Decimal Equivalent of Gray Code and its Inverse

Given a decimal number n. Find the gray code of this number in decimal form.

Examples:

Input : 7 
Output : 4 
Explanation: 7 is represented as 111 in binary form. The equivalent gray code 
of 111 is 100 in binary form, whose decimal equivalent is 4.

Input : 10 
Output : 15 
Explanation: 10 is represented as 1010 in binary form. The equivalent gray code 
of 1010 is 1111 in binary form, whose decimal equivalent is 15. 

The following table shows the conversion of binary code values to gray code values: 

Decimal Value	Binary Equivalent	Gray Code Equivalent	Decimal Value of Gray Code Equivalent
0	000	000	0
1	001	001	1
2	010	011	3
3	011	010	2
4	100	110	6
5	101	111	7
6	110	101	5
7	111	100	4

Below is the approach for the conversion of decimal code values to gray code values.
Let G(n) be the Gray code equivalent of binary representation n. Consider bits of a number n and a number bit G(n). Note that the leftmost set bits of both n and G(n) are in the same position. Let this position be i and positions on the right of it be (i+1), (i+2), etc. The (i + 1)^th bit in G(n) is 0 if (i+1)th bit in n is 1 and vice versa is also true. The same is true for (i+2)-th bits, etc. Thus we have G (n) = n xor (n >> 1): 

C++

// CPP Program to convert given
// decimal number into decimal
// equivalent of its gray code form
#include <bits/stdc++.h>
using namespace std;

int grayCode(int n)
{
    /* Right Shift the number by 1
       taking xor with original number */
    return n ^ (n >> 1);
}

// Driver Code
int main()
{
    int n = 10;
    cout << grayCode(n) << endl;
    return 0;
}

Java

// Java Program to convert given
// decimal number into decimal
// equivalent of its gray code form
class GFG {

    static int grayCode(int n)
    {

        // Right Shift the number
        // by 1 taking xor with
        // original number
        return n ^ (n >> 1);
    }

    // Driver Code
    public static void main(String[] args)
    {

        int n = 10;

        System.out.println(grayCode(n));
    }
}

// This code is contributed by
// Smitha Dinesh Semwal

Python3

# Python 3 Program to convert
# given decimal number into
# decimal equivalent of its
# gray code form

def grayCode(n):

    # Right Shift the number
    # by 1 taking xor with
    # original number
    return n ^ (n >> 1)


# Driver Code
n = 10
print(grayCode(n))

# This code is contributed
# by Smitha Dinesh Semwal

C#

// C# Program to convert given
// decimal number into decimal
// equivalent of its gray code form
using System;

public class GFG {

    // Function for conversion
    public static int grayCode(int n)
    {

        // Right Shift the number
        // by 1 taking xor with
        // original number
        return n ^ (n >> 1);
    }

    // Driver Code
    static public void Main ()
    {
        int n = 10;

        Console.WriteLine(grayCode(n));
    }
}

// This code is contributed by Ajit.

PHP

<?php
// PHP Program to convert given
// decimal number into decimal
// equivalent of its gray code form

function grayCode($n)
{
    /* Right Shift the number by 1
       taking xor with original
       number */
    return $n ^ ($n >> 1);
}

    // Driver Code
    $n = 10;
    echo grayCode($n) ;

// This code is contributed by nitin mittal.
?>

Javascript

<script>

// Javascript Program to convert given
// decimal number into decimal
// equivalent of its gray code form

function grayCode(n)
{
    /* Right Shift the number by 1
       taking xor with original number */
    return n ^ (n >> 1);
}

// Driver Code
var n = 10;
document.write( grayCode(n) );


</script>

Output:

15

Time Complexity: O(1) 
Auxiliary Space: O(1)

Finding the Inverse Gray Code
Given a decimal equivalent number n of a gray code. Find its original number in decimal form.

Examples:

Input : 4 
Output : 7

Input : 15 
Output : 10

Below is the approach for the conversion of gray code values to decimal code values.
We will go from the older bits to the younger ones (even the smallest bit has the number 1, and the oldest bit is numbered k). We obtain such relations between the bits of the n_i number n and the bits of the g_i number g: 

 Steps to solve this problem:

• Initialize a variable inv to 0.
•  Iterate over the binary digits of n from the rightmost digit to the leftmost digit and right shift n by one bit.
  • Take the bitwise XOR of the current value of inv with the value of n.
• return the value of inv.

 nk = gk, 
 nk-1 = gk-1 xor nk = gk xor gk-1
 nk-2 = gk-2 xor nk-1 = gk xor gk-1 xor gk-2 
 nk-3 = gk-3 xor nk-2 = gk xor gk-1 xor gk-2 xor gk-3
 ... 

C++

// CPP Program to convert given
// decimal number of gray code
// into its inverse in decimal form
#include <bits/stdc++.h>
using namespace std;

int inversegrayCode(int n)
{
    int inv = 0;

    // Taking xor until n becomes zero
    for (; n; n = n >> 1)
        inv ^= n;

    return inv;
}

// Driver Code
int main()
{
    int n = 15;
    cout << inversegrayCode(n) << endl;
    return 0;
}

Java

// Java Program to convert given
// decimal number of gray code
// into its inverse in decimal form
import java.io.*;

class GFG {

    // Function to convert given
    // decimal number of gray code
    // into its inverse in decimal form
    static int inversegrayCode(int n)
    {
        int inv = 0;

        // Taking xor until n becomes zero
        for ( ; n != 0 ; n = n >> 1)
            inv ^= n;

        return inv;
    }

    // Driver code
    public static void main (String[] args)
    {
        int n = 15;
        System.out.println(inversegrayCode(n));
    }
}

// This code is contributed by Ajit.

Python3

# Python3 Program to convert
# given decimal number of
# gray code into its inverse
# in decimal form

def inversegrayCode(n):
    inv = 0;

    # Taking xor until
    # n becomes zero
    while(n):
        inv = inv ^ n;
        n = n >> 1;
    return inv;

# Driver Code
n = 15;
print(inversegrayCode(n));

# This code is contributed
# by mits

C#

// C# Program to convert given
// decimal number of gray code
// into its inverse in decimal form
using System;

class GFG {

    // Function to convert given
    // decimal number of gray code
    // into its inverse in decimal form
    static int inversegrayCode(int n)
    {
        int inv = 0;

        // Taking xor until n becomes zero
        for ( ; n != 0 ; n = n >> 1)
            inv ^= n;

        return inv;
    }

    // Driver code
    public static void Main ()
    {
        int n = 15;
        Console.Write(inversegrayCode(n));
    }
}

// This code is contributed by nitin mittal.

PHP

<?php
// PHP Program to convert given
// decimal number of gray code
// into its inverse in decimal form

function inversegrayCode( $n)
{
    $inv = 0;

    // Taking xor until
    // n becomes zero
    for (; $n; $n = $n >> 1)
        $inv ^= $n;

    return $inv;
}

    // Driver Code
    $n = 15;
    echo inversegrayCode($n);

// This code is contributed by anuj_67.
?>

Javascript

<script>

// JavaScript Program to convert given
// decimal number of gray code
// into its inverse in decimal form

function inversegrayCode(n)
{
    let inv = 0;

    // Taking xor until n becomes zero
    for (; n; n = n >> 1)
        inv ^= n;

    return inv;
}

// Driver Code
    let n = 15;
    document.write(inversegrayCode(n));

</script>

Output:

10

Time Complexity: O(log n) 
Auxiliary Space: O(1)

Please suggest if someone has a better solution which is more efficient in terms of space and time.
This article is contributed by Aarti_Rathi. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above