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Base Conversion ToolsFree Interactive Tool

Custom Base Converter

Configure arbitrary custom radices with user-defined alphabets and symbol sets. Designed for software developers, electrical engineers, students, and computer architecture researchers requiring deterministic client-side accuracy.

Engine: Client-Side Verified (0ms Latency)

Convert across custom radices up to base 36.

Calculated Output

Primary Representation
Calculating...

Step-by-Step Mathematical Proof

Active Derivation
Ready. Enter input above to generate derivation.
Concept

What Is Custom Base Converter?

The Custom Base Converter allows users to convert numbers using custom source and target bases from base 2 up to base 36 with full proof generation.

Methodology

How Does It Work?

Parses the input against the source radix, converts to arbitrary precision BigInt, and expresses the quotient in the target radix.

Formula & Rules

Mathematical Algorithm

N_{10} = \sum d_i \text{base}_1^i \xrightarrow{} N_{\text{target}}
Worked Problem

Step-by-Step Example

Convert 100 from decimal to base 26: 100 / 26 = 3 remainder 22 (M) 3 / 26 = 0 remainder 3 Result: 3M_{26}.

Important Rules & Edge Cases

  • Supports custom radices between 2 and 36.

Practical Applications in Engineering

  • Designing spreadsheet column indexing (A-Z base 26).
  • Creating custom encoding schemes.

Common Mistakes to Avoid

  • Caution: Using duplicate symbols in custom bases.
FAQ

Frequently Asked Questions

How are Excel spreadsheet column letters related to base 26?

Excel columns use a modified bijective base-26 system where A=1, B=2, ..., Z=26, AA=27.