js-rhino, 91 bytes

Result

WA

Code [DL]

s= java.lang.System.in;
for(;s.readLine();)print(+!(Math.sqrt(8*parseInt(c.next(),2)+1)%1))

stdin

10101100
00100101
00001011
01101000
01001010
11111111
00100001
11100111
00101101
10110000
11101010
00010001
00000000
10001010
01101101
01101001
00010101
11011010
10001000
01001011
00000110
01011011
01101100
10101011
10011001
10111110
01111000
11000010
00001010
00000001
00011100
11111101
01000010
11010010
00011000
00100100
11010100
00100010
10010100
00011100
00000011
00001111
00110111
10010011
11111101
10111011
00010011
01001110
11000101
10000000

stdout

stderr

js: uncaught JavaScript runtime exception: TypeError: Cannot find function readLine in object java.io.BufferedInputStream@449b2d27.

strace