What question did this study set out to answer?

The aim is to introduce a new numeration system that improves upon standard positional notations.

May 17, 2026Open Access

Bentu Numeration System (BNS)

Key Points

The aim is to introduce a new numeration system that improves upon standard positional notations.
Defined five foundational rules governing the system.
Established five theorems with proven properties for the numeration framework.
Conducted computational verification to validate the system's arithmetic properties.
Demonstrated elegant arithmetic properties through the new system.
Outlined natural divisibility rules that allow for easy inspection.
Shown compatibility with standard base 10 arithmetic, enhancing its usability.

Abstract

Bentu Numeration System (BNS) is a novel positional numeration framework in which every base N employs digits 0 through N — one more digit than standard positional notation. This single extension produces a coherent system with elegant arithmetic properties: a shifted carry threshold, natural divisibility rules readable by inspection, compact representation of powers, and full compatibility with standard base 10 arithmetic. Five foundational rules define the system, and five theorems — each with proof and computational verification — establish its key properties.

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