python3, 54 bytes

Result

AC

Code [DL]

while 1:print(0 if(1+8*int(input(),2))**.5%2-1 else 1)

stdin

11010010
01010010
10111110
01111110
10101011
11101110
11011001
00110000
10000001
10110010
01101001
11110101
00000001
10011001
10101101
00001111
01001111
11000111
01001110
01011011
10001000
00000000
00100100
11100111
01000010
00111100
01000110
00011100
00000110
01101110
00000011
11100010
11111101
01011100
10001011
10111110
00110111
00110101
01111001
00010101
01101011
01111000
11001101
00101101
00011000
10110001
00001010
01110001
11000010
01111000

stdout

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

stderr

Traceback (most recent call last):
  File "/volume/CODE", line 1, in <module>
    while 1:print(0 if(1+8*int(input(),2))**.5%2-1 else 1)
EOFError: EOF when reading a line

strace