In this paper, we utilize a reconfigurable artificial neural network (RANN) to design digital logic gates, which serve as the fundamental components of a digital subsystem. We achieve hardware implementation of AND, OR, and Inverter (AOI) gates through both single and multi-layer perceptron models using feed-forward neural networks (FFNNs). The FFNNs are trained using Python and MATLAB. We apply the proposed AOI gates methodology via RANN to design the XOR gate, considering it as a combinational circuit. This technique is developed in Verilog for testing using Field-Programmable Gate Array (FPGA). Additionally, we present the register-transistor logic (RTL) design results for the individual gates and the AOI model to investigate resource utilization—including DSP slices, LUTs, flip-flops—and the dynamic power consumption of the ZYNQ ZedBoard. Furthermore, our methodology offers a foundation for generating new methods for VLSI system design on dedicated hardware like FPGA in the future, providing a more flexible and efficient system design approach with reduced development time.