python3, 65 bytes

Result

AC

Code [DL]

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

stdin

01011110
11111101
10101011
10101011
00100100
11110101
01111000
00011100
00110111
01000010
10100000
01101001
01111110
11010010
10001000
11001001
00001000
00000001
10010010
01010110
00001111
11000110
01101000
11110001
00001010
10111000
00010101
00101010
00010111
00101101
00001110
01100100
01100111
01101100
10011001
00101101
00000011
10110101
00000000
01001110
01101111
00000110
10011101
11100111
00010100
01111001
01011011
11001110
10111110
01011000

stdout

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

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(int(y*y==x))
EOFError: EOF when reading a line

strace