php, 72 bytes

Result

AC

Code [DL]

<?php for(;$c=fgets(STDIN);){$j=sqrt(8*bindec($c)+1);echo 1^$j<=>$j%50;}

stdin

01000010
11010010
01111110
00000011
10010000
00001010
00010000
00000001
10011111
00001111
00010101
00000000
11111101
00010010
11001110
00100100
00011100
01011010
01100101
10001010
01011011
11000010
01101101
00110111
10111101
11100111
11000101
00101101
11001101
10001000
00101100
00000011
00111001
10111110
10111100
00010111
00111010
10101011
01101001
10100001
01001110
00000110
11111110
00001010
01010101
01000101
11100011
10011001
01111000
00100110

stdout

11010101011110011000100101010101010001101101000110

stderr

strace