crystal, 52 bytes

Result

WA

Code [DL]

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

stdin

10101011
00100100
00101010
00011100
11111101
11001110
00001010
01100010
01000010
01100001
10010010
10011111
00010101
00000000
11010101
00001010
01001110
00101000
00011101
00011010
01111010
11110101
00001111
00010101
00110111
00111110
00111001
10011001
10101000
00000110
00010010
11100111
00010011
01011011
01111000
10010000
11010010
00000011
10001000
10110001
10101010
00000001
10111110
10100111
00101101
10001001
10100100
01101100
01000101
01101001

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

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

stderr

strace