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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