Number base converter
Convert a number between binary, octal, decimal, and hexadecimal. Enter a value and its input base, and the tool instantly calculates the other three representations. Useful for programming, debugging code, working with colors, and computer science homework — no install, and nothing is ever sent to a server.
How the numeral system converter works
A numeral system (base) determines how many distinct digits are used to write numbers and what weight each position carries. Decimal (base 10) uses digits 0–9, binary (base 2) uses only 0 and 1, octal (base 8) uses digits 0–7, and hexadecimal (base 16) uses digits 0–9 plus letters A–F for values 10–15. Any number in one base can be converted to the same value in any other base — it's just a different way of writing the same quantity.
The tool takes your input text, checks that it only contains characters valid for the chosen input base (for example, only 0 and 1 for binary), converts it internally to a decimal number, and then calculates its representation in the remaining three bases. The whole calculation runs directly in your browser.
How to use the numeral system converter
- Enter a number in the Value field.
- Select which base the value is written in (decimal, binary, octal, or hexadecimal).
- Read the result — the tool automatically shows the same number in all four bases.
| Input | Input base | Decimal | Binary | Hexadecimal | Octal |
|---|---|---|---|---|---|
| 255 | Decimal | 255 | 11111111 | FF | 377 |
| 1010 | Binary | 10 | 1010 | A | 12 |
What the numeral system converter is useful for
Programmers use it for debugging code, working with bitmasks or subnet masks, where binary and hexadecimal notation are frequently swapped. Hexadecimal is the basis of color codes (#FF0000), MAC addresses, and hashes. Octal is mostly used today for Unix file permissions (e.g. chmod 755). Computer science students find it handy for practicing base conversions. Since everything runs client-side in JavaScript, no value you enter is ever sent to or stored on a server.
FAQ
Which numeral systems does the tool support?
The four most common ones: binary (2), octal (8), decimal (10), and hexadecimal (16). Other bases (e.g. base 36) are not supported.
Why doesn't the tool accept negative numbers or decimal points?
It only works with non-negative integers. Negative and fractional numbers require a different representation (e.g. two's complement or floating point) that the tool doesn't handle, so the output stays unambiguous.
Do I need to type uppercase letters for hexadecimal input?
No, the tool accepts both lowercase and uppercase letters and normalizes them internally. The hexadecimal output is always shown in uppercase (A–F), which is the common convention.
What happens if I enter a character that isn't valid for the chosen base?
All outputs stay blank (–) until you enter a value valid for the selected input base — for instance, the digit 8 can't be entered as an octal number.
How large a number can the tool convert accurately?
Precision is limited by JavaScript's standard number type, safely up to 2^53−1 (about 9 quadrillion). That's more than enough for typical uses — IP addresses, colors, bytes, debugging code.
Is the number I enter sent to a server?
No. The entire calculation runs directly in your browser using JavaScript; no value is ever sent or stored anywhere.
What is hexadecimal most commonly used for?
Most often for CSS colors (#FF0000), MAC addresses, hashes, and memory debug dumps — it's more compact than binary and easier to read.
What's the practical difference between octal and hexadecimal?
Octal is rarely used today, mainly for Unix file permissions (chmod 755). Hexadecimal is far more common in IT generally — colors, hashes, memory addresses.
📅 Last updated: 16 July 2026