goruby, 45 bytes

Result

AC

Code [DL]

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

stdin

00000001
11100000
00100000
00001010
00100100
10001001
10101011
10101100
00000110
01100010
10001111
01011011
01010110
00101101
11010010
01111101
11101000
01111000
11111101
00000011
01000011
01110000
10010010
01101001
00011010
00010101
01101001
11101010
00110111
01010010
10111110
00111101
11100111
11110000
01001110
10001000
10000101
11111101
10110011
00011100
00000000
01000010
10011001
01011101
00110010
00000111
11001111
00001111
11011000
10011010

stdout

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