In summary, we have proposed and modelled a novel design of a non-volatile broadband hybrid EO plasmonic switch based on an electrically controlled phase change material ‘GST’ embedded in a plasmonic slot waveguide. The proposed switch exhibits excellent performance in several important categories, including large extinction ratio (> 28 dB), high bandwidth (BW > 400 nm), low power consumption, and low footprint (length of the GST is 0.5 µm). The structures proposed in this paper are easy to fabricate and are compatible with non-volatile photonic integrated circuits and silicon photonics. Using this hybrid plasmonic switch as an active element, other EO switches based on ring resonators and MZIs have also been proposed. It was demonstrated that basic logic gates (i.e. NOT, AND, OR, NAND, NOR, XOR and XNOR), a plasmonic combinational logic circuit such as a 1-bit half adder circuit, as well as plasmonic asynchronous sequential latch circuits (i.e., SR, JK, D, and T latch) can be implemented using the plasmonic switches as the active elements. These devices can be useful in the fields of optical computing, optical memories, in-memory computation, and signal processing.