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 Bianry 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++
// 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
// 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
# 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#
// 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
<?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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