js-rhino, 114 bytes

Result

AC

Code [DL]

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

stdin

00000110
00011100
00101101
00010101
01011011
00001001
10111101
11111101
11100111
01001110
10111110
00000001
10001000
11010101
00110111
11110000
00111001
01011100
00110101
01111000
10000100
10101011
01100100
00000011
11101011
11010010
01111100
11010000
00110000
00100100
00100001
11100000
00101001
01101001
00000000
00001010
01010100
01110101
01011101
10011001
10011111
10010110
00101010
01110011
01110100
00000001
01011011
00001111
00011011
01000010

stdout

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

stderr

strace