I think the simplest way to do it is with the &, |, ^, and ~ operators. An example:

#!/usr/bin/perl
use warnings;
use strict;
use constant EXECUTE => 1;
use constant WRITE => 2;
use constant READ => 4;

my $Permissions = 0;
$Permissions |= READ; # Set READ to true
$Permissions |= WRITE; # Set WRITE to true
$Permissions &= ~READ; # Set READ to false
$Permissions ^= EXECUTE; # Toggle EXECUTE
print $Permissions, "\n";
[download]

Prints "3" (that's WRITE and EXECUTE).
Is this what you were looking for?

-BronzeWing

Update:
Oops! I completely forgot getting the info back out again. To check the status of a bit:

if ($Permissions & READ) {
    print "You can read.\n";
} else {
    print "You can't read.\n";
}
[download]

The Secret to Fortune Cookies in One Line
print join("... in bed", `fortune fortunes` =~ m/^(.*)(\.|\?|\!)$/), "\n";