DigitalZoul: Let's Code Gray Code !!

We All know that physical quantities have continuous values, and in order to convert physical quantities to digital systems we need to perform analog-to-digital conversion. However sometimes fast transition from one analog value to another may cause huge error if we use binary system.

For example, take the decimal value 3 which is equivalent to 0011 in binary now let's say that a noise cause the third bit to flipped to 1, now we have 0111 in binary which is equivalent to 7 in decimal , which means that we just jump from 3 to 7 by flipping one bit !!.
In Gray code (named after Frank Gray) only one bit change at time, which is reduces the error in case if one bit flipped in transition from one decimal value to another. The following table shows the conversion from decimal to binary and Gray code

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

From the table we can notice that only one bit get flipped at a time, take for example the transition from 5 to 6 in binary we need to flip two bits while in Gray code only the
second bit get flipped. Now we want to know how we can decide to flip a bit or not in Gray code. The conversion flows the following formula :

$Gray code=(decimal value)XOR(decimal value>>1)$
Conversion from decimal to Gray code

Let's take the decimal value 2 for example which is 0010 in binary, so the first step we need to shift the value to the right by 1, so we will have 0001, last we need to perform XOR operation (0010) XOR (0001) which is equals to (0011) in Gray code. Using this formula can convert any unsiged int number to Gray code equivalent value. Now let's write a c code that can convert decimal values to Gray code the values will be return in decimal representation so use can use the given table to check the values


#include <stdio.h>
#include <stdint.h>
unsigned int DecimalToGray(unsigned int num) 
{
    return (num ^ (num >> 1));
}


int main(int argc, char **argv) 
{

    for (unsigned int i=0;i<16; i++)
    {
        printf("Decimal value: %u, Gray code equivalent: %u\n",i,DecimalToGray(i));
    }
    
    
    
    return 0;
}

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Let's Code Gray Code !!