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Formal Analysis of Hybrid Prefix/Carry-Select Arithmetic Systems

Arithmetic circuits play an important role in high-performance digital systems. The paper considers a generic architecture of hybrid prefix/carry-select arithmetic systems. A novel proof methodology is proposed to model and verify hybrid addition systems. Algebraic structures and first-order recursive equations are harnessed in proof derivations. Case studies on several typical classes of hybrid prefix/carry-select adders and special cases with pseudo-carries such as Ling's carry demonstrate the effectiveness of the proposed approach.