**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:**

# 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; }

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(Logn).

**Uses: **Parity is used in error detection and cryptography.

References:

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