crystal, 58 bytes

Result

WA

Code [DL]

while true
puts (8*STDIN.gets.to_i(2)+1)**0.5%2==1?1:0
end

stdin

11011010
01000001
11011100
11010010
11100111
01010101
00000000
10111110
10100100
10101011
01111000
00010010
00011100
10100000
00000011
10110010
00000110
00110111
01001110
00110101
01000011
11000011
00010001
10001000
11100110
01100100
10000110
01000010
00000001
00000001
11111101
10000011
10011001
01011011
00100100
10111011
00001010
00011101
11001101
00101101
11110101
00010101
01101001
11100101
10001000
10011000
00101110
01101011
00001111
01001100

stdout

Error in /volume/CODE:2: undefined method 'to_i' for Nil (compile-time type is (String | Nil)) (did you mean 'to_s'?)

puts (8*STDIN.gets.to_i(2)+1)**0.5%2==1?1:0
                   ^~~~

Rerun with --error-trace to show a complete error trace.

stderr

strace