Dual logic based polarity conversion and polarity optimization method is proposed for logic synthesis of mixed polarity RM (Reed-Muller) circuits.The correctness of the proposed method is proved in theory

and the validity and feasibility is verified by experiments.The proposed method can contribute to applying the methods for polarity conversion and optimization of MPRM (Mixed-Polarity RM) to MPDRM (Mixed-Polarity Dual form of RM).The results of mapping to FPGA (Field Programmable Gate Array) after logic synthesis for fifteen XOR-based logic circuits from MCNC show that on average

compared to the FPGA implementations of optimized designs obtained by logic synthesis tools such as Espresso and ABC

mixed polarity RM circuits have superiority in area and speed

and MPDRM circuits can achieve optimal FPGA implementations.