Convert between binary and decimal instantly. This free binary to decimal converter works both directions – type in either field and see the other update, plus hex and octal equivalents.
How the Binary to Decimal Converter Works
This converter reads whatever you type into either the Binary or Decimal field and instantly recalculates the other, along with the hexadecimal and octal equivalents. It works in both directions at once, so you never have to pick a “from” and “to” mode.
Formula: A binary number is converted to decimal by treating each digit as a power of 2 counting from the right (starting at 2^0) and summing the powers where the digit is 1 — for example 101101 = (1×2^5) + (0×2^4) + (1×2^3) + (1×2^2) + (0×2^1) + (1×2^0) = 45. Going the other way, a decimal number is converted to binary by repeated division by 2, recording the remainders. The hexadecimal and octal values shown are simply the same decimal number re-expressed in base 16 and base 8.
- Binary — a base-2 number made only of 0s and 1s, entered in the Binary field.
- Decimal — the equivalent base-10 whole number, entered in the Decimal field or generated automatically.
- Hexadecimal — the same value re-expressed in base 16, shown automatically below the main result.
- Octal — the same value re-expressed in base 8, shown automatically below the main result.
Example Scenarios
| Binary Input | Decimal Output |
|---|---|
| 1010 | 10 |
| 100000 | 32 |
| 101101 | 45 |
| 11001000 | 200 |
| 11111111 | 255 |
Binary to Decimal Converter FAQ
How do I convert binary to decimal by hand?
Write out the place values from right to left as powers of 2 (1, 2, 4, 8, 16…), multiply each binary digit by its place value, then add up the results where the digit is 1. For example, 1101 = (1×8) + (1×4) + (0×2) + (1×1) = 13.Why does typing in the decimal field also update the binary field?
The converter listens for input in both fields at once. Typing a valid whole number into the Decimal field automatically recalculates and fills in the matching Binary, Hexadecimal, and Octal values, so you can convert in whichever direction is easier for your task.What happens if I type letters or invalid characters into the binary field?
The Binary field only accepts 0s and 1s. If you type anything else, the tool clears the Decimal field and shows a message asking for a valid binary number instead of returning an incorrect or partial conversion.How is the hexadecimal value calculated from a binary number?
The tool first converts your binary input to its decimal value, then re-expresses that same decimal number in base 16, using digits 0-9 and letters A-F. The hexadecimal and octal outputs are always calculated from the decimal value, not directly from the binary digits.Can I convert negative binary numbers with this tool?
No. This converter is built for unsigned (non-negative) whole numbers only, since it validates binary input against a pattern of just 0s and 1s and decimal input against digits only, with no minus sign or two’s complement handling.What’s the difference between binary, octal, and hexadecimal number systems?
They’re all positional number systems that differ only in their base, or how many unique digits they use before carrying over: binary uses base 2 (0-1), octal uses base 8 (0-7), and hexadecimal uses base 16 (0-9 and A-F). The same quantity looks different in each but represents the same value.Related Calculators
If you work with networking or need more number-base tools, the subnet calculator for IP address math relies on the same binary logic used here. Designers can also try the hex to RGB color converter for web design values, or use the scientific notation converter for very large or small numbers.