Number Base Converter
Convert numbers between binary, octal, decimal, and hexadecimal.
About this tool
Binary, octal, decimal, hexadecimal — programmers and computer science students work with all four. The Number Base Converter instantly converts between them, saving you from manual place-value calculations.
How the Number Base Converter works
The Number Base Converter converts numbers between four common numeral systems: binary (base-2), octal (base-8), decimal (base-10), and hexadecimal (base-16). It handles the conversion logic, including hex digits A-F for values 10-15.
How to use this tool
- Enter the number in its original base format (e.g., '1010' for binary, 'FF' for hexadecimal).
- Select the source base from the 'From base' dropdown.
- Select the target base from the 'To base' dropdown.
- Click 'Convert' to see the result.
Common use cases
Converting binary to decimal when reading computer science textbooks
Understanding Unix file permissions in octal (chmod 755)
Decoding hexadecimal color codes (#FF5733) to RGB values
Working with memory addresses displayed in hexadecimal
Examples
- Binary 1010 = Decimal 10 = Octal 12 = Hexadecimal A.
- Hexadecimal FF = Decimal 255 = Binary 11111111. Octal 755 = Binary 111101101 — Unix permission rwxr-xr-x.
Tips & best practices
- Each hexadecimal digit maps to exactly 4 binary bits. Each octal digit maps to exactly 3 binary bits.
- Binary is base-2 (0,1), octal is base-8 (0-7), decimal is base-10 (0-9), hexadecimal is base-16 (0-9, A-F).
- For large hexadecimal numbers like '1A3F', enter them exactly as shown — the converter handles A-F digits automatically.
Common mistakes to avoid
❌ Entering digits that don't exist in the source base — binary only contains 0 and 1, octal only 0-7, decimal only 0-9.
❌ Confusing the letter 'O' with the number '0' in hexadecimal — valid hex digits are 0-9 and A-F only.
Frequently Asked Questions
What is binary?
Binary is base-2, using only 0 and 1. Computers use binary because digital circuits have two stable states: on (1) and off (0).
What is hexadecimal used for?
Hexadecimal (base-16) is used for color codes (#FF5733), memory addresses in debugging, MAC addresses, and compact representation of binary data.
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