js-rhino, 84 bytes

Result

WA

Code [DL]

for(;;)print(+!(Math.sqrt(parseInt(java.lang.System.console().readLine(),2)*8+1)%1))

stdin

10001010
00010101
10010011
00001111
00001000
00110101
10110010
00011100
11100111
11010010
00000110
10101001
00011111
00000011
10011110
11110110
11111101
01010001
00001010
10100101
11011000
00110111
10001000
10101011
10001111
01011011
00000110
01010100
01111000
00101001
10100001
10111101
10011001
01011101
01000011
00000000
10111110
11001011
00001110
01001110
10011101
00100100
10001001
10001101
01101001
00000001
01010101
11010010
00101101
01000010

stdout

stderr

js: uncaught JavaScript runtime exception: TypeError: Cannot call method "readLine" of null

strace