use common::sense;

my $a = '';
my $b = '';

$a += 1 << 0;
$a += 1 << 1;

$b += 1 << 1;
$b += 1 << 2;

my $i = $a & $b;
my $u = $a | $b;

my $i_cnt = unpack '%32b*', $i;
my $u_cnt = unpack '%32b*', $u;

printf "a is %#032b  %d\n", $a, $a;
printf "b is %#032b  %d\n", $b, $b;
printf "intersection is %#032b  %d\n", $i, $i;
printf "union is %#032b  %d\n", $u, $u;
say "set bit count in intersection: $i_cnt";
say "set bit count in union: $u_cnt";

##</code><code>##

a is 0b000000000000000000000000000011  3
b is 0b000000000000000000000000000110  6
intersection is 0b000000000000000000000000000010  2
union is 0b000000000000000000000000000111  7
set bit count in intersection: 3
set bit count in union: 5

##</code><code>##

a is 0b000000000000000000000000000011  3
b is 0b000000000000000000000000000110  6
intersection is 0b000000000000000000000000000010  2
union is 0b000000000000000000000000000111  7
set bit count in intersection: 1
set bit count in union: 3