格雷码的十进制等效及其逆

给定一个十进制数n。用十进制形式找到该数字的格雷码。

例子 ：

Input : 7
Output : 4
Explanation: 7 is represented as 111 in binary form. The 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 gray code
of 1010 is 1111 in binary form whose decimal equivalent is 15

下表显示了将二进制代码值转换为格雷代码值的方法：

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
4	100	110	6
5	101	111	7
6	110	101	5
7	111	100	4

以下是将十进制代码值转换为格雷代码值的方法。
令G(n)为等效于二进制表示n的格雷码。考虑数字n和数字比特G(n)的比特。注意，n和G(n)的最左置位在同一位置。假设此位置为i，其右边的位置为(i + 1)，(i + 2_等)。如果n中的第i位为1，则G(n)中的^第(i +1)位为0，并且反之亦然，第(i + 2)位也是如此，以此类推，因此我们有G(n)= n xor(n >> 1)：

C++

// CPP Program to convert given
// decimal number into decimal
// equivalent of its gray code form
#include 
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

Python 3

# 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

> 1);
}
  
    // Driver Code
    $n = 10;
    echo grayCode($n) ;
  
// This code is contributed by nitin mittal.
?>

输出：

15

查找灰色逆代码
给定格雷码的十进制等效数字n。查找十进制形式的反数字。

例子：

Input : 4
Output : 7

Input : 15
Output : 10

下面是将格雷码值转换为十进制码值的方法。
我们将从较旧的位转到较年轻的位(即使最小的位也具有数字1，而最老的位则被编号为k)。我们获得第n _i个数字n的位与第g _i个数字g的位之间的这种关系：

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 
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.

的PHP

> 1)
        $inv ^= $n;
  
    return $inv;
}
  
    // Driver Code
    $n = 15;
    echo inversegrayCode($n);
  
// This code is contributed by anuj_67.
?>

输出：

10