), where alpha is an arbitrary integer in the range r/2> alpha >r. The most important property of OSD number representation systems is the possibility of performing carry-free addition and (by changing all the digit signs in the subtrahend) borrow-free subtraction. Generalized signed-digit (GSD) number systems cover all useful redundant number representations as special cases. Most GSD number systems support carry-free addition and borrow-free subtraction, and even those that do not can be dealt with using limited-carry or limited-borrow algorithms which yield the ith sum or difference digit z/sub i /as a function of the digits x/sub i/, y/sub i/, x/sub i-1/, y/sub i-1/, x/sub i-2/ and y/sub i-2/ of the operands x and y. Additional topics that are important for practical implementation of arithmetic functions using GSD number systems are treated. Because GSD number systems may have asymmetric digit sets, one must consider subtraction (or at least sign change for representations with alpha <0 and beta <0) explicitly. Zero detection, sign detection, and overflow handling are also treated in depth.</p>

INDEX TERMS

zero detection; arithmetic support functions; generalized signed-digit number systems; OSD number representation; borrow-free subtraction; redundant number representations; carry-free addition; sign detection; overflow handling; digital arithmetic.

CITATION

B. Parhami, "On the Implementation of Arithmetic Support Functions for Generalized Signed-Digit Number Systems",

*IEEE Transactions on Computers*, vol. 42, no. , pp. 379-384, March 1993, doi:10.1109/12.210182