Graph based Synthesis for Low power Combinational logic with a maximal/minimal disjoint Function Set

This paper discusses a new, systematic approach to the synthesis of a class of non-regenerative Boolean networks, described by FON[FOFF]={mi}[{Mi}], where for every mj[Mj]∈{mi}[{Mi}], there exists another mk[Mk]∈{mi}[{Mi}], such that their Hamming distance HD(mj, mk)=HD(Mj, Mk)=O(n), (where ‘n ’ represents the number of distinct primary inputs). The method automatically ensures exact minimization for certain important self-dual functions with 2n-1 points in its one-set. The elements meant for grouping are determined from a newly proposed weighted adjacency matrix. Then the binary value corresponding to the candidate pair is correlated with another proposed binary information matrix to enable synthesis. The algorithm can be implemented in any high level language and achieves best cost optimization for the problem dealt with, irrespective of the number of inputs. For other cases, the method is iterated to reduce it to a problem of O(n-1), O(n-2),…. and then solved. In addition, it leads to optimal results for problems exhibiting higher degree of adjacency, compatible with standard synthesis methods. Circuit level simulations demonstrate mean savings in power, gate and literal counts by 11.7%, 29.4 % and 4.8 % respectively, over a wide range of examples compared with other existing techniques