Number Base Converter
Convert numbers between decimal, binary, hexadecimal and octal. Type in any base and the others update instantly.
How it works
We count in base 10 (decimal) because we have ten digits, 0 through 9. But computers work in base 2 (binary), with only 0 and 1, and programmers often use base 16 (hexadecimal) and base 8 (octal) as compact ways of writing binary values.
This tool converts a whole number between these four bases at once. Type a value into any field and the other three are recalculated instantly. Enter 255 in decimal and you immediately see 11111111 in binary, FF in hexadecimal and 377 in octal — all representations of the same number.
Each field only accepts the digits valid for its base: binary takes only 0 and 1, hexadecimal takes 0 to 9 and A to F, and so on. If you type an invalid character, the tool warns you instead of producing a wrong result. Everything runs in your browser.
When to use
Base conversion is routine in programming and electronics. Hexadecimal shows up in color codes, memory addresses and byte values. Binary appears when working close to the hardware, with bit flags and low-level operations. Octal turns up in file permissions on Unix-like systems.
It's useful for students learning number systems, developers debugging values that appear in one base and need to be understood in another, and anyone dealing with hardware, networks or file permissions. Having the four bases side by side removes the mental math and the risk of a slip in the conversion.
Practical examples
A color byte
The value 255 is the maximum of a color channel. In hexadecimal it's FF — which is why pure white is #FFFFFF. Typing 255 in decimal instantly shows the FF used in HEX codes.
File permissions
The Unix permission 755 is octal. Converting it helps understand the underlying bits: each digit represents read, write and execute permissions for a group of users.
Common mistakes
The most common mistake is mixing up valid digits for each base. Trying to use the digit 2 in binary, or the letter G in hexadecimal, produces an invalid value. Each base has its own set of allowed symbols, and the tool enforces that.
Another slip is forgetting that hexadecimal uses letters. A to F represent the values 10 to 15. People new to it sometimes read "FF" as if it were only letters, when it actually means 255 in decimal.
There's also confusion about leading zeros and negative numbers. This converter works with whole, non-negative numbers. Adding minus signs or non-numeric symbols falls outside what base conversion covers here, so keep the input to valid digits for the chosen base.
Frequently asked questions
How do I convert decimal to binary?
Type the number into the decimal field and the binary value appears automatically in its own field, along with hexadecimal and octal. No manual calculation needed.
Why does hexadecimal use letters?
Because base 16 needs sixteen symbols. After 0 to 9, the letters A to F represent the values 10 to 15. So "F" is 15 and "FF" is 255 in decimal.
Do I need to choose the conversion direction?
No. The four fields are linked. Type in any base and the other three update instantly, in every direction.
Does it convert decimal (fractional) numbers?
This tool works with whole numbers. Fractional values in different bases follow a different logic and aren't covered here.
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