Inter-processing element communication encounters significant hurdles arising from constraints in power consumption, physical space, and data transfer speed. Storing data packets temporarily during communication uses a lot of the chip's power. Many contemporary network-on-chip (NoC) architectures are heavily resource-intensive due to the extensive use of router buffers. Eliminating these buffers and virtual channels can streamline router design and reduce power consumption. The routing and arbitration strategies implemented within a NoC router are pivotal for optimizing the overall performance of the NoC mesh. The routing algorithm plays a critical role in NoC systems, as it is responsible for balancing traffic load across network channels, even in scenarios of asymmetric traffic distribution. This paper introduces a model for X-Y routing algorithms, specifically tailored for implementation on FPGA platforms utilizing a flexible state diagram. The distinctive contribution of this research lies in its synthesis and optimized realization of the X-Y routing algorithm on FPGAs, providing Network-on-Chip (NoC) designers with a robust framework for developing efficient routers tailored to their FPGA architectures.