Modulo 2n−2 arithmetic units

A modulo 2ⁿ-2 value has been proposed in Residue Number System (RNS)-based systems for the design of FIR filters and communication components. However, all modulo 2ⁿ-2 arithmetic units that were used have been based either on look-up tables or on generic modulo arithmetic structures. In this work we propose novel modulo 2ⁿ-2 adder, multiplier as well as residue generation architectures that take advantage of the inherent properties of modulo 2ⁿ-2 arithmetic. The proposed circuits are based on corresponding circuits for modulo 2^n-1-1 arithmetic and some simple logic resulting that way to efficient implementations regarding the area, delay and average power dissipation. The evaluation and experimental results of the proposed circuits confirm their efficiency.