## 1 Introduction
Some capabilities of the digital implementation are its high-degree of flexibility, reduced timing process, and power supply. In this approach, using programmable boards such as FPGAs can be very fast and flexible. This paper presents a hardware implementation of the DSSN model in the case of a digital system. The basic challenge of this realization is the quadratic term of the original neuron model. In the general case, the quadratic term (because of its multiplier operation) causes the speed-down in the final system. In other words, in the CNS, the speed of the neuronal activity is a very important factor. If the final system does not have an acceptable frequency, it influences the neural system. Thus, this nonlinear term must be removed or converted to another simple term. Different approaches can be applied to obtain simple mathematical equations. Among these approaches, converting the quadratic terms to hyperbolic functions may be the best way. Indeed, by converting the nonlinear terms of the original model to a set of hyperbolic functions, we have a new model (by protecting all behaviors of the original mode) which converts all multiplier operations to a set of digital SHIFTs and ADDs (This method will be explained). Consequently, using the proposed new model, we have a low-cost, high-speed, and high-efficiency system which can trace the original neuron model with a high-degree of similarity and performances. The overall method for implementing the neuronal networks can be explained. The efficient modeling, simulation, and implementation of biological neural networks are significant. Neuromorphic engineering is a very significant subject that takes inspiration from biology, physics, mathematics, computer science, and electronic engineering to design neural systems. In the field of biology and biomedicine, the theoretical and experimental aspects of neuroscience are evaluated to have a better understandings of the brain structure. Consequently, studying, modeling, simulation, and implementing brain-like systems to realize the brain behaviors are a vital requirement. At first step, it is necessary that the neuron model is selected. In this approach, many different neuron models have been presented for spiking neural networks to reproduce their dynamical behavior. Some neuron models have biological behaviors and other models reproduce the spiking patterns of the human brain. The DSSN neuron model is a widely accepted model that can reproduce the spiking patterns of the brain. After model selection, the time domain and dynamical behaviors of the proposed neuron model have been evaluated. Indeed, the proposed model is a modified case of the basic neuron model with low-error state and low-cost hardware attributes. Since the original models have nonlinear terms and functions with high-cost realizations, it is necessary that the model is modified to a new low-cost model for its implementation on hardware platforms. To validate the proposed model in case of following the original model, spiking patterns and dynamics must be considered. These evaluations have been performed using MATLAB software simulations. Finally, to test and validate the proposed model in hardware form, we have used the FPGA system design. In fact, the Hardware Description Language (HDL) of the proposed neuron model has been considered using the ModelSim and Xilinx ISE software. In this part, the proposed model's overhead costs have been compared to the original model cost realization. The proposed model must be more efficient in comparison with the original model in case of overhead costs (overall saving in FPGA) and speed-up (maximum frequency). This paper is organized as follows. In Section 2, the background of the DSSN model will be explained. In Section 3, the proposed procedure is evaluated. Section 4 presents the dynamic behaviors and time domain analysis. Synaptic coupling is described in Section 5. Overall hardware implementation is performed in Section 6 in detail. Production results are presented in Section 7.