Converter Traversal Using Power of Two Bit Operations

The patent changes the parameter representation from decimal-based division/modulo operations to binary-based bit manipulation operations. By representing page numbers in binary format, the patent transforms complex arithmetic operations into simple bit-shifting and masking operations, maintaining accuracy while dramatically improving computational speed.

The patent substitutes the mechanical arithmetic system (division and modulo operations) with a more efficient electronic/bit-level operation system. Instead of performing sequential arithmetic calculations, the patent uses parallel bit manipulation operations that can be executed more rapidly by modern processors, effectively replacing a computationally intensive mechanism with a lighter-weight alternative.

The patent introduces a new parameter representation where page numbers are expressed in binary format with specific bit positions representing different hierarchical levels. By changing how page numbers are represented and interpreted, the patent enables flexible page organization without requiring power-of-two branch sizes, while the bit manipulation operations keep the determination process relatively simple.

The patent segments the binary representation of page numbers into distinct bit fields, where different segments correspond to different levels of the converter tree. This segmentation allows the system to handle variable branch sizes by selectively using different portions of the binary representation, maintaining adaptability while simplifying the identification process through structured bit field manipulation.