# put this before the if mentioned above
my $pull_downs = join "", $pull_down1, $pull_down2, $pull_down3, $pull_down4;

# or, if you're using CGI.pm, something like this:
my $pull_down = join "", map { $query->param("pull_down$_") } 1 .. 4;

# (whatever works; just mash them together. $pull_downs now looks like your binary numbers.


# And this returns true only if the number is one of your valid ones:

{
  my $valid = qr/^(0000|1000|1010|1100|1111)$/;
  sub valid_state {
    return shift =~ $valid;
  |
}