ruby2.4, 42 bytes

Result

AC

Code [DL]

$<.map{|q|p (1+8*q.to_i(2))**0.5%2==1?1:0}

stdin

00000001
10101011
11010001
10111110
00000110
10110000
01001101
11100011
00010101
00000000
11001011
00001010
11010010
00110001
11011011
01100101
10110011
10100110
00000011
00110111
11001100
01001110
00000110
01101010
10001000
10101001
00011100
10110101
00001111
00101101
01100111
11111101
01110111
11100111
01000010
01101001
10100101
10011001
11100111
00100011
00111110
00011010
00100100
01011011
11111011
01110000
01111000
00110010
01100100
10100001

stdout

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

stderr

strace