Free Binary to Decimal Converter Online
Convert binary numbers to decimal with positional notation steps and batch processing support.
Features
- Multi-base output - Decimal, octal, and hexadecimal
- Batch conversion - Convert multiple binary numbers
- Positional steps - Understand the math behind conversion
- Quick presets - Common binary values
- Validation - Checks for valid binary input
How Binary to Decimal Works
Each binary digit has a positional value based on powers of 2:
Example: 101010 to Decimal
| Position | 5 | 4 | 3 | 2 | 1 | 0 |
|---|---|---|---|---|---|---|
| Binary | 1 | 0 | 1 | 0 | 1 | 0 |
| Power | 2⁵ | 2⁴ | 2³ | 2² | 2¹ | 2⁰ |
| Value | 32 | 16 | 8 | 4 | 2 | 1 |
| × Bit | 32 | 0 | 8 | 0 | 2 | 0 |
Sum: 32 + 0 + 8 + 0 + 2 + 0 = 42
Common Binary to Decimal Conversions
| Binary | Decimal | Use |
|---|---|---|
| 1010 | 10 | Common test |
| 1111 | 15 | Max 4-bit |
| 11111111 | 255 | Max 8-bit (1 byte) |
| 100000000 | 256 | 1 byte + 1 |
| 1111111111 | 1023 | Max 10-bit |
Powers of 2 Reference
| Power | Value | Binary |
|---|---|---|
| 2⁰ | 1 | 1 |
| 2¹ | 2 | 10 |
| 2² | 4 | 100 |
| 2³ | 8 | 1000 |
| 2⁴ | 16 | 10000 |
| 2⁸ | 256 | 100000000 |
| 2¹⁰ | 1024 | 10000000000 |
Use Cases
Programming
- Reading memory addresses
- Understanding byte values
- Debugging binary data
Networking
- IP address calculations
- Subnet masks
- MAC addresses
Education
- Learning binary
- Computer science fundamentals
- Digital electronics
FAQs About Binary to Decimal
What if I enter invalid binary?
Our tool shows an error if you use any character other than 0 and 1.
How do I handle large binary numbers?
Use batch mode to convert multiple numbers, or enter one at a time.
What are the other bases shown?
We also show octal (base 8) and hexadecimal (base 16) equivalents.
Why do computers use binary?
Digital circuits have two states (on/off), making binary natural for computing.
Why Use Our Binary to Decimal Converter?
- Free forever - No registration
- Step-by-step - Learn positional notation
- Batch mode - Convert many numbers
- Multiple bases - Decimal, octal, hex
- Validation - Catches input errors