Hybrid number representations with bounded carry propagation chains

A novel, hybrid number representation is proposed. It includes the two's complement representation and the signed-digit representation as special cases. Such a hybrid representation is capable of bounding the maximum 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 one and the entire word length. The framework reveals a continuum of number representations between the two extremes 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.<
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