Binary to Decimal Converter

How Binary-to-Decimal Conversion Works

Each binary digit represents a power of 2 based on its position (rightmost = 2^0, next = 2^1, and so on) - the decimal value is the sum of the powers of 2 where a binary digit is 1.

How to Use It

1. Enter a binary number (digits 0 and 1 only).
2. The decimal equivalent and place-value breakdown appear instantly.

Limitations

This handles arbitrarily large binary integers accurately using BigInt - there's no binary-point/fraction support, since fractional binary values require a different (and less standardized) interpretation.

Worked Example

Convert 101101 to decimal. Write the power of 2 under each digit, starting with 2⁰ on the right:

Add the place values where the digit is 1: 32 + 8 + 4 + 1 = 45.

Handy Values to Remember

• 1111 = 15 (the largest 4-bit value, one hex digit)
• 11111111 = 255 (the largest 8-bit value, one byte - the maximum in an IPv4 octet or an RGB channel)
• 10000000000 = 1024 (2¹⁰, the "binary kilo")

Where You Meet Binary

• Subnet masks: 255.255.255.0 is 24 ones followed by 8 zeros.
• Bit flags and permissions in code and databases.
• Computer science exercises and exams.

Convert the other way with Decimal to Binary, or between any bases with the Number Base Converter. Combine bits with the Bitwise Calculator.