ruby2.4, 40 bytes

Result

AC

Code [DL]

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

stdin

10101011
10001000
10000001
00000110
11000001
11101001
00011100
10111110
11000110
00000001
11111110
01000100
11111101
10111000
01110111
01001110
11111001
01110000
00000011
10110001
11011000
00111001
01111000
00100100
11010010
00011001
01110110
00100100
00110111
01000010
11001111
10011001
01000110
00101101
00010100
00001111
01101001
10010110
11100111
00011100
10011111
00010101
10011011
00001010
10111100
01011011
00000000
00101100
10001100
11110001

stdout

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