php, 64 bytes

Result

AC

Code [DL]

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

stdin

11111101
01101001
01010010
01111010
10001000
00001101
01100001
00011100
00110111
10010100
01010100
11101001
11011110
10011101
10111101
10100011
01001110
10101011
00111100
11010010
10111110
01001010
10010110
11101011
00000011
00000110
00111111
00100010
00010101
10011001
01111000
01000010
00000001
11100111
01000010
11100010
01000101
01011001
00001111
00101101
00000000
00001010
00111101
01101001
01010101
00110000
00111000
01011011
01000011
00100100

stdout

11001001100000001101100011001111111000111101000101

stderr

strace