Binary to Decimal Converter: Convert Number Systems
Convert between binary and decimal number systems instantly. This binary to decimal converter helps programmers, students, and engineers understand number base conversions. Perfect for learning computer science, working with hardware, or performing quick number system conversions in development and technical work.
Understanding Number Systems
Different number systems are fundamental to computing and mathematics:
- Decimal (Base 10): Human-readable numbers using digits 0-9. Used in everyday life
- Binary (Base 2): Computer's native language using only 0 and 1
- Hexadecimal (Base 16): Uses digits 0-9 and letters A-F. Shorthand for binary
- Octal (Base 8): Uses digits 0-7. Less common but still used in some systems
- Why binary: Electronics work with two states: on/off, 1/0
- Computing: All computer data is ultimately stored as binary
- Conversion: Understanding conversions bridges human and machine languages
How to Convert Binary to Decimal
- Enter a binary number (only 0s and 1s)
- Or select "Decimal to Binary" to convert the other direction
- Click the input field or press Enter
- Converted value appears instantly in the result field
- Copy the result for use elsewhere
Conversion Examples
| Binary |
Decimal |
Explanation |
| 0 |
0 |
No value |
| 1 |
1 |
Single unit |
| 10 |
2 |
1×2¹ + 0×2⁰ |
| 11 |
3 |
1×2¹ + 1×2⁰ |
| 1010 |
10 |
1×8 + 0×4 + 1×2 + 0×1 |
| 11111111 |
255 |
8-bit maximum value |
Binary Conversion Formula
Binary to Decimal: Multiply each digit by its power of 2, then sum the results.
Formula: (d₇×2⁷) + (d₆×2⁶) + (d₅×2⁵) + (d₄×2⁴) + (d₃×2³) + (d₂×2²) + (d₁×2¹) + (d₀×2⁰)
Decimal to Binary: Repeatedly divide by 2 and record remainders. Read remainders in reverse.
Common Binary Values
- 1 byte: 8 bits, ranges from 0 to 255 in decimal
- 1 kilobyte: 1024 bytes = 2¹⁰ bytes
- Powers of 2: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024...
- Max signed byte: 127 (positive) or -128 (negative)
- Hexadecimal shorthand: Every 4 binary digits = 1 hex digit
Why Learn Binary?
- Programming: Bitwise operations require binary understanding
- Networking: IP addresses, subnet masks use binary logic
- Hardware: Understanding computer internals requires binary knowledge
- Data storage: Compression and encoding depends on binary concepts
- Security: Cryptography and encryption use binary mathematics
- Debugging: Understanding binary helps with low-level debugging
Frequently Asked Questions
Why do computers use binary?
Computers use binary because electronic circuits have two states: on/off, high/low voltage. This naturally maps to binary digits (bits). Everything in computing ultimately reduces to binary.
Can I convert large binary numbers?
Yes. The converter handles any size binary or decimal number. Larger numbers just have more digits. JavaScript can handle very large numbers accurately.
Is binary conversion used in real programming?
Yes. Programmers use binary frequently for bitwise operations, flags, permissions, and low-level data manipulation. Understanding binary is essential for advanced programming.
What about hexadecimal conversion?
Hexadecimal is often easier than binary for humans because it's more compact. Every 4 binary digits = 1 hex digit, making conversion straightforward.
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