Number Base Converter
What is Number Base Converter
A number base converter translates integers between the four most common numeral systems: binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). Each system represents the same value using a different set of digits — decimal uses 0–9, binary uses only 0 and 1, octal uses 0–7, and hexadecimal uses 0–9 plus A–F. This tool converts all four simultaneously the moment you type in any field.
How to use
- Type or paste a number into any of the four fields (decimal, binary, octal, or hex).
- Watch the other three fields update instantly with the equivalent value.
- Click the Copy button next to any field to copy that representation to your clipboard.
- Click Clear to reset all fields and start a new conversion.
When to use it
Chasing a Linux permission bug and the file mode shows as octal 755? Type 755 in the octal field and you instantly get the binary (111 101 101), so you can confirm owner, group, and others each have the read, write, and execute bits you expect. The decimal (493) is right there too when you need it for documentation.
Frequently asked questions
What is a number base?
A number base (or radix) defines how many unique digits a positional numeral system uses. Base 10 (decimal) has digits 0–9. Base 2 (binary) has 0 and 1. Base 8 (octal) uses 0–7, and base 16 (hexadecimal) adds letters A–F to represent values 10–15.
Why do programmers use hexadecimal?
Hexadecimal is compact and maps neatly to binary: every hex digit represents exactly four binary bits (a nibble). This makes memory addresses, color codes (#RRGGBB), and byte values much shorter and easier to read than their binary equivalents. For example, 0xFF is two hex digits but eight binary digits.
How do I convert binary to decimal by hand?
Each binary digit position is a power of 2, starting from the right. For 1101: (1×8) + (1×4) + (0×2) + (1×1) = 8 + 4 + 0 + 1 = 13. This tool does that calculation instantly for any size number.
What is the largest number this converter handles?
The converter uses JavaScript's standard 32-bit safe integer range. For very large numbers (beyond 2^53 − 1), use a specialized big-integer library instead.
Are negative numbers supported?
Yes. Prefix any value with a minus sign (e.g. -255) and all four bases will show the negative equivalent. The converter uses sign-magnitude representation rather than two's complement.
Can I share this tool with my inputs pre-filled?
Yes. The URL updates automatically as you type. Copy it from the address bar or use the Share button — anyone who opens the link will see your exact inputs ready to go.
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