network and broadcast address calculation

To simplify that article: network is the lowest possible address in the range of ip addresses left over from the netmask. broadcast is the highest numbered ip address in that range. The "range of ip addresses left over from the netmask" is known as the local network.

"The network" typically means everyone above you, including the Internet. To get to "the network", the network address is used. In reality, most people call "the network" anything with ethernet cables that can talk to each other.

Example: your ISP gives you info to type into a wireless router: a static IP address of 99.1.81.209 and your netmask is 255.255.255.224. Now you're wanting to set up an ubuntu firewall and need to set up your public interface:

Calculate network IP address:
255.255.255.224 -> last octet = E0
 99.  1. 81.209 -> last octet = D1
Logical AND the mask and your ip: 
E0 & D1 = C0 = 192
--> network = 99.1.81.192

Calculate broadcast address:
255.255.255.224 : E0 -> there are 1F = 31,
-> broadcast = 99.1.81.192 + .31 = 99.1.81.223

The other way...

Calculate broadcast address:
255.255.255.224 -> last octet = E0
 99.  1. 81.209 -> last octet = D1
Hosts' IPs = 1F 
Logical OR the hosts ips with your ip:
1F | D6 = DF = 223 
--> broadcast = 99.1.81.223

Often, you'll see networks described with a /. Here's this network:

255.255.255.224 is the netmask, add up the "1" bits:
 8 + 8 + 8 + 3  = 27
so "this network" gets /27 notation
and can be described as 99.1.81.192/27

DEV=eno1

BROADCAST=`ip address show $DEV | grep 'inet .* brd ' | head -1 | sed -e 's/^.* brd \([0-9\.]*\) .*$/\1/'`

dc@dc-Precision-T7600:/etc/network$ echo $BROADCAST
192.168.0.255