Data Structures and Algorithms

Scaled Bergman Numeral System (SBNS) and a New Filter as a New Basis for Computing

Authors: Andrey V. Voron
Comments: 14 Pages.

The paper proposes and formalizes the Scaled Bergman Numeral System (SBNS) — a new numerical basis for computing that utilizes an irrational base (the golden ratio) and a fixed weight scale factor of k = 0.2. This approach aims to overcome the physical limitations of the von Neumann architecture. The introduction of the 0.2 scale factor successfully eliminates the primary drawbacks of the traditional Bergman system: the "wandering carry effect" and the "infinite information tail". The paper demonstrates the invariance of the sum of truncated weights of active digits for a pair of valid code states (the working code "A" and the check code "B") isolated by the hardware filter. It is also shown that within the SBNS framework, fractional noise and rounding errors mutually cancel each other out.
Category: Data Structures and Algorithms