goruby, 37 bytes

Result

WA

Code [DL]

loop{p (8*gt.t_(2)+1)**0.5%2==1 ?1:0}

stdin

01111000
00000001
00001010
00101100
00100011
00110101
10111001
11101110
10001101
10011001
00110111
00000000
10101111
00101101
11111101
00001111
00000110
10010101
10010010
10010111
01000010
01001110
01110111
01101001
10011011
11010010
01011011
00100001
10101011
00101010
11111110
01010101
00100100
10011100
10111110
11101100
00000011
01111010
00011000
01101001
10100000
00010101
00011100
11100111
00111000
10001000
10100101
11000110
00010101
11011111

stdout

stderr

<internal:golf_prelude>:87:in `to_a': wrong number of arguments (given 1, expected 0) (ArgumentError)
	from <internal:golf_prelude>:14:in `method_missing'
	from /volume/CODE:1:in `block in <main>'
	from /volume/CODE:1:in `loop'
	from /volume/CODE:1:in `<main>'

strace