To convert binary to decimal, you add up the place values wherever the binary number has a 1. Binary 1101 has a 1 in the eight, four, and one positions, so it is 8 plus 4 plus 1, which is 13. The same binary string can also be written as hexadecimal or octal, and each is just a different, shorter way of showing the same value. This guide shows how to convert binary to decimal, hex, and octal, with the rule behind each and a free tool for the job.
In this guide
The place-value rule
Binary has two digits, 0 and 1, and each position is worth twice the one to its right: 1, 2, 4, 8, 16, and so on. Reading a binary number means adding the position values wherever a 1 sits. That single rule is the basis of every conversion here, and it is covered in more depth in our guide to number systems.
Decimal, hexadecimal, and octal are simply three different groupings of those same bits. Decimal is the everyday base-10 form, hex groups the bits in fours, and octal groups them in threes. Nothing about the underlying value changes between them.
Convert binary to decimal
Decimal is the base-10 system people count in, so converting binary to decimal turns a machine value into a number you can read at a glance. You add the place values for every 1 in the string, exactly as in the rule above.
For a short number this is quick, but for a long byte or a 16-bit value it is slow and easy to miscount, so the binary to decimal converter does it instantly. Paste the binary and it returns the decimal number.
Convert binary to hexadecimal
Hexadecimal uses sixteen digits, 0 to 9 then A to F, and its key feature is that one hex digit is exactly four bits. That makes hex the compact, readable form of binary used for colour codes, memory addresses, and raw byte data.
To convert by hand you split the binary into groups of four bits from the right and write each group as its hex digit. The binary to hex converter handles the grouping and lookup for you, which removes the most common mistake, splitting the bits in the wrong place.
Convert binary to octal
Octal uses eight digits, 0 to 7, and one octal digit is exactly three bits. It is the older shorthand still seen in Unix and Linux file permissions, where a value like 755 is octal. The binary to octal converter groups the bits in threes and returns the octal value.
One number, three formats
Take the byte 11010110. As decimal it is 214. Grouped into fours, 1101 and 0110, it is D6 in hex. Grouped into threes from the right, 11 010 110, it is 326 in octal. Three different notations, one identical value. Run any of them through the matching converter and you get the same result, because the conversion only changes how the value is written, never the value itself.
Free converters used in this guide
Why these conversions matter
Programmers meet all of these systems daily. A memory address is read in hex, a file permission is set in octal, and a calculated result is checked in decimal. Being able to move a value between them, or letting a converter do it, is part of routine debugging and low-level work. It is also the first thing most computer science courses teach, because it explains how a machine that only knows 0 and 1 can store any number at all.
Frequently asked questions
How do I convert binary to decimal?
Add the place values for every 1 in the binary string, where the positions from the right are worth 1, 2, 4, 8, and so on. A binary to decimal converter adds them up for you.
What is binary 1101 in decimal?
Binary 1101 is 8 plus 4 plus 1, which is 13 in decimal.
Why is hexadecimal grouped in fours?
Because one hexadecimal digit represents exactly four bits, so any group of four binary digits maps cleanly to a single hex digit.
Is converting binary to decimal reversible?
Yes. The value is identical in every base, so the conversion is lossless and the same number can be written back in binary without any change.
What is octal still used for?
Most commonly Unix and Linux file permissions, where a setting such as 755 is an octal number. One octal digit equals three bits.