perl, 46 bytes

Result

WA

Code [DL]

print((1+8*(oct"0b".$_))**0.5%2-1?0:1),$\for<>

stdin

00001000
00101111
00111011
00000001
10000010
00001111
00000110
11111101
00101101
00001010
00110111
11101000
00100100
01101010
00010011
11010101
01011010
00000000
01110001
01111000
00000011
11010000
01000010
01101001
00111100
00011111
01000010
11010010
01100100
10111110
01110110
01011011
10001011
11111000
10011001
01111110
10101011
01010100
01000100
10101010
00010101
00101110
01001110
10100101
10111101
11100111
10110011
10001000
00011100
00110111

stdout

01110111111111010101101111110101101111101110011111

stderr

strace