Gray code

Gray code

Gray Code Wheel

“The reflected binary code is called Gray code after the name of Frank Gray.”

·         4 bit code.

·         Contains 0-15 decimal numbers.

Decimal	Binary	Gray code
0	0000	0000
1	0001	0001
2	0010	0011
3	0011	0010
4	0100	0110
5	0101	0111
6	0110	0101
7	0111	0100
8	1000	1100
9	1001	1101
10	1010	1111
11	1011	1110
12	1100	1010
13	1101	1011
14	1110	1001
15	1111	1000

   Binary to Gray code conversion

To convert a binary number to Gray code, apply following steps;

Step 1:
 left most bit of gray code and its corresponding binary code is same.

Step2:
going from left to right, add each adjacent pair of binary digit to get the next gray code digit, regardless carries.

e.g convert binary number (0100)₂ to gray code.

Step1:
             0    1    0    0       (binary code of 4)

             ↓

             0

Step2:
            0 +  1    0     0

            ↓      ↓

            0      1

Step3:
             0      1   +   0     0

             ↓       ↓       ↓

             0      1        1

Step4:
             0       1       0  +   0

             ↓       ↓        ↓        ↓

             0       1        1       0     (Gray code)

 Gray code to binary conversion

It has following steps.

Step1:
 write down left most bit of gray code as it is same in binary code.

Step2:
 going from left to write, add last single bit of binary into next bit of gray code then write down the answer and continue till last bit.

e.g convert gray code (0101) into binary code.

Step1:
             0     1     0    1

             ↓

             0

Step2:
             0     1      0      1

             ↓ +  ↓

             0           1

Steo3:
                   0       1          0       1

                   ↓        ↓    +    ↓

                   0        1          1

Step4:
                  0       1       0       1

                  ↓       ↓        ↓   +  ↓

                  0        1       1       0