Binary to decimal converter
Convert binary to decimal with BigInt, view unsigned and signed (two’s complement) results, and generate padded hex/octal. Includes steps and quick copy.
Binary to Decimal Calculator Online (Step-by-Step)
Convert binary to decimal in seconds with BigInt, view unsigned and signed (two's complement) values, and get padded hex/oct outputs. Clear vertical blocks without distractions.
Decimal
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Normalized binary
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Signed decimal (two's complement)
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Padded hex
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Octal
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Automatic steps: sum of powers of two
Bit Position 2^pos
| Bit | Position | 2^position | Contribution | Running total |
|---|
How to convert binary to decimal
Formula: decimal = \sum bit_i \times 2^i. Example with 1101: 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 13.
Negative (two's complement, n bits): signed = unsigned - 2^n. Pedagogical method: invert bits, add 1, prepend the negative sign.
0 → 0
1 → 1
10 → 2
101 → 5
1111 → 15
We accept 0s and 1s with an optional 0b prefix and space/underscore separators. Before calculating we clean the string to keep only bits.
We use the real binary length. If the most significant bit is 1, you'll see a hint because in two's complement it could represent a negative number.
We calculate the signed value as
signed = unsigned - 2^n using n bits. We also recall the didactic method: invert bits and add 1 to get the negative.
To keep things readable, we show the decomposition into powers of two up to 2048 bits. Above that size we still calculate but omit the detailed table.
Yes. The grouping selector lets you separate into blocks of 4 or 8 bits, and the shortcuts lead to other base calculators while preserving the entered value.
