octave, 63 bytes

Result

AC

Code [DL]

while(1)printf("%d",!rem((bin2dec(fgetl(0))*8+1)^.5,1))endwhile

stdin

00110111
10000001
11101110
00011111
10001000
00100011
00101101
10101011
00100100
00001010
00010110
01000001
10011001
01110001
01100101
10000000
01101001
01001011
11111101
00000110
00000000
01100000
10111110
00110010
10011010
00111100
00000011
00001111
11010010
10011101
00011100
01000111
11000001
01011100
10001111
10110000
01000010
11100101
10111101
10101111
01111000
00010101
10111100
01011011
01001110
00100100
01101001
10000101
11100111
00000001

stdout

10001011110010001011101000111010000010001101111011

stderr

octave: X11 DISPLAY environment variable not set
octave: disabling GUI features
error: base2dec: S must be a string or cellstring
error: execution exception in /volume/CODE

strace