ruby2.4, 39 bytes

Result

WA

Code [DL]

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

stdin

01000000
11010000
11111100
00100001
10011101
01111000
11100111
00011100
00001010
01000001
00101101
10101011
00100010
01101101
00000011
10111110
01010101
00001111
01100100
00000000
01011011
10011100
00001001
10001000
11111101
00011000
00101101
00000001
00010101
01110100
11010010
10001011
00101001
00110111
00101111
10011001
00100100
11001101
01000010
01111110
01001111
01101001
00001101
10000111
10000101
11010110
01100101
01001110
00001111
00000110

stdout

stderr

/volume/CODE:1: syntax error, unexpected tINTEGER, expecting ')'
loop{p (1+8*gets.to_i 2)**0.5%2==1?1:0}
                       ^
/volume/CODE:1: syntax error, unexpected '}', expecting end-of-input
+8*gets.to_i 2)**0.5%2==1?1:0}
                              ^

strace