python3, 57 bytes

Result

AC

Code [DL]

while 1:x=eval("0b"+input())*8+1;print(int(x**0.5)**2//x)

stdin

01110111
00001111
11011010
00110111
01110010
10001000
10000101
00011101
10010010
10101011
11111111
10010110
10000010
00001111
00000000
00110111
00101101
00001010
01100101
01111000
11100111
01001110
00100100
01011011
10111110
00000001
00000011
10011001
01101001
01010110
00010000
00010101
11101110
00001001
10101111
00011100
01000011
00100010
10001101
11000101
01010011
01100011
11111101
10111111
11011110
00111101
01000000
00000110
01000010
11010010

stdout

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

stderr

Traceback (most recent call last):
  File "/volume/CODE", line 1, in <module>
    while 1:x=eval("0b"+input())*8+1;print(int(x**0.5)**2//x)
EOFError: EOF when reading a line

strace