js-rhino, 93 bytes

Result

WA

Code [DL]

for(a=new java.util.Scanner(System.in);;)print(+!(Math.sqrt(parseInt(a.nextLine(),2)*8+1)%1))

stdin

11101010
01011011
01011011
00011100
00001111
01111000
11100111
00010101
00000001
00110111
01101001
01101111
01101101
01001110
10111111
00101000
00001110
00101101
01110110
11010010
00110110
00001010
11101110
10111011
00111100
00110100
01000010
10010000
11011000
10101011
10100100
11001111
01111000
11111000
00000110
01110111
11011011
01100100
10011001
10110111
11010100
10111110
10001000
10001110
01010010
00100100
00000011
11010101
11111101
00000000

stdout

stderr

js: uncaught JavaScript runtime exception: ReferenceError: "System" is not defined.

strace