Fig. 1.
Definition of $p_{i}$ = 0(1, 2).
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| Citation: |
Pengjun Wang, Zhenhai Wang, Rui Xu, Zhidi Jiang, Disheng Wang. Conversion algorithm for MPRM expansion[J]. Journal of Semiconductors, 2014, 35(3): 035007. doi: 10.1088/1674-4926/35/3/035007
P J Wang, Z H Wang, R Xu, Z D Jiang, D S Wang. Conversion algorithm for MPRM expansion[J]. J. Semicond., 2014, 35(3): 035007. doi: 10.1088/1674-4926/35/3/035007.
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Abstract
Conversion of the Reed-Muller (RM) expansion between two different polarities is an important step in the synthesis and optimization of RM circuits. By investigating XOR decomposition, a new conversion algorithm is proposed to convert MPRM expansion from one polarity to another. First, the relationship between XOR decomposition and mixed polarity is set up. Second, based on this, the operation relation of term coefficients between the two polarities is derived to realize MPRM expansion conversion. And finally, with the MCNC Benchmark, the results of our algorithm show that it is more suitable for dealing with MPRM expansion with more terms. Compared to the previous tabular technique, the conversion efficiency is improved up to approximately 44.39%. -
References
[1] Hirayama T, Nishitani Y. Exact minimization of andexor expressions of practical benchmark functions. Journal of Circuits, Systems and Computers, 2009, 18(3):465 doi: 10.1142/S0218126609005356[2] Rahaman H, Das D K, Bhattacharya B B. Testable design of AND-EXOR logic networks with universal test sets. Computers and Electrical Engineering, 2009, 35(5):644 doi: 10.1016/j.compeleceng.2009.01.006[3] Mizuki T, Tsubata H, Nishizeki T. Minimizing AND-EXOR expressions for two-variable multiple-valued input binary output functions. Journal of Multiple-Valued Logic and Soft Computing, 2010, 16(1/2):197 http://dblp.uni-trier.de/db/journals/mvl/mvl16.html#MizukiTN10[4] Pradhan S N, Chattopadhyay S. Two-level AND-XOR network synthesis with area-power trade-off. International Journal of Computer Science and Network Security, 2008, 8(9):365 http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.385.8574&rep=rep1&type=pdf[5] Wang L, Almaini A E A. Optimisation of Reed-Muller PLA implementations. IEE Proceedings:Circuits, Device and System, 2002, 149(12):119 http://ieeexplore.ieee.org/xpl/abstractAuthors.jsp?reload=true&arnumber=1020018&filter%3DAND%28p_IS_Number%3A21944%29[6] Wang L, Almaini A E A. Exact minimisation of large multiple output FPRM functions. IEE Proceedings:Computers and Digital Techniques, 2002, 149(5):203 doi: 10.1049/ip-cdt:20020674[7] Jassani B A Al, Urquhart N, Almaini A E A. Optimization of MPRM functions using tabular techniques and genetic algorithms. The Mediterranean Journal of Electronics and Communications, 2008, 4(4):115 http://researchrepository.napier.ac.uk/id/eprint/3499[8] Zhang, J S, Chrzanowska-Jeske M, Mishchenko A, et al. Linear cofactor relationships in Boolean functions. IEEE Trans Computer-Aided Design of Integrated Circuits and Systems, 2006, 25(6):1011 doi: 10.1109/TCAD.2005.855951[9] Jassani B A Al, Urquhart N, Almaini A E A. Manipulation and optimisation techniques for Boolean logic. IET Computers and Digital Techniques, 2010, 4(3):227 doi: 10.1049/iet-cdt.2009.0007[10] Yu H Z, Wang P J, Wang D S, et al. Discreteternary particle swarm optimization for area optimization of MPRM circuits. Journal of Semiconductors, 2013, 34(2):025011 doi: 10.1088/1674-4926/34/2/025011[11] Yang M, Wang L, Tong J R, et al. Techniques for dual forms of Reed-Muller expansion conversion. Integration, the VLSI Journal, 2008, 41(1):113 doi: 10.1016/j.vlsi.2007.02.001[12] Wang Pengjun, Li Hui, Wang Zhenhai. Tabular techniques for mixed-polarity and its application in area optimization of MPRM circuits. Chinese Journal of Computer-Aided Design & Computer Graphics, 2011, 23(3):527 doi: 10.1007/s11390-017-1723-1 -
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