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As the CMOS technology is gradually scaling down to inherent physical device limits, significant challenges emerge related to scalability, leakage, reliability, etc. Alternative technologies are under research for next-generation VLSI circuits. Memristor is one of the promising candidates due to its scalability, practically zero leakage, non-volatility, etc. This paper proposes a novel design methodology for logic circuits targeting memristor crossbars. This methodology allows the optimization of the design of logic function, and their automatic mapping on the memristor crossbar. More important, this methodology supports the execution of Boolean logic functions within constant number of steps independent of its functionality. To illustrate the potential of the proposed methodology, multi-bit adders and multipliers are explored; their incurred delay, area and energy costs are analyzed. The comparison of our approach with …