This paper develops path concepts for the execution of different algorithms on a reconfigurable architecture. New architecture concepts demand for permanent evaluation of such extensions, also including validating case studies. The recently patented synchronous bit-serial pipelined architecture, which we investigate in this paper, comprises synchronous and systematic bit-serial processing without a central controlling instance. It targets future high speed applications due to the abdication of long wires. The application specificity of the basic version of the architecture can be overcome by so called routers, achieving a reconfigurable system. This paper focuses on the difficulty to conceptualize these routers and proposes several variations for implementation. The case study, which comprises a combined version of the FDCT/IDCT algorithm, serves as an application example for the reconfigurability of the architecture.