A bit of creativity with constant and vec would probably be the way I'd go about it if I wanted precisely the code you had. More likely, though, would be that I'd take strings, and convert to a number in a hash, and then use vec. More likely still, I'd just leave everything as a hash (yeah, waste a lot of memory), and then pack it all together at the last minute when I actually had to send it somewhere in binary format (if such a requirement was actually there). No, I don't concern myself with memory too much these days.

Example 1:

use constant powerOn => 0;
use constant lightOn => 1;
{ my $status;
sub setStatus
{
  my $bit = shift;
  vec($status, $bit, 1) = 1;
}
sub resetStatus
{
  my $bit = shift;
  vec($status, $bit, 1) = 0;
}
sub getStatus
{
  my $bit = shift;
  vec($status, $bit, 1);
}

}
[download]

Example 2:

{ my $status;
my %types = ( powerOn => 0, lightOn => 1 );
sub _bit { if (exists $types{$_[0]}) { $types{$_[0]} } else { die "Unk
+nown bit $_[0]"} }
sub setStatus
{
  my $bit = _bit(shift);
  vec($status, $bit, 1) = 1;
}
# etc.
}
# call as...
setStatus('powerOn');
[download]

I don't think the last one needs an example.

Update: missing close-brace, as pointed out by fenLisesi.