Base Converter

Mathematical Principles & Theorems

Converts numbers between arbitrary radices \(b_1\) and \(b_2\). Conversion from source base \(b_1\) to intermediate decimal \(D\) uses Horner's method: \(D = (\dots((d_n b_1 + d_{n-1})b_1 + d_{n-2})\dots) + d_0\). Conversion from decimal \(D\) to target base \(b_2\) uses the Euclidean repeated division algorithm: \(D_k = q_k b_2 + r_k\), where remainders \(r_k\) read in reverse yield the target digits.

Operating Instructions

• Enter the source number string in the input field.
• Set the source base \(b_1\) and target base \(b_2\) (ranges 2 to 36).
• Click Convert to view the formatted target representation.
• Inspect the step-by-step division table showing quotient progressions and accumulated remainders.