Memristors show great potential for being integrated into CMOS technology and provide new approaches for designing computing-in-memory (CIM) systems, brain-inspired applications, trimming circuits and other topologies for the beyond-CMOS era. A crucial characteristic of the memristor is multi-state 1 switching. Memristors are capable of representing information in an ultra-compact fashion, by storing multiple bits per device. However, certain challenges remain in multistate memristive circuits and systems design such as device stability and peripheral circuit complexity. In this paper, we review the state of the art of multi-state memristor technologies and their associated CMOS/Memristor circuit design, and discuss the challenges regarding device imperfection factors, modelling, peripheral circuit design and layout. We present measurement results of our in-house fabricated multi-state memristor as an example to further illustrate the feasibility of applying multistate memristors in CMOS design, and demonstrate their related future applications such as multi-state memristive memories in machine learning, memristive neuromorphic applications, trimming and tuning circuits, etc. In the end, we summarize past and present efforts done in this field and envisage the direction of multi-state memristor related research.

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