php, 63 bytes

Result

AC

Code [DL]

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

stdin

10000011
10110000
00100000
01010101
00101101
10011001
00000000
10010111
10100001
01101001
11100111
11010100
00000110
10101011
10000000
10001000
01000101
11010010
01001110
11111011
01000010
00010101
10011011
01000000
10011010
00001111
01011011
00001010
01001110
00010110
00010100
01010100
10001011
01001100
11111101
00000001
10011101
00011100
10011001
01111000
10111110
01100000
00000011
00100100
00110111
01111001
01011001
01010011
00011011
10110010

stdout

00001110011011010110110001111000001101111011100000

stderr

strace