csharp, 134 bytes

Result

WA

Code [DL]

using System;class A{static void Main(){try{for(;;)Console.Write(Math.Sqrt(8*Convert.ToByte(Console.ReadLine(),2)+1)%2==1?1:0);}catch}

stdin

00101101
01111001
11011001
00100100
10110100
01001110
00000110
00011011
01010101
01100111
11111101
00001010
10000011
00001111
10101010
00110101
00011100
10011001
00000001
00000011
10001000
00111110
11010010
01110111
10001100
00110111
00001111
00000000
00001110
00110001
10101011
10111011
11101000
00110110
00111111
11100111
10100000
00001001
01011011
10101101
01101001
01000010
11000001
00010101
00000100
01011011
11000111
10111110
10011110
01111000

stdout

Compilation failed: 2 error(s), 0 warnings

stderr

/tmp/code.cs(1,133): error CS1524: Unexpected symbol `}', expecting `(', `{', or `when'
/tmp/code.cs(1,134): error CS1519: Unexpected symbol `end-of-file' in class, struct, or interface member declaration
Cannot open assembly '/tmp/code.exe': No such file or directory.
rm: cannot remove '/tmp/code.exe': No such file or directory

strace