Number Base Converter
Enter a number and its base to see it converted to binary, octal, decimal, and hexadecimal.
How number base conversion works
A number base (or radix) determines how many unique digits are used to represent numbers. Decimal (base 10) uses digits 0-9; binary (base 2) uses only 0 and 1; octal (base 8) uses 0-7; and hexadecimal (base 16) uses 0-9 plus A-F to represent values 10 through 15.
Converting between bases works by first converting the input to decimal (summing each digit multiplied by the base raised to its position), then repeatedly dividing by the target base to build up the digits of the new representation.
Frequently asked questions
Why is binary used in computing?
Binary maps directly onto the two physical states of digital electronics (on/off, high/low voltage), making it the natural number system for how computers store and process data.
What does hexadecimal A-F represent?
In hexadecimal, A through F stand for the decimal values 10 through 15, since a single hex digit needs to represent 16 possible values (0 through 15).
Why do programmers use hexadecimal instead of binary directly?
Each hex digit represents exactly 4 binary digits, so hexadecimal is a much more compact way to write binary values — useful for things like memory addresses and color codes.