Data Structures and Algorithms

Implementation of Basic Arithmetic Operations in the Scaled Bergman Number System (SBNS)

Authors: Andrey V. Voron
Comments: 5 Pages.

The paper examines the algorithmic specifics of performing basic arithmetic operations in the Scaled Bergman Number System (SBNS) with a fixed weight scale factor of k = 0.2. The mechanisms for implementing linear operations (addition and subtraction) are analyzed, and the specific hardware phases for executing non-linear operations — multiplication and division under conditions of a scaled basis shift — are decomposed and described in detail. Using a concrete example of bitwise numerical multiplication, the operation of a two-phase arithmetic logic unit (ALU) utilizing a cyclic multiplier by a constant of 5 for scale code correction is demonstrated. A three-stage division cycle is described that employs a hardware parity filter to eliminate redundancy and ensure a fast, unambiguous bitwise comparison operation.
Category: Data Structures and Algorithms