Abstract : Memristors indeed represent a growing area with a range of intriguing properties, rendering them valuable for both storage and computing high level applications. To leverage memristor logic in complex Neuromorphic Computing Systems, particularly in models like Memristor-based Neural Networks for optimizations, the integration of high-speed and low-latency sub-systems such as adders and multipliers becomes crucial. The inherent properties of memristors, coupled with their ability to perform various logic operations, make them well-suited for the demands of neuromorphic computing, where parallelism, efficiency, and adaptability are paramount. By harnessing memristors in adders and multipliers, these systems can achieve enhanced computational capabilities, supporting the development of efficient and powerful neural network models. As first cut of this work, The design of a memristor was evaluated in terms of current, voltage, and resistance using the MATLAB tool, with its performance thoroughly analyzed. Subsequently, a high-speed, low-latency multiplier with enhanced throughput was implemented, accompanied by a detailed examination of its benefits and its integration with Content Addressable Memory (CAM). High-speed memory CAM and fundamental arithmetic operations are integrated to enhance the Artificial Neural Network (ANN) model. In order to gain a deeper understanding of mathematical models, their features, and strategy aspects, comprehensive comparative analyses are conducted and essential metrics, such as Figures of Merit, are used to validate the suggested system. The design initially synthesized in Cadence Genus tool and using MATLAB validated the fundamental properties of the memristor and synthesized it in the Vivado Design Suite 2018.1 platform, the efficacy of the suggested design is demonstrated and contrasted with theoretical computations based on the hardware utilization, speed, throughput, and latency results.