By reaching to the CMOS scaling limitation based on the Moore's law and due to the increasing disparity between the processing units and memory performance, the quest is continued to find a suitable alternative to replace the conventional technology. The recently discovered two terminal element, memristor, is believed to be one of the most promising candidates for future very large scale integrated systems.;This thesis is comprised of two main parts, (Part I) modeling the memristor devices, and (Part II) memristive computing. The first part is presented in one chapter and the second part of the thesis contains five chapters. The basics and fundamentals regarding the memristor functionality and memristive computing are presented in the introduction chapter. A brief detail of these two main parts is as follows:;Part I: Modeling- This part presents an accurate model based on the charge transport mechanisms for nanoionic memristor devices. The main current mechanism in metal/insulator/metal (MIM) structures are assessed, a physic-based model is proposed and a SPICE model is presented and tested for four different fabricated devices. An accuracy comparison is done for various models for Ag/TiO2/ITO fabricated device. Also, the functionality of the model is tested for various input signals.;Part II: Memristive computing- Memristive computing is about utilizing memristor to perform computational tasks. This part of the thesis is divided into neuromorphic, analog and digital computing schemes with memristor devices.;-- Neuromorphic computing- Two chapters of this thesis are about biological-inspired memristive neural networks using STDP-based learning mechanism. The memristive implementation of two well-known spiking neuron models, Hudgkin-Huxley and Morris-Lecar, are assessed and utilized in the proposed memristive network. The synaptic connections are also memristor devices in this design. Unsupervised pattern classification tasks are done to ensure the right functionality of the system.;-- Analog computing- Memristor has analog memory property as it can be programmed to different memristance values. A novel memristive analog adder is designed by Continuous Valued Number System (CVNS) scheme and its circuit is comprised of addition and modulo blocks. The proposed analog adder design is explained and its functionality is tested for various numbers. It is shown that the CVNS scheme is compatible with memristive design and the environment resolution can be adjusted by the memristance ratio of the memristor devices.;-- Digital computing- Two chapters are dedicated for digital computing. In the first one, a development over IMPLY-based logic with memristor is provided to implement a 4:2 compressor circuit. In the second chapter, A novel resistive over a novel mirrored memristive crossbar platform. Different logic gates are designed with the proposed memristive logic method and the simulations are provided with Cadence to prove the functionality of the logic. The logic implementation over a mirrored memristive crossbars is also assessed.
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