js-rhino, 115 bytes

Result

AC

Code [DL]

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

stdin

01011011
00010001
01101001
00011011
01010010
00010011
11000010
01111000
00000001
00001111
10001001
00000011
01000010
10010010
11101110
01110000
10101011
00001010
10111110
10010101
11111101
00101111
11110101
11010010
00111000
00100100
10001000
10110011
11100010
11100011
11011100
00110111
01001110
00010010
11010000
00011100
00010101
00000000
10011010
11100111
10111111
01000010
01011100
00101101
00101101
00000110
00011110
01111111
10011001
01010101

stdout

1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0

stderr

strace