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my $string1 = '01010110111000';
my $string2 = '11101101100010';
...
    ( $string1 & $string2 )  =~ tr[1][1],      # count 11

);

my $len = length $unpacked_string;
my $packed_string = pack qq{b$len}, $unpacked_string;

my $unpacked_string = unpack qq{b$len}, $packed_string;