js-rhino, 98 bytes

Result

WA

Code [DL]

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

stdin

00000110
11010000
01010011
00101000
11111101
01011011
10011110
11111111
10011001
00010101
00000000
11010010
11010011
10011001
10101011
01011101
00000011
10111110
11011100
00000001
10001000
10110111
01101001
10011111
01000010
00101101
01111000
00011100
10111101
10001111
00110110
01001110
01010111
01010010
01111100
00001010
11100010
11001010
01110101
01111000
11100111
00101010
01001011
00001111
00100100
11011000
11101001
10000011
01010000
00110111

stdout

stderr

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

strace