Binary To Decimal Converter
Enter the binary value to convert to decimal or Decimal to Binary.
Binary:
A binary number system has two digits "0" and "1" and is known as the Base-2 number system. It is used in digital electronics and computing, where 0 represents OFF and 1 represents ON.
Decimal:
A decimal number system is also called Base-10 (Hindu-Arabic) number system. It uses 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
How to Convert Binary to Decimal — Formula:
Decimal = Σ(dᵢ × 2ⁱ) where dᵢ is each binary digit and i is its position from right (starting at 0).
Example: Binary 1010 = (1×2³) + (0×2²) + (1×2¹) + (0×2⁰) = 8 + 0 + 2 + 0 = 10 decimal.
Technical Details:
Binary is the native language of all digital computers. A single binary digit (bit) can represent 2 states. 8 bits = 1 byte (0-255). 32-bit integers can represent values up to 4,294,967,295. JavaScript uses 64-bit floating point (IEEE 754) for all numbers.
Binary To Decimal Converter:
Our free online binary to decimal converter instantly converts binary numbers to decimal. It supports integer and fractional binary numbers with step-by-step calculation.
Binary to Decimal: How Each Bit Has a Value
128 + 32 + 16 + 4 + 2 = 182
How to Convert Binary to Decimal
- Write down the binary number
- Multiply each digit by 2 raised to its position power (starting from 0 on the right)
- Add all the values together
Formula
Example
Binary: 11010110
= 1×2⁷ + 1×2⁶ + 0×2⁵ + 1×2⁴ + 0×2³ + 1×2² + 1×2¹ + 0×2⁰
= 128 + 64 + 0 + 16 + 0 + 4 + 2 + 0
= 214
Binary to Decimal Conversion Table
| Binary | Decimal | Binary | Decimal |
|---|---|---|---|
| 0000 | 0 | 1000 | 8 |
| 0001 | 1 | 1001 | 9 |
| 0010 | 2 | 1010 | 10 |
| 0011 | 3 | 1011 | 11 |
| 0100 | 4 | 1100 | 12 |
| 0101 | 5 | 1101 | 13 |
| 0110 | 6 | 1110 | 14 |
| 0111 | 7 | 1111 | 15 |
Frequently Asked Questions
How do I convert Binary to Decimal?
Decimal = Σ(dᵢ × 2ⁱ) where dᵢ is each binary digit and i is its position from right (starting at 0).
What is the Binary number system?
A binary number system has two digits "0" and "1" and is known as the Base-2 number system. It is used in digital electronics and computing, where 0 represents OFF and 1 represents ON.
What is the Decimal number system?
A decimal number system is also called Base-10 (Hindu-Arabic) number system. It uses 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Where is Binary to Decimal conversion used?
Binary is the native language of all digital computers. A single binary digit (bit) can represent 2 states. 8 bits = 1 byte (0-255). 32-bit integers can represent values up to 4,294,967,295. JavaScript uses 64-bit floating point (IEEE 754) for all numbers.
Can I convert large binary numbers?
Yes. This converter handles numbers of any practical size. For very large numbers, the conversion is performed using arbitrary-precision arithmetic to ensure accuracy.