Edinburgh Napier University

  A number of different representations of the Boolean function are used in order to find a good circuit representation in terms of area, speed and power performance. In this paper, an effective decomposition method is proposed for the bidirectional transformation between Reed-Muller (RM) and the Dual Form of Reed-Muller (DFRM) expansions with the same fixed polarity. An efficient algorithm is then employed to find a good efficient solution while avoiding the time consuming exhaustive search. Traditionally, conversion from RM expansion to DFRM or from DFRM expansion to RM is achieved using the transformation matrix. In the proposed method, the matrix is recursively decomposed into smaller matrices. The calculation of the duplicated matrix is avoided, resulting in reduced memory space and computation time. The experimental results show that the method achieves CPU time within the range of a few seconds even for large variable functions.