Gray Code Conversion

What is grey code?

#include<stdio.h>
#include<conio.h>
void main()
{int a[10],i=0,c=0,n,b[10];
printf("\n enter the binary code");
scanf("%d",&n);
while(n!=0)
{a[i]=n%10;
n/=10;
i++;
c++;
}
for(i=c-1;i>=0;i--)
{
b[i]=a[i];
}
for(i=c-1;i>=0;i--)
{
if(b[i]==1)
{
if(a[i-1]==1)
a[i-1]=0;
else
a[i-1]=1;
}
}
printf("\n the gray code is");
for(i=c-1;i>=0;i--)
printf("%d",a[i]);
getch();
}

Here is a more refined version that only requires one array, can be up to 32bit and includes a proving decode that's useful in its own right for rotary encoders.

/* 
   Convert decimal number to Grey code and back again
*/

# include<stdio.h>

#define SIZE 32

int bits[SIZE], i; // could be chars in 8 bit machine
unsigned long num; // could be int if less than 17 bit Grey code

void main(){
  printf("\n    ");
  printf("%d",SIZE);
  printf(" bit number conversion\n");

  printf("\n Enter number     ");
  scanf("%lu",&num);

  /* converting number to binary equivalent */
  /* MSB is 1st element in array */
  for(i = 0; i < SIZE; i ++){
    bits[SIZE-1-i] = (num >> i) & 1;
  }

  /* printing binary */
  printf(" Binary           ");
  for(i = 0; i < SIZE; i ++){
    printf("%d",bits[i]);
  }

  /* in-line gray code conversion */
  for(i = SIZE-1; i > 0; i --){
    bits[i] = bits[i] ^ bits[i - 1];
  }

  /* printing gray code */
  printf("\n Gray code        ");
  for(i = 0; i < SIZE; i ++){
    printf("%d",bits[i]);
  }

  /* in-line conversion back to binary */
  for(i = 1; i < SIZE; i++){
    bits[i] = bits[i] ^ bits[i - 1];
  }

  /* reprinting binary */
  printf("\n Restored binary  ");
  for(i=0;i<SIZE;i++){
    printf("%d",bits[i]);
  }
  
   /* convert back to decimal */
  num = 0;
  for (i = 0; i < SIZE; i ++){
    num = (num<<1) | bits[i];
  }

  /* reprinting decimal number */
  printf("\n Restored decimal ");
  printf("%lu",num);
  printf("\n");
}

x^(x>>1)

Wait, what? No!

Really not trying to be rude here, but this code gives "ineffective" a whole new meaning and it's listed to high on google not to include a post with the proper way of doing this.

// Convert binary to gray-code
unsigned bin2gray(unsigned bits) {
  return (bits >> 1) ^ bits; // works with any word size
}

// Convert gray-code to binary
unsigned gray2bin(unsigned bits) {
  bits ^= bits >> 16; // remove if word is 16 bits or less
  bits ^= bits >>  8; // remove if word is 8 bits or less
  bits ^= bits >>  4;
  bits ^= bits >>  2;
  bits ^= bits >>  1;
  return bits;
}

Gray code is part of a class of codes called minimum change codes.

It's a scheme where each increment in value changes only one bit of a word. For example, with regular binary code: 7+1=8. 7 is b0111, 8 is b1000. That's four bits changed.

This can be a problem in many cases such as simple rotary encoders, where several physical tracks are used to encode a parallel output. A transition that changes many bits can not be reliably implemented, as one track will always loose or achieve contact with it's wiper before others, leading to transient glitches in the output of completely incorrect values. Gray code will limit the possible error to just one value up/down as any glitches will only affect the one bit and can easily be filtered out if desired.

There are many other applications of minimum change codes. Google and wikipedia is your friend here.