Binary to Decimal Calculator
Convert a binary number to decimal, with the hexadecimal and octal forms.
How it works
decimal = sum of each digit × 2 raised to its position (counting from 0 on the right)
Binary is base 2: every position is a power of two, doubling from right to left as 1, 2, 4, 8, 16 and so on. To convert to decimal, add up the place values wherever a 1 appears. The same value is also shown in hexadecimal (base 16) and octal (base 8), the two shorthands most often used to write binary compactly.
Worked example
The binary number 1011 has 1s in the 8, 2 and 1 places, so it equals 8 + 2 + 1 = 11 in decimal. That same value is B in hexadecimal and 13 in octal.
Frequently asked questions
How does binary place value work?
Each position is a power of two, doubling from right to left: 1, 2, 4, 8, 16 and onward. Add the place values wherever a 1 appears — 1011 is 8 + 2 + 1 = 11.
Why do computers use binary?
Electronic circuits are built from switches with two stable states, on and off, which map naturally onto 1 and 0. Text, images and sound are all ultimately encoded in these two digits.
What are hexadecimal and octal for?
They are shorthand for binary. One hex digit packs exactly four bits and one octal digit exactly three, so long binary strings become short and readable — which is why they appear in color codes and memory addresses.
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This calculator is for educational purposes. Double-check important results before acting on them.