Finding the Parity of a number Efficiently

Given an integer N. The task is to write a program to find the parity of the given number.

Note: Parity of a number is used to define if the total number of set-bits(1-bit in binary representation) in a number is even or odd. If the total number of set-bits in the binary representation of a number is even then the number is said to have even parity, otherwise, it will have odd parity.

Examples:



Input : N = 13 
Output : Odd Parity
Binary representation of 13 is (1101)

Input : N = 9 (1001)
Output : Even Parity

The parity of a number represented by 32-bits can be efficiently calculated by performing the following operations.

Let the given number be x, then perform the below operations:

  • y = x^(x>>1)
  • y = y^(y>>2)
  • y = y^(y>>4)
  • y = y^(y>>8)
  • y = y^(y>>16)

Now, the rightmost bit in y will represent the parity of x. If the rightmost bit is 1, then x will have odd parity and if it is 0 then x will have even parity.

So, in order to extract the last bit of y, perform bit-wise AND operation of y with 1.

if(y&1==1)
    odd Parity
else
    even Parity

Below is the implementation of the above approach:

C++

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// Program to find the parity of a given number
#include <bits/stdc++.h>
  
using namespace std;
  
// Function to find the parity
bool findParity(int x)
{
    int y = x ^ (x >> 1);
    y = y ^ (y >> 2);
    y = y ^ (y >> 4);
    y = y ^ (y >> 8);
    y = y ^ (y >> 16);
  
    // Rightmost bit of y holds the parity value
    // if (y&1) is 1 then parity is odd else even
    if (y & 1)
        return 1;
    return 0;
}
  
// Driver code
int main()
{
    (findParity(9)==0)?cout<<"Even Parity\n":
                            cout<<"Odd Parity\n";
      
    (findParity(13)==0)?cout<<"Even Parity\n":
                            cout<<"Odd Parity\n";
      
    return 0;
}

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Java














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// Program to find the 


// parity of a given number 


import java.io.*; 


  


class GFG  


{ 


  


// Function to find the parity 


static boolean findParity(int x) 


{ 


    int y = x ^ (x >> 1); 


        y = y ^ (y >> 2); 


        y = y ^ (y >> 4); 


        y = y ^ (y >> 8); 


        y = y ^ (y >> 16); 


  


    // Rightmost bit of y holds 


    // the parity value 


    // if (y&1) is 1 then parity  


    // is odd else even 


    if ((y & 1) > 0) 


        return true; 


    return false; 


} 


  


// Driver code 


public static void main (String[] args)  


{ 


    if((findParity(9) == false)) 


        System.out.println("Even Parity"); 


    else


        System.out.println("Odd Parity"); 


      


    if(findParity(13) == false) 


        System.out.println("Even Parity"); 


    else


        System.out.println("Odd Parity"); 


} 


} 


  


// This Code is Contributed by chandan_jnu. 



















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Python3














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# Program to find the 


# parity of a given number 


  


# Function to find the parity 


def findParity(x): 


    y = x ^ (x >> 1); 


    y = y ^ (y >> 2); 


    y = y ^ (y >> 4); 


    y = y ^ (y >> 8); 


    y = y ^ (y >> 16); 


  


    # Rightmost bit of y holds  


    # the parity value if (y&1) 


    # is 1 then parity is odd 


    # else even 


    if (y & 1): 


        return 1; 


    return 0; 


  


# Driver code 


if(findParity(9) == 0): 


    print("Even Parity"); 


else: 


    print("Odd Parity\n"); 


  


if(findParity(13) == 0): 


    print("Even Parity"); 


else: 


    print("Odd Parity"); 


      


# This code is contributed by mits 



















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C#














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// Program to find the 


// parity of a given number 


using System; 


  


class GFG  


{ 


  


// Function to find the parity 


static bool findParity(int x) 


{ 


    int y = x ^ (x >> 1); 


        y = y ^ (y >> 2); 


        y = y ^ (y >> 4); 


        y = y ^ (y >> 8); 


        y = y ^ (y >> 16); 


  


    // Rightmost bit of y holds 


    // the parity value 


    // if (y&1) is 1 then parity  


    // is odd else even 


    if ((y & 1) > 0) 


        return true; 


    return false; 


} 


  


// Driver code 


public static void Main ()  


{ 


    if((findParity(9) == false)) 


        Console.WriteLine("Even Parity"); 


    else


        Console.WriteLine("Odd Parity"); 


      


    if(findParity(13) == false) 


        Console.WriteLine("Even Parity"); 


    else


        Console.WriteLine("Odd Parity"); 


} 


} 


  


// This Code is Contributed  


// by chandan_jnu 



















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PHP














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<?php 


// Program to find the 


// parity of a given number 


  


// Function to find the parity 


function findParity($x) 


{ 


    $y = $x ^ ($x >> 1); 


    $y = $y ^ ($y >> 2); 


    $y = $y ^ ($y >> 4); 


    $y = $y ^ ($y >> 8); 


    $y = $y ^ ($y >> 16); 


  


    // Rightmost bit of y holds  


    // the parity value if (y&1) 


    // is 1 then parity is odd 


    // else even 


    if ($y & 1) 


        return 1; 


    return 0; 


} 


  


// Driver code 


(findParity(9) == 0) ?  


 print("Even Parity\n"): 


 print("Odd Parity\n"); 


  


(findParity(13) == 0) ?  


print("Even Parity\n"): 


print("Odd Parity\n"); 


      


// This Code is Contributed by mits 


?> 



















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Output:


Even Parity
Odd Parity






          
          
          
          

            

    

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