php, 62 bytes

Result

WA

Code [DL]

<?php for(;$c=fgets(STDIN);){echo (sqrt(8*bindec($c)+1)%1>0);}

stdin

00000011
10111110
11001111
01101011
00110111
00011100
11001100
01000010
00000001
00000000
11010001
10000000
00101101
00001010
10100100
00010101
01001110
00001111
11010010
11101011
00000110
00110000
10001000
10010011
10101001
00010110
01011011
10011101
01111000
10010010
10011001
00011010
11110101
01010100
11101110
00100110
00001100
01011011
11100111
10101011
01101001
00011101
01101010
00100100
00000000
11001001
11011110
11111011
11111101
10101010

stdout

stderr

strace