php, 61 bytes

Result

WA

Code [DL]

<?= for(;$c=fgets(STDIN);)echo+!fmod(sqrt(8*bindec($c)+1),1);

stdin

10110001
01011001
10001110
01001010
11001101
11100111
00110111
01111000
01101001
00001010
00100100
01010011
11111100
00010101
00111100
01111110
10100011
10111000
11011011
10011100
01101001
10111110
10101011
01111000
10010000
00000001
11010010
10001000
11010001
00000110
00001110
00001111
10011010
01001110
11001000
11101110
10011001
10000001
10000010
01000010
11101101
11111101
01011011
11101001
01010001
00000000
00101101
10000000
00011100
00000011

stdout

stderr

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

strace