What are the rules of Gray code?

Gray code is a binary code. The difference between adjacent Gray codes is only one bit, that is, the Hamming distance is 1. Generation method: Write down the Gray code [0, 1] of length 1. Invert the Gray code of length n-1 and append it to the end. Add 0 before the sequence generated in step 2 to connect the sequence of step 2 and step 3.

The rules of Gray code

Gray code is a binary code that has the following properties: continuous The two Gray codes differ only in one bit. That is, in Gray code, the Hamming distance between two adjacent codes is 1.

Generate Gray code

The method of generating Gray code is as follows:

1. Write the Gray code with length 1: [0, 1 ]
2. For a Gray code of length n, invert the Gray code of length n-1 and append it to the end of the Gray code of length n-1.
3. Add 0 before the sequence generated in step 2.
4. Connect the sequences generated in step 2 and step 3.

Example

Generate Gray code with length 3:

• Gray code with length 1: [0, 1]
• Length 2 Gray code: [00, 01, 11, 10] (reverse and append the length 1 Gray code)
• Length 3 Gray code: [000, 001, 011, 010, 110, 111, 101, 100] (Add 0 before the length 2 Gray code, and then connect)

Application

Gray code has applications in many fields, such as:

• Error detection and correction
• Data transmission
• Address decoding
• Cyclic redundancy check (CRC)

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