Another option would be to convert the IP addresses to 4 byte strings, and use the string behavior, rather than the numeric, of the bitwise operators. Thanks to pack, the conversion is very easy.

#!/usr/local/bin/perl

my $ip1 = '255.255.240.0';
my $ip2 = '206.170.14.76';

my $packed_ip1 = pack 'C*', split /\./, $ip1;
my $packed_ip2 = pack 'C*', split /\./, $ip2;

my $and = $packed_ip1 & $packed_ip2;
my $or  = $packed_ip1 | $packed_ip2;
my $xor = $packed_ip1 ^ $packed_ip2;

for ($and, $or, $xor) {
  print join('.', unpack 'C*', $_), "\n";
}
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