python3, 47 bytes

Result

AC

Code [DL]

while 1:print(+((1+8*int(input(),2))**.5%2==1))

stdin

00111011
01011001
11100101
00100100
10111110
11111101
00110111
00101111
11000001
01101001
10000111
00001010
00010101
00010010
10101100
00011100
10100111
10010001
11010101
00000011
01000010
01110011
01101110
01011011
01111011
10101011
10011001
10101110
01101111
00000010
00001111
10000011
11101011
11010010
01111000
11111000
01000010
10001000
01100100
00000000
00101101
00000110
11110110
11101101
00001000
11101000
00000001
01001110
00011100
11100111

stdout

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

stderr

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

strace