js-rhino, 118 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

00110111
00010101
01011011
10101111
10001000
00011100
10111001
01000010
11010010
01001110
01111110
00001010
10010011
01111000
00001111
00000001
00110010
01110101
11010011
11011001
00101101
11000011
11101111
10111110
01110011
10101011
11111101
01010100
10010010
00011010
11010000
10011001
01100000
00000110
00001011
00000000
00000011
01100011
00100100
11111101
10101110
01000000
00010110
01101001
11000001
00000000
00100001
00100011
11100111
00011110

stdout

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

stderr

strace