**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 parityExample: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++

`// C++ program to find parity ` `// of an integer ` `# include<bits/stdc++.h> ` `# define bool int ` `using` `namespace` `std; ` ` ` `// 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; ` ` ` `cout<<` `"Parity of no "` `<<n<<` `" = "` `<<(getParity(n)? ` `"odd"` `: ` `"even"` `); ` ` ` ` ` `getchar` `(); ` ` ` `return` `0; ` `} ` |

## C

`// C program to find parity ` `// of an integer ` `# 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". ` |

## C#

`// C# program to find parity of an integer ` `using` `System; ` ` ` `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` `bool` `getParity(` `int` `n) ` ` ` `{ ` ` ` `bool` `parity = ` `false` `; ` ` ` `while` `(n != 0) ` ` ` `{ ` ` ` `parity = !parity; ` ` ` `n = n & (n-1); ` ` ` `} ` ` ` `return` `parity; ` ` ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `Main () ` ` ` `{ ` ` ` `int` `n = 7; ` ` ` `Console.Write(` `"Parity of no "` `+ n ` ` ` `+ ` `" = "` `+ (getParity(n)? ` ` ` `"odd"` `: ` `"even"` `)); ` ` ` `} ` `} ` ` ` `// This code is contributed by nitin mittal. ` |

## PHP

`<?php ` `// PHP program to find the parity ` `// of an unsigned integer ` ` ` `// Function to get parity of ` `// number n. It returns 1 ` `// if n has odd parity, and ` `// returns 0 if n has even ` `// parity ` `function` `getParity( ` `$n` `) ` `{ ` ` ` `$parity` `= 0; ` ` ` `while` `(` `$n` `) ` ` ` `{ ` ` ` `$parity` `= !` `$parity` `; ` ` ` `$n` `= ` `$n` `& (` `$n` `- 1); ` ` ` `} ` ` ` `return` `$parity` `; ` `} ` ` ` ` ` `// Driver Code ` ` ` `$n` `= 7; ` ` ` `echo` `"Parity of no "` `,` `$n` `,` `" = "` `, ` ` ` `getParity(` `$n` `)? ` `"odd"` `: ` `"even"` `; ` ` ` `// This code is contributed by anuj_67. ` `?> ` |

**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.

**References:**

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

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