A Way to Build Efficient Carry-Skip Adders
IEEE Transactions on Computers
Carry-Free Addition of Recoded Binary Signed-Digit Numbers
IEEE Transactions on Computers
Generalized Signed-Digit Number Systems: A Unifying Framework for Redundant Number Representations
IEEE Transactions on Computers
IEEE Transactions on Computers
Redundant Radix Representations of Rings
IEEE Transactions on Computers
IEEE Transactions on Computers
Leading Guard Digits in Finite Precision Redundant Representations
IEEE Transactions on Computers
Constant-time addition with hybrid-redundant numbers: Theory and implementations
Integration, the VLSI Journal
Decimal Division Algorithms: The Issue of Partial Remainders
Journal of Signal Processing Systems
Hi-index | 14.99 |
Ordinary signed-digit (OSD) number representation systems have been defined for any radix r 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