js-rhino, 171 bytes

Result

AC

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

11100111
11100110
11010010
00001111
01111011
10110000
00011100
10000000
11011101
01000010
00110111
10011001
01110001
00000011
10101011
00100100
01011011
00000100
00011010
00101101
01111000
01111010
00000110
01010001
01101001
01000010
10100001
00111101
01000000
01101111
10001000
10010110
10011000
10011110
11101010
01010000
00001010
10011010
11010010
00010011
11010011
00000000
10111110
00101011
11111010
01101100
00010101
00000001
11111101
01001110

stdout

1
0
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1

stderr

strace