Write a C program to find the parity of an unsigned integer

3.1

Parity: Parity of a number refers to whether it contains an odd or even number of 1-bits. The number has “odd parity”, if it contains odd number of 1-bits and is “even parity” if it contains even number of 1-bits.
Main idea of the below solution is – Loop while n is not 0 and in loop unset one of the set bits and invert parity.

Algorithm: getParity(n)
1. Initialize parity = 0
2. Loop while n != 0      
      a. Invert parity 
             parity = !parity
      b. Unset rightmost set bit
             n = n & (n-1)
3. return parity

Example:
 Initialize: n = 13 (1101)   parity = 0

n = 13 & 12  = 12 (1100)   parity = 1
n = 12 & 11 = 8  (1000)   parity = 0
n = 8 & 7 = 0  (0000)    parity = 1

Program:

C

# include <stdio.h>
# define  bool int

/* Function to get parity of number n. It returns 1
   if n has odd parity, and returns 0 if n has even
   parity */
bool getParity(unsigned int n)
{
    bool parity = 0;
    while (n)
    {
        parity = !parity;
        n      = n & (n - 1);
    }        
    return parity;
}

/* Driver program to test getParity() */
int main()
{
    unsigned int n = 7;
    printf("Parity of no %d = %s",  n, 
             (getParity(n)? "odd": "even"));
    
    getchar();
    return 0;
}

Java

// Java program to find parity
// of an integer
import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.BigInteger;

class GFG
 {
    /* Function to get parity of number n.
    It returns 1 if n has odd parity, and
    returns 0 if n has even parity */
    static boolean getParity(int n)
    {
        boolean parity = false;
        while(n != 0)
        {
            parity = !parity;
            n = n & (n-1);
        }
        return parity;
        
    }
    
    /* Driver program to test getParity() */
    public static void main (String[] args)
    {
        int n = 12;
        System.out.println("Parity of no " + n + " = " +
                         (getParity(n)? "odd": "even")); 
    }
}
/* This code is contributed by Amit khandelwal*/ 

Python3

# Python3 code to get parity.

# Function to get parity of number n. 
# It returns 1 if n has odd parity, 
# and returns 0 if n has even parity
def getParity( n ):
    parity = 0
    while n:
        parity = ~parity
        n = n & (n - 1)
    return parity

# Driver program to test getParity()
n = 7
print ("Parity of no ", n," = ",
     ( "odd" if getParity(n) else "even"))

# This code is contributed by "Sharad_Bhardwaj".


Output:

Parity of no 7 = odd

Above solution can be optimized by using lookup table. Please refer to Bit Twiddle Hacks[1st reference] for details.

Time Complexity: The time taken by above algorithm is proportional to the number of bits set. Worst case complexity is O(Log n).

Uses: Parity is used in error detection and cryptography.

Compute the parity of a number using XOR and table look-up

References:
http://graphics.stanford.edu/~seander/bithacks.html#ParityNaive – last checked on 30 May 2009.

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