The on-going research for low power, faster operation speed nonvolatile memory device with tremendous packing density has attracted the researchers towards the evolution of a new nanoscale solid state ionic device, in particular memristor for future modern electronic systems. Memristor (the so called Resistive Random Access Memory (ReRAM)) is the promising candidate for the replacement of conventional memory technologies facing major design issues related to continuous scaling down of the device. This paper focuses on the implementation of 1-bit Arithmetic Logic Unit (ALU) using memristors based on Voltage Threshold Adaptive Memristor (VTEAM) model in Cadence Virtuoso environment. Considering the size of Memristor in nano regime helped in decreasing the feature size thus enhancing the density. This will lead to reduction of the die area in comparison to Complementary Metal Oxide Semiconductor (CMOS) based ALU.