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Binary to Decimal Converter
Convert binary bits (0s and 1s) to base-10 decimal with interactive powers of 2 breakdown.
Only binary digits 0 and 1 are accepted.
Sample Bit Sequences:
Decimal Integer (Base 10)
42
Hexadecimal: 0x2APowers of 2 (Place Value Expansion)
| Bit Position (n) | Bit Value | Weight ($2^n$) | Calculation |
|---|---|---|---|
| 5 | 1 | 2^5 = 32 | 1 × 32 = 32 |
| 4 | 0 | 2^4 = 16 | 0 × 16 = 0 |
| 3 | 1 | 2^3 = 8 | 1 × 8 = 8 |
| 2 | 0 | 2^2 = 4 | 0 × 4 = 0 |
| 1 | 1 | 2^1 = 2 | 1 × 2 = 2 |
| 0 | 0 | 2^0 = 1 | 0 × 1 = 0 |
Conversion Formula & Standards
Conversions follow International System of Units (SI) and ISO standard constants.
Decimal = Σ(Bit × 2ⁿ) for n = 0 to length-1
How to Use Binary to Decimal Converter
01
Enter a binary sequence composed of 0s and 1s (e.g. 101010).
02
The tool validates your bit string in real time.
03
See the calculated decimal integer and the place-value power expansion.
Frequently Asked Questions
How do you calculate 1010 in decimal?
(1 × 2³) + (0 × 2²) + (1 × 2¹) + (0 × 2⁰) = 8 + 0 + 2 + 0 = 10.
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