goruby, 59 bytes

Result

AC

Code [DL]

loop{a=(((8*gets.to_i(2)+1)**(0.5)-1)/2);p(a.to_i==a ?1:0)}

stdin

11010000
00100000
01111011
00100110
00010101
00000110
11100111
00101110
10111110
10110001
01111000
01000000
00000000
11011111
01101001
00111011
10101011
10010101
11100111
10001000
01011000
10100011
11111110
11010010
00001111
10001100
00010110
11100001
10011001
11010011
00000010
10001111
00000011
11001010
01001110
00110111
10101011
10011011
11000100
00001010
00100100
01000010
01011011
11111001
00011100
00000001
11111101
00101101
10010001
10110011

stdout

0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0

stderr

/volume/CODE:1:in `to_i': wrong number of arguments (given 1, expected 0) (ArgumentError)
	from /volume/CODE:1:in `block in <main>'
	from /volume/CODE:1:in `loop'
	from /volume/CODE:1:in `<main>'

strace