Decimal To Binary
Convert decimal numbers to binary with our fast and easy-to-use Decimal to Binary Converter. Designed for students, developers, and electronics engineers, this tool simplifies number conversions and enhances understanding of binary systems used in computing and digital logic.
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What is Decimal to Binary Conversion?
Decimal to Binary conversion involves converting a number from the base-10 system (used by humans) into the base-2 system (used by computers). In binary, only two digits exist: 0 and 1. Every decimal number can be represented as a unique binary equivalent.
Example:
Decimal:10
Binary:1010
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👉 Decimal to Binary
Why Use Decimal to Binary Conversion?
Decimal numbers are standard in daily life, while binary is the native language of computers. Converting from decimal to binary is essential in:
Programming and software development
Computer architecture
Digital circuit design
Networking and data transmission
Cryptography and embedded systems
Want to convert back? Try our Binary to Decimal tool.
How to Convert Decimal to Binary Manually
Step-by-Step Process:
Divide the decimal number by 2
Write down the remainder (0 or 1)
Divide the quotient by 2 and record the next remainder
Repeat until the quotient is 0
The binary number is the remainders in reverse order
Example:
Convert 13 to binary
13 ÷ 2 = 6 remainder 1
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Read remainders bottom-up: 1101
Decimal 13 = Binary 1101
Decimal to Binary Table (0–15)
| Decimal | Binary |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
| 8 | 1000 |
| 9 | 1001 |
| 10 | 1010 |
| 11 | 1011 |
| 12 | 1100 |
| 13 | 1101 |
| 14 | 1110 |
| 15 | 1111 |
Try converting these using our tool:
👉 Decimal to Binary
Decimal to Binary Converter for Large Numbers
Our Decimal to Binary Converter handles very large integers efficiently. You can convert:
Large memory addresses
Data packet values
CPU register data
32-bit and 64-bit values
Example:
Decimal:1023
Binary:1111111111
Decimal to Binary in Python
Here’s a quick Python example:
decimal_number = 13
binary_value = bin(decimal_number)[2:]
print(binary_value)
# Output: '1101'
The bin() function returns a binary string prefixed with 0b, so we slice it with [2:].
Use Cases of Decimal to Binary Conversion
💻 Programming
Languages like C, Java, and Python work closely with binary data. Understanding the binary form of decimal values helps with:
Bitwise operations
Flag checking
Memory manipulation
⚙️ Digital Electronics
Microcontrollers and CPUs use binary logic. Engineers convert decimal to binary to:
Program digital logic
Analyze control systems
Debug firmware
📘 Education
Decimal to binary is a staple concept in:
Computer science courses
Engineering studies
Software bootcamps
Decimal to Binary with Floating Point Numbers
Our tool currently supports integer conversion. For floating-point conversion:
Convert integer part as usual
Multiply the fractional part by 2
Record the integer part of the result
Repeat with the new fractional part
Example:
Decimal:4.75
Integer part = 4 →100
Fraction:0.75 × 2 = 1.5 → 10.5 × 2 = 1.0 → 1
Final result = 100.11
Internal Links for Related Conversions
Binary Representation Tips
Each bit represents a power of 2
Leading zeros don't change the value
Binary numbers can be grouped in 4s (nibbles) or 8s (bytes) for readability
Example:
Decimal: 255
Binary: 11111111
Explanation: 2⁷ + 2⁶ + ... + 2⁰ = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255
Decimal to Binary Chart (16–31)
| Decimal | Binary |
|---|---|
| 16 | 10000 |
| 17 | 10001 |
| 18 | 10010 |
| 19 | 10011 |
| 20 | 10100 |
| 21 | 10101 |
| 22 | 10110 |
| 23 | 10111 |
| 24 | 11000 |
| 25 | 11001 |
| 26 | 11010 |
| 27 | 11011 |
| 28 | 11100 |
| 29 | 11101 |
| 30 | 11110 |
| 31 | 11111 |
Convert instantly:
👉 Decimal to Binary
Common Decimal to Binary Mistakes
❌ Forgetting to reverse the remainders
❌ Misplacing power-of-two values
❌ Using commas or decimals in input
❌ Confusing binary with hexadecimal (e.g., 1010 vs A)
Advantages of Our Decimal to Binary Converter
✅ Supports unlimited digits
✅ Fast & real-time results
✅ Works on mobile, tablet, and desktop
✅ No login or signup required
✅ 100% free and accurate
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👉 Decimal to Binary
Decimal to Binary vs Decimal to Hex
| Feature | Decimal to Binary | Decimal to Hex |
|---|---|---|
| Output Base | Base-2 (0 and 1) | Base-16 (0–F) |
| Use Case | Programming logic | Memory debugging |
| Readability | Less human-readable | More compact format |
Explore more:
👉 Decimal to Hex
Final Thoughts
The Decimal to Binary conversion is one of the most fundamental operations in computing. Whether you're writing low-level code, learning computer architecture, or designing circuits, understanding binary representation is essential.
Our Decimal to Binary Converter simplifies the entire process, offering fast, accurate, and clean results in seconds.
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