Representation of complex numbers in redundant numeration systems

This is my work-in-progress bachelor's degree project. It's available both in PDF and in HTML (as a website).


Understanding this project requires a basic understanding of calculus (complex numbers, limits), discrete mathematics (modular arithmetic, solving linear recurrences), linear algebra (vectors, matrices) and graph theory (graphs, adjacency matrices). No knowledge about the specific topic (positional numbering systems) is required.

PDF version

The PDF version is available here.

HTML version — chapters

  1. Introduction
  2. Basics
  3. NAF and 3-NAF representations of complex integers
  4. Counting optimal representations
  5. w-NAF representations of quaternions
  6. Conclusion