The neuron can be called the main cell of a nervous system that can transmit messages from one neuron to another neuron or another cell through electrical signals. In neuromorphic engineering, the hardware realization and simulation of these neurons are crucial. To accomplish a proper digital implementation (i.e. reducing hardware resources and increasing speed and accuracy) of three important neuron models including Hodgkin-Huxley, Morris-Lecar, and Izhikevich, this study proposes a set of multiplier-less mathematical equations based on converting nonlinear functions to 2x functions. Then optimizes the proposed equations based on reducing the number of different 2x terms. The suggested model can accurately recreate the behavioral characteristics of the original neuron models. The suggested model was synthesized and implemented on the Zynq XC7Z010 (3CLG400) reconfigurable board (FPGA) to validate the mathematical simulation findings. The results of hardware synthesizing and implementations of the proposed model show that different biological behavior can be replicated with greater efficiency and at substantially reduced implementation costs. This method (implemented on the zynq board) can raise the frequency of the proposed models at least by up to 3.5 times that of the original model and reduce power consumption between 20% and 60% for different proposed models. Also, due to the reduction of hardware resources in the proposed model, it is possible to implement a much larger number of neurons (between 4 and 12 times) relative to the original model on a single zynq board.
