TABLE OF CONTENTS Numerous algorithms for fast addition, as well as other arithmetic operations, have been developed and implemented since the early days of digital computers, and newer ones are still being proposed. The main reason for the continuing research and development of new algorithms for the basic arithmetic operations is the rapid change in the technology that is used to implement them. An algorithm that can be optimally implemented in one technology is not necesarily the best in a different technology. Consequently, designers need to continuously reevaluate the available algorithms for a certain arithmetic operation and their suitability to the current technology.
In addition to the dependence on the technology employed for the implementation of the algorithm, the performance of a given algorithm is heavily affected by the unique features of the algorithm itself and/or the number system used to represent the operands and results. Thus, many studies have been performed that compare various algorithms in an effort to determine which will perform better, preferably independently of the technology used for the implementation. More importantly, the objective of some studies was to find the limit (bound) on the performance of any algorithm in executing a given arithmetic operation.
The execution time of addition, being highly dependent on the way carries are propagated, can reach its minimum in algorithms, which avoid the propagation of carries altogether, or incur a very limited carry-propagation. Therefore, number systems that are characterized by almost carry-free addition, can provide optimal algorithms...
