Base Converter
Convert numbers in real time between Binary, Octal, Decimal, Hexadecimal, and Custom Bases 2 through 36 with floating-point fraction support.
Multi-Radix Synchronized Board
Edit any base in real time. All other bases convert instantly in O(1) time (precision ceiling: 2^53 - 1 / 9,007,199,254,740,991).
Step-by-Step Positional Expansion
Algebraic polynomial breakdown converting Decimal into Decimal:
0–15 Nibble Reference Table
Quick lookup table comparing Decimal, 4-bit Binary, Octal, and Hexadecimal:
Itemized Plaintext Audit Receipt
Copy a complete formatted text block for engineering notes and code comments:
Positional Number Systems & Radix Reference
Key characteristics of standard computer engineering radices:
| System | Radix | Allowed Digits / Symbols | Common Engineering Application |
|---|---|---|---|
| Binary | Base 2 | 0, 1 | Digital logic, machine code, transistors |
| Octal | Base 8 | 0 through 7 | Unix file permissions (e.g. chmod 755), legacy PDP architectures |
| Decimal | Base 10 | 0 through 9 | Human standard arithmetic, financial balances |
| Hexadecimal | Base 16 | 0–9, A–F | Memory addresses, HTML/CSS colors, byte representations |
| Base 32 / 36 | Base 32 / 36 | 0–9, A–V / A–Z | Case-insensitive hashes, short alphanumeric identifiers |
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Frequently Asked Questions
The workstation uses successive multiplication by the target radix for fractional digits and negative power polynomial summation for decoding. For example, decimal 10.625 converts to binary 1010.101 and hexadecimal A.A with zero IEEE-754 precision drift, capped at 10 decimal places for non-terminating repeating fractions.
Yes, 100%. All number conversions, string formatting, polynomial expansions, and plaintext audit receipts are processed entirely in your local browser volatile memory via native JavaScript. Zero numeric data is transmitted to external servers or telemetry systems.
The tool natively supports Binary (Base 2), Octal (Base 8), Decimal (Base 10), and Hexadecimal (Base 16) simultaneously, alongside an arbitrary Custom Base configurable from Base 2 through Base 36 using standard alphanumeric encoding (0–9 and A–Z).
To ensure immediate copy-paste compatibility with compilers, debuggers, memory inspectors, and code editors without syntax errors caused by artificial nibble spaces or grouping commas.
The tool accurately supports integer and floating-point magnitudes up to Number.MAX_SAFE_INTEGER (9,007,199,254,740,991 or 2^53 - 1). Values exceeding this bound trigger an explicit inline warning rather than silently clamping to prevent subtle precision truncation.