octave, 65 bytes

Result

AC

Code [DL]

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

stdin

10111101
00111011
00000000
00011100
00001111
01100110
10101110
01110010
01000010
11000010
10111000
11101111
10001000
00000110
10000100
11100111
11000001
00000001
00111001
10101011
00010010
11010010
01111110
00110111
00100111
01001110
01101001
00000011
01011100
00000110
00010101
10010001
01010100
10011001
10000110
00100100
11111101
00001010
10111010
01111000
10100101
11101001
00111111
10111110
00000110
00101101
01011011
01111101
01000101
11000000

stdout

00111000100011010101010101110110010111010001111000

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