goruby, 56 bytes

Result

AC

Code [DL]

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

stdin

01000010
10010001
00001111
11000111
11100111
10011101
01001010
10000110
00001011
01010101
11110010
01000010
01111011
10111100
00000110
11111110
10011100
00000011
10101011
01101000
10001000
01111000
01110011
10011001
00101101
00000001
01110110
10101010
00001010
01011011
00100100
00000000
01001110
11110000
10101110
10010111
00010101
01000110
00101010
00110111
00000100
10111110
11111101
10100010
10101011
11010010
01101001
01011000
00011100
00110010

stdout

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