Probably not what they want, but the best I could come up with on short notice without cheating and just telling Perl to convert directly.
use strict;
use warnings;
my $nd = 186;
my $nb = '';
for (reverse (0..7)) {
if ($nd >= 2**$_) {
$nb .= '1'; $nd -= 2**$_;
} else {
$nb .= '0';
}
}
print $nb;
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