Convert binary numbers to Gray code instantly with this simple and accurate converter. Enter your binary value, click Convert, and get the equivalent Gray code in seconds.
Enter a binary number (e.g., 1101) into the converter below to get the corresponding Gray code.
Binary to Gray Code Converter
Binary to Gray Code Formula
The conversion from binary to Gray code follows this logical operation:
The first (most significant) bit remains the same.
Each subsequent bit is the XOR (exclusive OR) of the current and previous binary bits.
Mathematical Representation:
Gray[i]=Binary[i]⊕Binary[i−1]
Where:
Gray[i] = The i-th bit in the Gray code
Binary[i] = The i-th bit in the binary input
⊕ = XOR operation (0 if bits are the same, 1 if different)
Example Conversion:
Binary: 1011
First bit (MSB): 1 (unchanged)
Second bit: 1 (prev) XOR 0 (current) = 1
Third bit: 0 XOR 1 = 1
Fourth bit: 1 XOR 1 = 0
Gray Code: 1110
What is Binary Code?
Binary code is the fundamental language of computers, consisting of 0s and 1s. Each bit represents an on (1) or off (0) state, forming the basis of digital data representation.
What is Gray Code?
Gray code (also called reflected binary code) is a binary numeral system where two successive values differ by only one bit. This property makes it useful in digital systems where minimizing transition errors is critical.
Key Features of Gray Code:
✔ Single-bit changes between consecutive numbers (reduces errors in digital circuits).
✔ Used in rotary encoders, Karnaugh maps, and error correction systems.
✔ Prevents glitches in switching between values.
Binary to Gray Code Examples
| Binary Input | Gray Code Output |
|---|---|
0000 | 0000 |
0001 | 0001 |
0010 | 0011 |
0101 | 0111 |
1010 | 1111 |
1111 | 1000 |
How to Use the Binary to Gray Code Converter
- Enter a binary number (e.g.,
1101) in the input field. - Click “Convert to Gray” to get the result.
- Copy the Gray code output for your use.
FAQs
🔹 Why use Gray code instead of binary?
Gray code ensures only one bit changes at a time, reducing errors in digital circuits (e.g., rotary encoders).
🔹 Is Gray code reversible?
Yes! You can convert Gray code back to binary using a similar XOR-based algorithm.
🔹 Where is Gray code used in real life?
- Rotary encoders (mechanical & optical sensors)
- Karnaugh maps (digital logic simplification)
- Error-resistant communication systems
🔹 Does Gray code have a fixed length?
No, it can represent any binary number of any bit length.
🔹 Is Gray code unique for each binary value?
Yes, each binary number has exactly one corresponding Gray code.
🔹 Can I convert decimal to Gray code?
Yes, first convert decimal to binary, then binary to Gray.
🔹 Is Gray code used in quantum computing?
Yes! Some quantum error-correction techniques use Gray-like codes to minimize bit-flip errors.
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