On the sparsity of binary numbers

TL;DR

This paper introduces a method to convert binary numbers into a sparse form using negative coefficients, which significantly improves computational efficiency in binary systems.

Contribution

It presents a novel approach to transform binary numbers into a sparse representation using negative coefficients, enhancing computational speed.

Findings

Binary numbers can be transformed into a sparse form.

Sparse binary representations improve computational efficiency.

The method applies to decimal and binary systems.

Abstract

We introduce the concept of negative coefficients in various number-based systems, with a focus on decimal and binary systems. We demonstrate that every binary number can be transformed into a sparse form, significantly enhancing computational speed by converting binary numbers into this form.