Number Base Converter

Enter any integer into the box to instantly convert it across the four most common mathematical bases used in computer science: Binary (Base 2), Octal (Base 8), Decimal (Base 10), and Hexadecimal (Base 16). The tool automatically detects your selected input base and generates the corresponding outputs simultaneously.

This utility utilizes PHP's arbitrary-precision mathematics engine, meaning it can flawlessly handle extremely large numbers that would normally overflow standard 64-bit hardware integers. Your conversions run strictly on our secure backend and are never logged or saved.

How it works

In standard mathematics, we count in Decimal (Base 10) utilizing the digits 0-9. However, low-level computer hardware and software engineering frequently require different representations of data.

Binary (Base 2): Uses only 0s and 1s. This represents the raw electrical states (off and on) of transistors inside a computer processor. It is incredibly verbose but essential for machine-level logic.

Hexadecimal (Base 16): Uses digits 0-9 followed by letters A-F. Because exactly four binary bits fit perfectly into one hexadecimal character, hex is heavily used by programmers as a human-readable shorthand for binary data (like MAC addresses, IPv6 networks, and memory pointers).

Octal (Base 8): Uses digits 0-7. While largely legacy today, it was popular in early computing (like 12-bit and 36-bit systems) and is still explicitly used in Unix/Linux file permissions (e.g., chmod 777).

Arbitrary Precision: Standard calculators fail when numbers exceed roughly 19 digits. This tool leverages the BCMath extension, treating inputs as mathematical strings, allowing for mathematically perfect conversions of massive cryptographic keys and hashes without scientific notation rounding errors.

Frequently asked questions