Binary to Decimal Number Converter

What is the Binary to Decimal Converter?

The Binary to Decimal Converter switches a number between binary (base 2), decimal (base 10), hexadecimal (base 16) and octal (base 8), showing all four at once and the place-value working for the conversion you asked for. Type in any box and the others update. It is aimed at students learning number systems, developers reading memory addresses, colour codes and permissions, and anyone who needs to check a conversion quickly. It runs in your browser.

How to use it

1. Choose the base of the number you have, or just type in the matching box.
2. Read the other three bases.
3. Expand the steps to see the place values: for binary 1011, that is 8 + 0 + 2 + 1 = 11.

How the conversions work

• Binary to decimal: each digit is a power of two from the right; add up the ones that are set.
• Decimal to binary: divide by two repeatedly and read the remainders backwards.
• Binary to hex: group the bits in fours from the right; each group is one hex digit. 1011 1110 is BE.
• Binary to octal: the same, in groups of three.

How to do these by hand, why computers use binary, and where you already meet hex (CSS colours, MAC addresses, Unicode) and octal (Unix file permissions) is in binary, decimal and hex: how to convert by hand and where you already use them.

Everyday places you meet these

• CSS colours: #70DB50 is three hex bytes for red, green and blue.
• File permissions: chmod 755 is octal for rwxr-xr-x.
• Network masks and IP addresses in binary.
• Error codes and memory addresses in hex.

Related tools

Encode text rather than numbers with the Base64 Encoder, do further arithmetic in the Scientific Calculator, and convert data units with the Unit Converter.

Frequently asked questions

Does it handle fractions or negative numbers?

Whole numbers only. Negative values and two’s complement are covered in the guide.

How large a number can I convert?

Very large; the tool uses arbitrary-precision integers, so 64-bit and beyond are fine.

Is uppercase or lowercase hex correct?

Both are valid. The tool shows uppercase; CSS and most languages accept either.