Binary to Decimal Converter
Free online tool to instantly convert binary (Base 2) to decimal (Base 10). Includes quick conversion tables and step-by-step mathematical explanations.
How to convert Binary to Decimal
Converting from Binary (Base 2) toDecimal (Base 10) involves positional value evaluation.
Convert Binary to Decimal
Multiply each digit of the binary number by 2 raised to the power of its position index (starting from position 0 on the right). Sum all products together to obtain the decimal equivalent.
Binary to Decimal Quick Conversion Table
Common values converted between Binary (Base 2) and Decimal (Base 10):
| Binary (2) | Decimal (10) |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 10 | 2 |
| 11 | 3 |
| 100 | 4 |
| 101 | 5 |
| 110 | 6 |
| 111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
| 1010 | 10 |
| 1011 | 11 |
| 1100 | 12 |
| 1101 | 13 |
| 1110 | 14 |
| 1111 | 15 |
| 10000 | 16 |
| 100000 | 32 |
| 1000000 | 64 |
| 1100100 | 100 |
| 11111111 | 255 |
Binary to Decimal Frequently Asked Questions
Common questions and step-by-step mathematical answers about converting Binary (Base 2) to Decimal (Base 10).
1How do you convert binary to decimal?↓
Assign powers of 2 (2⁰, 2¹, 2², 2³, ...) to each bit from right to left. Multiply each bit by its positional value and add all terms together.
2What is the formula for binary to decimal conversion?↓
The formula evaluates the weighted sum: Decimal = bₙ·2ⁿ + bₙ₋₁·2ⁿ⁻¹ + ... + b₁·2¹ + b₀·2⁰.
3How do you convert binary to decimal manually?↓
Example with 1101₂: (1×8) + (1×4) + (0×2) + (1×1) = 8 + 4 + 0 + 1 = 13₁₀.
4What is 1010 in decimal?↓
(1 × 8) + (0 × 4) + (1 × 2) + (0 × 1) = 8 + 2 = 10₁₀.
5What is 10101 in decimal?↓
(1 × 16) + (0 × 8) + (1 × 4) + (0 × 2) + (1 × 1) = 16 + 4 + 1 = 21₁₀.
6What is 11111111 in decimal?↓
An 8-bit binary byte of all 1s equals 2⁸ - 1 = 256 - 1 = 255₁₀.
7How does binary place value work?↓
Unlike base-10 where positions represent powers of 10 (1, 10, 100), binary places represent powers of 2 (2⁰=1, 2¹=2, 2²=4, 2³=8, 2⁴=16).
8How do you convert binary fractions to decimal?↓
Example: 0.101₂ = (1 × 0.5) + (0 × 0.25) + (1 × 0.125) = 0.5 + 0.125 = 0.625₁₀.
9Can negative binary numbers be converted to decimal?↓
For two's complement binary with a leading 1 (sign bit), subtract 1 and invert the bits (or evaluate the MSB with a negative weight -2ⁿ⁻¹) to find the negative decimal value.
10How do you calculate the decimal value of a binary number?↓
Use positional evaluation or Horner's method (double the accumulator and add the next bit from left to right).