python3, 60 bytes

Result

AC

Code [DL]

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

stdin

10101011
01111111
10001000
11110010
00100100
10100010
10101100
00101101
10000000
00110111
11100111
10110101
01101010
10001100
01111101
00000000
01001000
10010111
00000001
11111010
10100111
01111000
11001101
10101110
00011100
00001010
00111000
00010101
01101001
10111110
01011011
01000010
11010010
01001110
00100100
10000111
01010100
00101000
11100001
00110101
11010011
00000110
10100011
00000011
10000001
00001111
01101001
10011001
01000111
11111101

stdout

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

stderr

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

strace