Automated Synthesis of Compact Multiplier Circuits for in-Memory Computing using ROBDDs

With Moore's law approaching physical limitations of transistor size, researchers have started exploring unconventional ways for performing computing. This has led to the discovery of several emerging devices for computing. One such recently discovered device is memristor; it can be used both for storage and in-memory computing. It can also be easily mass produced in the form of compact crossbars. In this work, we are proposing a generalized approach for in-memory computing of boolean functions on memristor crossbars. Existing techniques for in-memory computing using memristors either stop short of utilizing full potential of crossbars, or they have huge space or time complexity. Our flow based approach uses reduced ordered binary decision diagrams to control sneak paths in crossbars. Moreover, we have also proposed a simple efficient algorithm for mapping reduced ordered binary decision diagrams based memristive circuits onto crossbars. Consequently, our approach is not only capable of benefiting from economy of scale of massively producible compact crossbars, it is also computationally less intensive. Thus, it can be used for synthesizing crossbars for far more complex functions than the existing approaches. Additionally, we have also derived upper bound on function size that can be computed on a given crossbar. We have demonstrated our approach by designing eight crossbars for in-memory computing of all eight output bits of four bit multiplier.