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.