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On the sparsity of binary numbers

Meijun Zhu

TL;DR

It is demonstrated that every binary number can be transformed into a sparse form, significantly enhancing computational speed by converting binary numbers into this form.

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.

On the sparsity of binary numbers

TL;DR

It is demonstrated that every binary number can be transformed into a sparse form, significantly enhancing computational speed by converting binary numbers into this form.

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.

Paper Structure

This paper contains 3 sections, 1 theorem, 14 equations.

Table of Contents

  1. Introduction and motivation
  2. Main result: Sparsity on binary numbers
  3. Conclusion and outlook

Key Result

Theorem 2.2

Every binary number has a unique sparse form.

Theorems & Definitions (3)

  • Definition 2.1
  • Theorem 2.2
  • Remark 2.3