Binary To Decimal
Use our Binary to Decimal Converter to instantly transform binary numbers into readable decimal format. Whether you're learning binary math or debugging code, this free online tool simplifies the conversion process for students, programmers, and engineers.
Share on Social Media:
What is Binary to Decimal Conversion?
Binary to Decimal conversion involves translating a number written in the binary numeral system (base-2) into its equivalent in the decimal system (base-10). This is a critical operation in computer science, digital electronics, and data communication, as all binary data ultimately needs to be interpreted by humans in decimal form.
Example:
Binary:1010
Decimal:10
Try it here: Binary to Decimal
Why Convert Binary to Decimal?
Although computers store and process data in binary (using 0s and 1s), humans interpret and manipulate that data in decimal form. Converting binary to decimal is necessary when:
Debugging binary code
Understanding how computers interpret numbers
Performing data conversions in programming
Analyzing memory addresses and bit operations
Need the reverse? Try our Decimal to Binary converter.
How to Convert Binary to Decimal Manually
To convert a binary number to a decimal:
Step-by-Step:
Start from the rightmost bit (least significant bit)
Multiply each bit by 2 raised to the power of its position
Sum the results
Example:
Convert binary 1011 to decimal
= (1 × 2^3) + (0 × 2^2) + (1 × 2^1) + (1 × 2^0)
= 8 + 0 + 2 + 1
= 11
Binary to Decimal Table (0–15)
| Binary | Decimal |
|---|---|
| 0000 | 0 |
| 0001 | 1 |
| 0010 | 2 |
| 0011 | 3 |
| 0100 | 4 |
| 0101 | 5 |
| 0110 | 6 |
| 0111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
| 1010 | 10 |
| 1011 | 11 |
| 1100 | 12 |
| 1101 | 13 |
| 1110 | 14 |
| 1111 | 15 |
Convert any of these using our tool:
👉 Binary to Decimal
Use Cases for Binary to Decimal Conversion
🔧 Programming
Many programming languages represent values in binary internally. When debugging or working at a low level, converting to decimal helps interpret results clearly.
🧠 Education
Binary to decimal conversions are fundamental in:
Computer science courses
Digital logic design
Number system exercises
⚙️ Engineering
Digital circuits use binary logic. Engineers often convert binary outputs into decimal for testing and analysis.
Binary to Decimal in Python
binary_str = "1011"
decimal_value = int(binary_str, 2)
print(decimal_value)
# Output: 11
Try this for any binary number!
Binary to Decimal for Large Numbers
Our converter supports very large binary numbers, allowing you to:
Decode binary strings from memory dumps
Convert long binary keys or IDs
Handle 32-bit and 64-bit numbers without error
Example:
Binary:1111101000
Decimal:1000
Understanding Binary Positional Value
Each binary digit (bit) has a place value that doubles from right to left.
| Position | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
|---|---|---|---|---|---|---|---|---|
| Binary | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 |
| Value | 128 | 0 | 32 | 16 | 0 | 4 | 0 | 1 |
Sum = 128 + 32 + 16 + 4 + 1 = 181
Binary 10110101 = Decimal 181
Related Conversions (Internal Linking)
Frequently Asked Questions
❓ Can I input binary with spaces?
Yes! Our tool accepts input like 1101 0010 and automatically cleans and parses it.
❓ What’s the largest number I can convert?
Our converter handles binary numbers up to 64 bits and beyond.
❓ What if I enter invalid binary?
The tool detects and rejects invalid characters (anything other than 0 and 1).
❓ How is this different from Binary to Text?
Binary to Decimal focuses on numerical value, while Binary to Text translates to readable characters based on encoding.
Binary to Decimal vs Binary to Text
| Feature | Binary to Decimal | Binary to Text |
|---|---|---|
| Output | Numerical value (e.g., 27) | Character output (e.g., 'A') |
| Use Case | Programming, electronics | Data encoding, decoding |
| Input Format | Any binary number | Binary in ASCII format |
Need Binary to Text? Try Binary to Text
Benefits of Using Our Converter
✅ Fast and real-time results
✅ Supports large binary inputs
✅ Mobile and desktop-friendly
✅ Accurate up to 64-bit values
✅ No login or registration required
Start converting instantly:
👉 Binary to Decimal
Final Thoughts
Understanding how to convert binary to decimal is crucial in the world of computing. Whether you're a student, software developer, or hardware engineer, this skill helps bridge the gap between machine data and human logic.
Our Binary to Decimal Converter makes this process intuitive and effortless. Just paste your binary number, hit convert, and get precise decimal values instantly.
Explore more tools: