Binary to Decimal Converter - Convert Binary Numbers
Result:
1010 (bin) = 10 (dec)
Step-by-step calculation:
What is Binary to Decimal Conversion?
Binary to decimal conversion is the process of changing numbers from base 2 (binary) to base 10 (decimal). Binary numbers use only two digits: 0 and 1. Decimal numbers use ten digits: 0 through 9.
In binary, each position represents a power of 2. The rightmost digit is 2⁰ = 1, the next is 2¹ = 2, then 2² = 4, and so on. To convert binary to decimal, we multiply each digit by its position value and add them up.
For example, binary 1010 = (1×2³) + (0×2²) + (1×2¹) + (0×2⁰) = 8 + 0 + 2 + 0 = 10 in decimal.
How Binary to Decimal Conversion Works
Input Binary
Enter binary digits (0s and 1s)
Position Values
Each position is a power of 2
Multiply & Add
Multiply digits by position values
Binary to Decimal Conversion Table
| Binary | Decimal | Calculation |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | 1×2⁰ = 1 |
| 10 | 2 | 1×2¹ = 2 |
| 11 | 3 | 1×2¹ + 1×2⁰ = 3 |
| 100 | 4 | 1×2² = 4 |
| 101 | 5 | 1×2² + 1×2⁰ = 5 |
| 110 | 6 | 1×2² + 1×2¹ = 6 |
| 111 | 7 | 1×2² + 1×2¹ + 1×2⁰ = 7 |
| 1000 | 8 | 1×2³ = 8 |
| 1001 | 9 | 1×2³ + 1×2⁰ = 9 |
| 1010 | 10 | 1×2³ + 1×2¹ = 10 |
| 1111 | 15 | 1×2³ + 1×2² + 1×2¹ + 1×2⁰ = 15 |
| 10000 | 16 | 1×2⁴ = 16 |
| 11111 | 31 | 1×2⁴ + 1×2³ + 1×2² + 1×2¹ + 1×2⁰ = 31 |
| 100000 | 32 | 1×2⁵ = 32 |
Powers of 2 Reference Chart
Practice Problems with Solutions
Problem 1:
Convert binary 1101 to decimal
Problem 2:
Convert binary 10110 to decimal
Problem 3:
Convert decimal 25 to binary
Problem 4:
Convert binary 11111 to decimal
Common Examples
Binary to Decimal Examples
Real-World Applications
Computer Programming
Understanding binary is essential for programming and computer science
Digital Electronics
Binary represents on/off states in digital circuits
Data Storage
All digital data is stored in binary format
Frequently Asked Questions
What is binary?
Binary is a number system that uses only two digits: 0 and 1. It's also called base-2 system.
Why do computers use binary?
Computers use binary because it matches their electronic nature - switches can be either on (1) or off (0).
How do I convert binary to decimal?
Multiply each binary digit by its corresponding power of 2, then add all the results together.
What's the largest number in 8-bit binary?
The largest 8-bit binary number is 11111111, which equals 255 in decimal.