The parity of 1 is 1 (mod 2).
The parity of 10 is 1 (mod 2).
The parity of 1000 is 1 (mod 2).
The parity of 1010 is 2 (mod 2).
The parity of 10101 is 3 (mod 2).
The parity of 111011100110101100101000000000 is 13 (mod 2).
The parity of 1111111111111111111111111111110 is 30 (mod 2).
The parity of 1111111111111111111111111111111 is 31 (mod 2).