Register binding is a fundamental optimization problem in high-level synthesis, primarily aiming to minimize the number of employed registers while ensuring circuit functionality. Conventional approaches attempt to apply register allocation algorithms from compilers to register binding, but they often overlook the inherent disparities between the allocation and binding problems. Finally, this introduces additional resource constraints during the binding and utilizes compilation optimization techniques that are unsuitable for digital circuit design, causing resource waste. To this end, this study transforms the register binding problem into a continuous multicoloring one and proposes a heuristic solving method that combines the bit width and vertex degrees. This method provides a more fine-grained characterization and modeling of variables in information such as the bit width and live intervals, which further reduces register resource overhead compared to existing methods, without the insertion of additional instructions. Meanwhile, a comparison is conducted between the proposed algorithm and two typical algorithms. Experimental results demonstrate that the proposed algorithm yields a theoretically optimal solution in 96.72% of the test cases in the MiBench benchmark, improving 31.5% and 25.1% over other methods respectively. In the Rosetta benchmark, this algorithm consistently exhibits the optimal solution across all test cases, outperforming the other two methods by 7.41% and 7.39% respectively.