Novel Synthesis and Optimization of Multi-Level Mixed Polarity Reed-Muller Functions

Reed-Muller logic is becoming increasingly attractive. However, its synthesis and optimization are difficult especially for mixed polarity Reed-Muller logic. In this paper, a function is expressed into a truth vector. Product shrinkage, general sum shrinkage (GSS), elimination and extraction operators are proposed to shrink the truth vector. A novel algorithm is presented to derive a compact Multi-level Mixed Polarity Reed-Muller Form (MMPRMF) starting from a given fixed polarity truth vector. The results show that a significant area improvement can be made compared with published results. Supported in part by the National Natural Science Foundation of China (NSFC) under Grant No.60273093 and in part of the China-UK joint project supported by the NSFC and the Royal Society of the UK.