# step 1
sub binary {
   my ($n) = @_;
   return $n if $n == 0 || $n == 1;
#step 2
   my $k = int($n/2);
   my $b = $n % 2;
#step 3, recursion
   my $E = binary($k);
#step 4
   return $E . $b;
   }

##</code><code>##

# step 1
sub binary ($n) {
   return $n if $n == 0|1;
#step 2
   my $k = int($n/2);
   my $b = $n % 2;
#step 3, recursion
   my $E = binary($k);
#step 4
   return $E ~ $b;
   }

##</code><code>##

sub binary (0|1 $n) { $n }

sub binary ($n) {
   my $k = int($n/2);
   my $b = $n % 2;
   my $E = binary($k);
   return $E ~ $b;
   }

##</code><code>##

sub binary (Int where { $_ < 0 } $n)
{
   my $E= binary(-$n);
   return "-" ~ $E;
}

##</code><code>##

subset NegativeInt of Int where { $_ < 0 } # I decided to declare it after all
subset PositiveInt of Int where { $_ > 0 }

sub binary (NegativeInt $n, :$wordsize)
{
   if defined $wordsize {
      # do 2's complement mode
      PositiveInt $m= 2 ** $wordsize - $n;
      return binary($m);
      }
   else {
      return "-" ~ binary(-$n);
      }
}

##</code><code>##

   PRE { !defined($wordsize) || frac($wordsize)==0 }