Only 0s and 1s allowed. Spaces are ignored.
Decimal = Σ (bit × 2position)
Each bit position represents a power of 2, starting from 20 on the right.
Example: 1011
1×2³ + 0×2² + 1×2¹ + 1×2⁰
= 8 + 0 + 2 + 1 = 11
Two's complement is a method to represent signed integers. If the leftmost bit is 1, the number is negative.
Binary to decimal conversion is the process of converting a number expressed in the binary numeral system (base-2) to its equivalent in the decimal numeral system (base-10). Binary uses only two digits, 0 and 1, while decimal uses ten digits, 0 through 9. This conversion is fundamental in computer science as computers internally represent and process all data using binary numbers.
The conversion is performed by multiplying each binary digit by its positional value (a power of 2) and summing all the results. The rightmost position has a value of 2⁰ = 1, the next position to the left has a value of 2¹ = 2, then 2² = 4, and so on. This positional notation makes binary an efficient way to represent numbers in electronic circuits.
Enter your binary number in the input field using only 0s and 1s. You can include spaces for readability—they will be automatically ignored. Select a bit width if you want to work with a specific format (8-bit, 16-bit, etc.), or leave it on "Auto" to use the minimum required bits.
Enable "Two's Complement" if you're working with signed integers where the most significant bit represents the sign. When enabled, numbers starting with 1 will be interpreted as negative values. The step-by-step option shows you exactly how each bit contributes to the final decimal value.
Disclaimer
Binary to decimal conversions are based on standard positional and two's complement rules. Results depend on correct input formatting and selected options. This tool supports up to 64-bit numbers.