verilog, 86 bytes

Result

WA

Code [DL]

module c;real d;initial while($fscanf(1<<31,"%b",d))$write($sqrt(d*8+1)%2&1);endmodule

stdin

00000000
01111000
11111101
01000010
00000011
11011011
10101011
01001110
01000011
11110101
00101111
01011011
10010100
10010000
00011101
01110110
11111000
10001000
01101000
00001011
00000001
00101101
00001010
11101001
10010011
00000110
00011100
00110110
01010011
11010010
01101001
00110111
10010010
11100111
00100100
11000100
10001010
00010101
00001111
11010100
00101101
00001001
10011001
00001110
11111110
00000001
10111110
10000101
10110101
00000111

stdout

stderr

/volume/CODE:1: error: & operator may not have REAL operands.
1 error(s) during elaboration.
/home/esolang/bin/verilog: line 4: /tmp/code: No such file or directory
rm: cannot remove '/tmp/code': No such file or directory

strace