Residue Number Systems (RNS) offer efficient modular arithmetic and natural parallelism, but direct integer division in RNS remains a difficult and comparatively underdeveloped operation. This paper builds on the type-II division algorithm of Szabo and Tanaka and reformulates it for more efficient hardware implementation. A principal contribution is the introduction of a power-based RNS, in which moduli are selected as powers of natural primes, increasing dynamic range, improving bit efficiency, and providing greater flexibility for scaling during division. The paper further formalizes three decomposition methods required by the division process: multi-factor scaling for modulus-based division, mixed-radix conversion for base extension and comparison, and a new divisor decomposition method introduced in this work. Each method is supported by mathematical development, including analysis of modulus invalidation during computation. These results simplify the hardware structure of the algorithm and improve its scalability. Supported by hardware diagrams and performance tables, the work advances both the theory and practical implementation of direct RNS division.

翻译：残数系统（RNS）提供高效的模运算和天然的并行性，但RNS中的直接整数除法仍然是一个困难且相对不成熟的操作。本文基于Szabo和Tanaka的II型除法算法进行重构，以实现更高效的硬件实现。主要贡献在于引入了一种基于幂的残数系统，其中模数被选为自然素数的幂，从而增加了动态范围、提高了比特效率，并为除法过程中的缩放提供了更大的灵活性。本文进一步形式化了除法过程所需的三种分解方法：基于模数除法的多因子缩放、用于基扩展和比较的混合基数转换，以及本文引入的一种新的除数分解方法。每种方法都得到了数学推导的支持，包括对计算过程中模数失效的分析。这些结果简化了算法的硬件结构并提高了其可扩展性。在硬件框图和性能表格的支持下，本文推进了直接RNS除法的理论和实际实现。