Digital Filters and Signal Processing
Digital Filters and Signal Processing
Generalized Signed-Digit Number Systems: A Unifying Framework for Redundant Number Representations
IEEE Transactions on Computers
Journal of VLSI Signal Processing Systems
On the Implementation of Arithmetic Support Functions for Generalized Signed-Digit Number Systems
IEEE Transactions on Computers
IEEE Transactions on Computers
Area-Time Efficient Sign Detection Technique for Binary Signed-Digit Number System
IEEE Transactions on Computers
Fast decimal floating-point division
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Forward and Reverse Converters and Moduli Set Selection in Signed-Digit Residue Number Systems
Journal of Signal Processing Systems
CORDIC architectures: a survey
VLSI Design
VLSI architecture for low latency radix-4 CORDIC
Computers and Electrical Engineering
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Signed-digital number representation systems have been defined for any radix r驴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. 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 original definition of signed-digit arithmetic precludes the case of r=2 for which alpha cannot be selected in the proper range. Binary signed-digit numbers are known to allow limited-carry propagation with a somewhat more complex addition process. The author shows that a special 'recorded' representation of binary signed-digit numbers not only allows for carry-free addition and borrow-free subtraction but also offers other important advantages for the practical implementation of arithmetic functions. The recoding itself is totally parallel and can be performed in constant time, independent of operand lengths. It is also shown that binary signed-digit numbers compare favorably to other redundant schemes such as stored-carry and higher radix signed-digit representations.