How do I convert binary to decimal?
Read the binary digits from left to right. Start with a total of zero, double the total for each digit, and add the digit (0 or 1). The final total is the decimal value.
Number systems · Base 2 to base 10
Binary to Decimal Converter
Convert a binary number (base 2) into its decimal (base 10) equivalent. Get an instant result, validate your input, and follow the calculation one bit at a time.
Convert binary to decimal
Try a binary number
Choose an example to fill the calculator, then select “Convert to decimal.”
Binary
0
Binary
1
Binary
1011
Binary
11001010
Binary
11111111
Binary
100000000
How to convert binary to decimal
Binary uses place values that are powers of two. To convert a whole binary number to decimal, you can multiply each bit by its corresponding power of two and add the products. For long numbers, the doubling method gives the same result without having to write every power explicitly.
Positional-value formula: decimal = bn−1 × 2n−1 + … + b2 × 22 + b1 × 21 + b0 × 20, where every bit b is either 0 or 1 and position 0 is the rightmost digit.
Worked example: 1101₂
| Bit | Position | Place value | Contribution |
|---|---|---|---|
| 1 | 3 | 23 = 8 | 1 × 8 = 8 |
| 1 | 2 | 22 = 4 | 1 × 4 = 4 |
| 0 | 1 | 21 = 2 | 0 × 2 = 0 |
| 1 | 0 | 20 = 1 | 1 × 1 = 1 |
| Sum of contributions | 8 + 4 + 0 + 1 = 13 | ||
Related binary and number tools
Continue working with binary numbers using these related Binarios.org tools.
Decimal to Binary ConverterConvert a base-10 integer to binary.
Binary to Hexadecimal ConverterConvert binary digits to base 16.
Number Base ConverterExplore conversions between number systems.
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Bits to Bytes ConverterConvert between bit and byte quantities.
Binary Subtraction CalculatorPractice subtraction in base 2.
Frequently asked questions
What is 1011 in decimal?
1011₂ equals 11₁₀ because (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰) = 8 + 0 + 2 + 1 = 11.
Can I convert a long binary number?
Yes. This converter accepts up to 512 binary digits and uses decimal-string arithmetic, so the result is not limited to the usual PHP integer range.
Does this tool accept spaces or a 0b prefix?
Yes. Spaces, line breaks, underscores, and an optional leading 0b prefix are removed before validation. All remaining characters must be 0 or 1.
Does this converter handle signed two’s-complement values?
This tool treats the input as an unsigned binary integer. For signed two’s-complement interpretation, the bit width must be known and the sign bit must be interpreted accordingly.