Gray code
Karnaugh maps
Create functions to encode a number to and decode a number from Gray code.

Display the normal binary representations, Gray code representations, and decoded Gray code values for all 5-bit binary numbers (0-31 inclusive, leading 0's not necessary).

There are many possible Gray codes. The following encodes what is called "binary reflected Gray code."

Encoding (MSB is bit 0, b is binary, g is Gray code):

if b[i-1] = 1
   g[i] = not b[i]
else
   g[i] = b[i]
Or:

g = b xor (b logically right shifted 1 time)
Decoding (MSB is bit 0, b is binary, g is Gray code):

b[0] = g[0]

for other bits:
b[i] = g[i] xor b[i-1]
Reference
 Converting Between Gray and Binary Codes. It includes step-by-step animations.
 
public class Gray {
	public static long grayEncode(long n){
		return n ^ (n >>> 1);
	}
 
	public static long grayDecode(long n) {
		long p = n;
		while ((n >>>= 1) != 0)
			p ^= n;
		return p;
	}
	public static void main(String[] args){
		System.out.println("i\tBinary\tGray\tDecoded");
		for(int i = -1; i < 32;i++){
			System.out.print(i +"\t");
			System.out.print(Integer.toBinaryString(i) + "\t");
			System.out.print(Long.toBinaryString(grayEncode(i))+ "\t");
			System.out.println(grayDecode(grayEncode(i)));
		}
	}
}
 