On-the-fly conversion of redundant into conventional representations
IEEE Transactions on Computers
A General Proof for Overlapped Multiple-Bit Scanning Multiplications
IEEE Transactions on Computers
Generalized Signed-Digit Number Systems: A Unifying Framework for Redundant Number Representations
IEEE Transactions on Computers
The Set Theory of Arithmetic Decomposition
IEEE Transactions on Computers
A Spanning Tree Carry Lookahead Adder
IEEE Transactions on Computers - Special issue on computer arithmetic
Journal of the ACM (JACM)
IEEE Transactions on Computers
Redundant Radix Representations of Rings
IEEE Transactions on Computers
On-the-Fly Algorithms and Sequential Machines
IEEE Transactions on Computers
Constant-Time Addition and Simultaneous Format Conversion Based on Redundant Binary Representations
IEEE Transactions on Computers
Further Reducing the Redundancy of a Notation Over a Minimally Redundant Digit Set
Journal of VLSI Signal Processing Systems
Minimal Weight Digit Set Conversions
IEEE Transactions on Computers
Constant-time addition with hybrid-redundant numbers: Theory and implementations
Integration, the VLSI Journal
A fully redundant decimal adder and its application in parallel decimal multipliers
Microelectronics Journal
A new redundant binary booth encoding for fast 2n-bit multiplier design
IEEE Transactions on Circuits and Systems Part I: Regular Papers
An improved maximally redundant signed digit adder
Computers and Electrical Engineering
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The problem of digit set conversion for fixed radix is investigated for the case of converting into a non redundant, as well as into a redundant, digit set. Conversion may be from very general digit sets, and covers as special cases multiplier recodings, additions, and certain multiplications. We generalize known algorithms for conversions into non redundant digit sets, as well as apply conversion to generalize the O(log n) time algorithm for conditional sum addition using parallel prefix computation, and a comparison is made with standard carry-lookahead techniques. Examples on multi-operand addition are used to illustrate the generality of this approach. O(1) time algorithms for converting into redundant digit sets are generalized based on a very simple lemma, which provides a framework for all conversions into redundant digit sets. Applications in multiplier recoding and partial product accumulation are used as exemplifications.