What is gray code

Gray code is a binary encoding in which adjacent digits differ by only one bit. Features include: Consecutive Gray codes differ by only one binary bit. All possible binary combinations occur in Gray code sequences. Generate Gray code: write the previous Gray code in reverse order, add 0 to the original sequence, and add 1 to the reverse sequence. Applications: cyclic redundancy check, encoders and decoders, data transmission and storage.

What is Gray code?

Gray code is a special type of binary number encoding that makes the binary digits between adjacent numbers only differ by 1 bit.

Characteristics:

• For any two consecutive Gray codes, only one bit is different in their binary representation.
• In all Gray code sequences of length n, all possible binary combinations of this length will appear.

Generate Gray code:

n=1:

• 0

n>1:

• Write the n-1 bit Gray code sequence in reverse order.
• Add 0 in front of the original sequence and 1 in front of the reverse sequence.

For example, to generate a 4-digit Gray code:

1. The 3-digit Gray code sequence is written in reverse order: 011 100
2. Add in front of the original sequence 0, add 1 in front of the opposite sequence: 0001 1001 1110 1111

Therefore, the 4-bit Gray code sequence is: 0000 0001 0011 0010 0110 0111 0101 0100 1100 1101 1111 1110 1010 1011 1001 10 00

Application:

Gray code has applications in various fields, such as:

• Cyclic Redundancy Check (CRC)
• Error detection and correction
• Encoder and decoder
• Data transmission and storage

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