js-rhino, 122 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)%2));}

stdin

00000011
00000000
10001000
00001000
11100111
11010010
10101110
11110000
10010010
11100110
01111000
11110101
11111101
01101011
11110100
00001001
00101101
11100101
01111011
00000110
11110011
00001010
00011100
00011010
01010010
11010010
01101001
00110111
00100100
11010101
00100101
00001111
11111101
01011010
01000010
10111110
11010000
01011011
11111100
10100101
00110000
01101010
00000001
01101100
10101011
00010101
10100011
00011110
01001110
10011001

stdout

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

stderr

strace