Number Systems

Mathematical Principles & Theorems

Explores positional, historical, and non-standard numeral bases: (1) Standard bases 2 to 64; (2) Negative bases (nega-binary \(b=-2\), nega-decimal \(b=-10\)) representing signed integers without explicit sign bits; (3) Bijective base-26 (A–Z without zero digit); (4) Phinary (base-\(\phi\) using golden ratio \(\phi = \frac{1+\sqrt{5}}{2}\) and Bergman representation); (5) Roman numerals with vinculum multipliers; (6) Japanese Soroban abacus arithmetic.

Operating Instructions

• Use the top tabs to switch between Base Calculator, Radix Converter, Exotic Bases, Roman Numerals, and Abacus.
• Enter values in the parameter inputs to compute representations across multiple radices simultaneously.
• For the Abacus: Click upper deck (value 5) and lower deck (value 1) beads toward the beam to register values.
• Inspect the step-by-step arithmetic factoring and radix expansion equations.