Number Base Converter
Convert numbers between binary, octal, decimal and hexadecimal.
Convert a number between binary, octal, decimal and hexadecimal. Enter a value, pick the bases, and see the result plus its decimal value — handy for programming, networking and computer-science work.
Formula / method
Examples
255
10
Bases 2, 8, 10 and 16
A number base is just how many digit symbols a system uses before it rolls over to a new place. Decimal (base 10) uses 0-9; binary (base 2) uses only 0 and 1; octal (base 8) uses 0-7; and hexadecimal (base 16) adds A-F to stand for the values ten through fifteen. The underlying quantity never changes, only its written form, so 255 in decimal is FF in hex and 11111111 in binary.
This converter reads a value in any of the four bases and shows the other three at once, all computed locally in your browser.
Why programmers switch bases
Binary mirrors how hardware stores data, while hex is a compact shorthand where each digit maps to exactly four bits, which is why colors, memory addresses, and byte dumps are written in hex. Octal groups bits in threes and still appears in Unix file permissions like 755.
A frequent slip is mixing up which base you are reading: the string 10 means two in binary, eight in octal, ten in decimal, and sixteen in hex. For text encoded as raw byte values, use the hex to text tool on UtilGears instead.
Where it's used
- Converting a hex color or byte value to decimal, or back again
- Reading memory addresses and register values written in hexadecimal
- Working with Unix file permissions expressed in octal, such as 755
- Checking binary representations while learning how computers store numbers
- Programming, networking and computer-science coursework
Real-world examples
- FF in hexadecimal equals 255 in decimal and 11111111 in binary.
- Binary 1010 is 10 in decimal, 12 in octal and A in hex.
- The octal permission 755 is 111101101 in binary — rwx for the owner, r-x for group and others.
- Decimal 16 becomes 10 in hex and 20 in octal — the same value, three different forms.
A bit of history
Modern binary arithmetic — the base-2 system underlying these conversions — was formalized by Gottfried Wilhelm Leibniz, who published "Explication de l'Arithmétique Binaire" in 1703 using only the digits 0 and 1.
Did you know?
Hexadecimal is popular with programmers because each hex digit maps to exactly four binary bits, so one byte (8 bits) is always exactly two hex digits — which is why colors and byte dumps are written in hex.
FAQ
Which characters are valid?
Each base uses digits up to base−1: binary 0–1, octal 0–7, decimal 0–9, and hexadecimal 0–9 plus A–F.