A simple method for Conversion of Gray code to Binary and Binary code to Gray with Example

FIRST convert a Gray-coded number to binary by follow this method :-
The binary number and the Gray-coded number will have the same number of bits

1. The binary MSB (left-hand bit) and Gray code MSB will always be the same

2. To get the binary next-to-MSB (i.e. next digit to the right) add the binary MSB and the gray code next-to-MSB.

3. Record the sum, ignoring any carry.

4. Continue in this manner right through to the end.

example:-

Gray Code           Conversion                       Binary Code

                             Gmsb+1       Bmsb

1111                      1                                             1         (1)

1111                      1     +    1= 10                        10       (2), (3)

1111                      1     +    0=   1                        101     (4)

1111                      1     +    1= 10                        1010

Hence 1111 --> 1010

Lets try one more example:-

Gray Code           Conversion                       Binary Code

                             Gmsb+1       Bmsb

0101                     0                                             0       

0101                     1                                             01     

0101                     0     +    1=   1                         011   

0101                     1     +    1= 10                         0110

*(0 is not a significant digit)
Hence 0101 -->0110

Try same for:

Gray Code                 Binary Code

    0000                          0000

    0001                          0001

    0010                          0011

    0011                          0010

    0100                          0111

    0101                          0110

    0110                          0100

    0111                          0101

    1000                         1111

    1001                         1110

    1010                         1100

    1011                         1101

    1100                         1000

    1101                         1001

    1110                         1011

    1111                         1010

               

Now we will convert a Binary-coded number to Gray by following method :-

The binary number and the Gray-coded number will have the same number of bits.

1. Gray MSB (most significant bit) i.e left most and Binary MSB will be same.

2. To get Gray next to MSB (next digit to the right) subtract next MSB(to right) of Binary from its MSB.
 Bmsb - Bmsb+1=G

3. Ignore negative sign.

4. Continue through this manner right through the end

example:-

Binary Code           Conversion                       Gray Code

                             Bmsb       Bmsb+1

1111                      1                                            1         (1)

1111                      1     -     1=   0                        10       (2), (3)

1111                      1     -     1=   0                        100     (4)

1111                      1     -     1=   0                        1000

Hence 1111 --> 1000

Here we try one more example :- 

Binary Code           Conversion                       Gray Code

                             Bmsb       Bmsb+1

0101                     0                                            0        

0101                     1                                            01       

0101                     1     -     0=   1                        011    

0101                     0     -     1=   1                        0111

Hence 0101 -->0111

Try some more:-

Binary Code               Gray Code

    0000                          0000

    0001                          0001

    0010                          0011

    0011                          0010

    0100                          0110

    0101                          0111

    0110                          0101

    0111                          0100

    1000                         1100

    1001                         1101

    1010                         1111

    1011                         1110

    1100                         1010

    1101                         1011

    1110                         1001

    1111                         1000