js-rhino, 170 bytes

Result

WA

Code [DL]

importPackage(java.io);importPackage(java.lang);s=new BufferedReader(new InputStreamReader(System.in));while(l=s.readLine()){print(+!((Math.sqrt(8*parseInt(l,2)+1)-1)%2)}

stdin

11001001
00110010
00000100
00100111
01110111
10101011
10100011
10100101
00001111
10001000
11100111
00111100
11010010
10111110
11000010
00000000
11111101
00000110
01111000
00000000
10101000
00000011
01111001
00010101
01100001
01001110
00001010
01000010
00011100
00001000
10011001
01101001
01010000
11110110
11100101
11110000
11010011
00101101
00011101
01011011
11000111
10110101
11101101
00110111
10111110
00000001
10111010
00100100
00101011
10001011

stdout

stderr

js: "/volume/CODE", line 1: missing ) after argument list
js: importPackage(java.io);importPackage(java.lang);s=new BufferedReader(new InputStreamReader(System.in));while(l=s.readLine()){print(+!((Math.sqrt(8*parseInt(l,2)+1)-1)%2)}
js: .........................................................................................................................................................................^
js: "/volume/CODE", line 1: missing } in compound statement
js: importPackage(java.io);importPackage(java.lang);s=new BufferedReader(new InputStreamReader(System.in));while(l=s.readLine()){print(+!((Math.sqrt(8*parseInt(l,2)+1)-1)%2)}
js: .........................................................................................................................................................................^
js: "/volume/CODE", line 1: Compilation produced 2 syntax errors.

strace