Hybrid Number Representations with Bounded Carry Propagation Chains

rl novel, hybrid number representation is proposed in this paper. It includes the two’s complement representation and the signed-digit representation ar special cases. Such a hybrid representation is capable of bounding the mazimum length of carry propagation chains during addition. Thus, one can select a specific hybrid number representation that limits the maximum length of all the carry propagation chains to any desired value between 1 and the entire word length. The framework reveals a continuum of number representations between the two eztnimes of two’s complement and signed-digit number systems and allows a unified performance analysis of the entire spectrum of adders based on the representation selected. 1