A new formulation of fast diminished-one multioperand modulo 2n+1 adder

We introduce a new concept of composite carry-save adders with complementary end-around carry (CCSA with CEAC) to model the multioperand modulo 2ⁿ+1 adder. The CCSA with CEAC is a combination of CSA with EAC and a constant residue counter, where the latter is used to account for the intrinsic residues generated by the diminished-one modulo 2ⁿ+1 additions at various levels of the multioperand modulo adder (MOMA). With the proposed reduction rules, we prove that the companion residue counter tree can be eliminated. The resultant architecture is a universal structure for the diminished-one multioperand modulo 2ⁿ+1 adder, consisting of only a CSA with CEAC tree and a 2-input diminished-one adder. The latter can be implemented by any of the efficient solutions reported in the literature, which make the proposed structure operates as fast as the high-speed modulo 2ⁿ-1 MOMA.