This work presents the first fabricated electrophysiology-optogenetic closed-loop bidirectional brain-machine interface (CL-BBMI) system-on-chip (SoC) with electrical neural signal recording, on-chip sleep staging and optogenetic stimulation. The first multiplexer with static assignment based table lookup solution (MUXnet) for multiplier-free NN processor was proposed. A state-of-the-art average accuracy of 82.4% was achieved with an energy consumption of only 0.2$μ$J/class in sleep staging task.