{
    my @nums = (0..9,'a'..'z','A'..'Z');
    my %nums = map { $nums[$_] => $_ } 0..$#nums;

    sub to_base
    {
        my $base   = shift;
        my $number = shift;
        return $nums[0] if $number == 0;
        my $rep = ""; # this will be the end value.
        while( $number > 0 )
        {
            $rep = $nums[$number % $base] . $rep;
            $number = int( $number / $base );
        }
        return $rep;
    }

    sub fr_base
    {
        my $base = shift;
        my $rep  = shift;
        my $number = 0;
        for( $rep =~ /./g )
        {
            $number *= $base;
            $number += $nums{$_};
        }
        return $number;
    }
}
[download]

You examples becomes

my $UniqueID = to_base( 62, $$ ) . to_base( 62, time );
[download]

print to_base( 16, 28 );
[download]

If you need your original syntax for some reason, just add

sub GenerateBase
{
    my $base = shift;
    return (
       sub { to_base( $base, $_[0] ) },
       sub { fr_base( $base, $_[0] ) },
    );
}
[download]

Then the user has the choice of syntax at no cost.