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Binary to Decimal Converter
Convert binary integers to decimal online with exact BigInt arithmetic. Accept optional 0b prefixes and grouped bits while rejecting signs and invalid digits.
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Convert Binary to Decimal
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Detailed conversion guide
How to Convert Binary to Decimal
Each bit contributes its value times a power of two. Binary 111011 is 1×32 + 1×16 + 1×8 + 0×4 + 1×2 + 1×1, giving decimal 59.
BigInt parses the validated bits as one exact non-negative integer. Grouping spaces and underscores do not create separate values. Leading zero bits do not change the decimal result.
| Input | Output | Meaning |
|---|---|---|
0 | 0 | zero |
1010 | 10 | decimal 10 |
111011 | 59 | decimal 59 |
11111111 | 255 | decimal 255 |
Binary to Decimal without Floating-Point Loss
The algorithm validates the representation before exact integer conversion, so malformed input never produces a plausible partial answer.
const bits = input.trim().replace(/^0b/i, "").replace(/[\s_]/g, "");
if (!/^[01]+$/.test(bits)) throw Error("Invalid binary integer");
const decimal = BigInt("0b" + bits).toString(10);Invalid Bits, Fractions, and Signed Interpretation
Digits other than 0 and 1, repeated prefixes, decimal points, and signs are rejected. This page does not infer two’s-complement width: 11111111 is decimal 255, not −1.
Grouped bits are joined into one number. A fractional input such as 0.1 needs a binary-fraction converter and is unsupported here. BigInt keeps large values exact, including values beyond 2^53 − 1.
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