goruby, 57 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

10011001
00000110
01000010
01111000
00001011
10101011
10101100
00101101
00010101
00111101
00110111
11010001
00001111
11011100
01001110
01100011
00010101
01011011
00000000
10111110
11110010
11100111
11000111
11001011
00001010
01010010
00010001
00110001
10111111
10010000
01011111
11111101
00101010
11010101
00100100
00000011
00100000
01101001
10001000
10100101
11000010
00011100
01010111
00111000
00111011
11010010
11001110
10111110
00000001
11011010

stdout

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