csharp, 135 bytes

Result

WA

Code [DL]

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

stdin

00001000
10001000
01001110
00001010
11110100
11111101
01111000
00100111
00001101
11001100
01111000
01011011
01100011
11011100
10101111
00110101
10111110
01000101
00000001
10011001
10011100
01101001
11000110
00000110
00101010
00101101
10101011
00001111
00000011
01010001
01010100
00100100
00011100
11100000
00001010
00100010
10000001
00110111
11000001
11100111
11101000
00000000
01000010
01111001
11111010
00011011
11010010
00001110
01001011
00010101

stdout

Compilation failed: 2 error(s), 0 warnings

stderr

/tmp/code.cs(1,44): error CS1525: Unexpected symbol `for', expecting `{'
/tmp/code.cs(1,127): error CS1525: Unexpected symbol `catch'
Cannot open assembly '/tmp/code.exe': No such file or directory.
rm: cannot remove '/tmp/code.exe': No such file or directory

strace