Base Calculator

Mathematical Principles & Theorems

Performs multi-digit arithmetic in arbitrary radices \(b \in [2, 36]\). Positional representation represents integers as \(N = \sum_{i=0}^{n} d_i \cdot b^i\) where \(d_i \in \{0, 1, \dots, b-1\}\). Columnar addition and multiplication propagate carries when column sums exceed \(b-1\); subtraction borrows base units \(b\) from the higher place value when minuend digit \(d_{1,i} < d_{2,i}\).

Operating Instructions

• Set the calculation Radix \(b\) between 2 (binary) and 36 (alphanumeric).
• Enter Operand A and Operand B using valid digits for the chosen base.
• Select arithmetic operation: Addition (+), Subtraction (−), Multiplication (×), or Division (÷).
• Review the columnar carry/borrow calculation trace and decimal cross-verification.