php, 76 bytes

Result

AC

Code [DL]

<?php for(;$c=fgets(STDIN);){$j=sqrt(8*bindec($c)+1);echo 1^$j<=>floor($j);}

stdin

00100000
11000100
01111111
11001100
11010000
01011011
11111101
00000110
01011000
00110111
11011010
01001011
00001111
00000000
00000000
00001000
00010110
00000011
01000010
10011001
00100101
00101101
01010110
00000110
11100111
00000001
00101010
11000101
00100100
11100010
10001000
11010010
00001010
11011011
00010101
01001110
10001001
00011100
10111110
10101011
00101000
01111000
01010001
00010010
00101001
10000011
01110110
10110100
01101001
11011001

stdout

00000111010011100111010111001011101101110100000010

stderr

strace