js-rhino, 84 bytes

Result

WA

Code [DL]

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

stdin

01101101
00010101
11001000
00000110
10111010
11010001
10011001
10001000
11110001
00011100
01111000
01100001
00101101
00001100
01000110
10110011
00011000
10111110
00001111
01110001
01110010
00001001
00000000
01011011
00001011
00110111
10110111
10101011
01101001
11111101
11100111
01000010
10101001
10001101
01001100
00000011
00000001
00101111
11100000
11010010
00001111
01001111
01001110
00001010
11001100
00111100
01000000
10001110
10011001
00100100

stdout

stderr

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

strace