verilog, 85 bytes

Result

WA

Code [DL]

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

stdin

00000000
10101001
01011100
10101011
00000001
11000000
11101011
01000010
00101101
00100100
01011011
00110111
00010101
00001010
11000110
10001000
10011000
01111000
00000110
01000010
00011100
10111001
01010011
10010000
00011110
10100001
01000011
10011110
01001110
11100111
10011001
00011101
11110010
10110101
11010011
00100110
10000111
11011010
11000101
11010010
11111101
01101001
01111010
11101001
11110000
11111001
00000011
00001111
10111110
01001110

stdout

stderr

/volume/CODE:1: syntax error
/volume/CODE:1: error: malformed statement
/home/esolang/bin/verilog: line 4: /tmp/code: No such file or directory
rm: cannot remove '/tmp/code': No such file or directory

strace