Gray code, also known as reflected binary code or unit distance code, is a binary numeral system where two consecutive values differ in only one bit. This unique property makes Gray code particularly useful in applications like rotary encoders, analog-to-digital converters, and error detection.
Gray Code Representation:
In Gray code, the transition from one value to the next involves flipping only one bit at a time. This is in contrast to binary representation, where two consecutive values may differ in multiple bits. Let's take a look at a simple example:
Decimal | Binary | Gray code |
0 | 000 | 000 |
1 | 001 | 001 |
2 | 010 | 011 |
3 | 011 | 010 |
4 | 100 | 110 |
5 | 101 | 111 |
6 | 110 | 101 |
You can observe that the Gray code changes only one bit at a time, reducing the chances of errors during transitions and providing a more robust representation.
Gray Code Conversion:
Converting binary to Gray code (and vice versa) involves straightforward algorithms.
Binary to Gray Code:
Start from the Most Significant Bit (MSB): Begin with the leftmost (MSB) bit of the binary number, as it remains unchanged in the Gray code.
Perform XOR Operation: For each subsequent bit, perform an exclusive OR (XOR) operation between the current bit and the previous bit from the binary number.
Example:
Binary: 101110 Gray Code: 111010
Gray Code to Binary:
MSB Remains Unchanged: The leftmost (MSB) bit of the Gray code remains the same in the binary representation.
Perform XOR Operation: For each subsequent bit, perform an XOR operation between the current bit of the Gray code and the previous bit from the binary representation.
Example:
Gray Code: 110011 Binary: 100010