crystal, 42 bytes

Result

WA

Code [DL]

while p (1+8*gets.to_i 2)**0.5%1>0?0:1;end

stdin

00100100
10000010
01101011
10001000
11111000
01011010
00000001
01001110
00011000
00001000
01101001
10111110
01101001
00010101
01110111
11011101
10010110
10101011
11101010
00001111
11110110
01100100
00111101
10011001
01111000
00011100
11111101
11100111
00110111
00011110
11100000
00101101
01000010
01111101
01010101
11010010
01101000
01010000
00111110
01011011
10110010
01000110
01010001
11111101
01011000
00000110
00000011
01110110
00000000
00001010

stdout

Error in /volume/CODE:1: undefined method 'to_i' for Nil (compile-time type is (String | Nil)) (did you mean 'to_s'?)

while p (1+8*gets.to_i 2)**0.5%1>0?0:1;end
                   ^~~~

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

stderr

strace