php, 75 bytes

Result

WA

Code [DL]

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

stdin

01011010
01011011
00101101
11111101
00110101
01001110
10100110
01000010
01010001
10111110
00101110
11101101
00000001
11010010
10001000
00111001
11111111
00110111
11100111
00010101
01000001
10000101
10101011
00011100
01101001
01111000
00100011
00001001
00000000
10011010
10011101
00001010
11000110
01110011
11000000
11111100
10011001
00010101
00010001
10111011
00000011
00000110
00001111
00110111
11101110
10001101
01001000
00100100
01010101
00111100

stdout

stderr

PHP Parse error:  syntax error, unexpected 'for' (T_FOR) in /volume/CODE on line 1

strace