IP Addressing & Routing
The problem
Billions of devices need unique, structured addresses so that any message can be delivered from anywhere to anywhere, and delivery needs a way to make step-by-step forwarding decisions without every device knowing the full path to every other device.
Why now
The layered network model placed IP at the network layer, but not how addressing or delivery decisions actually work. Number systems and bases already explained binary and positional representation; IP addresses and subnet masks are that exact binary math, applied to carve address space into routable chunks.
Mental model
An IP address plus a subnet mask splits the address into a 'network' part and a 'host' part — the same idea as an area code plus a local number. Routing is delivery by increasingly specific forwarding: a router doesn't know the full path to a destination, it just knows which direction gets a packet one hop closer, the same way you'd direct a stranger toward a city without knowing their exact street.
Requires
- Number Systems & BasesMathematical Thinking
An IP address is a 32-bit (or 128-bit) binary number, and subnet masks are binary AND operations over that number; without bases and binary representation, subnetting is unexplainable arithmetic.
- The Layered Network ModelNetworking
IP addressing and routing operate specifically at the network layer; you need that layer identified before its specific job (addressing and path-finding) is meaningful.
Unlocks
Used in
- Every device connected to the internet, uniquely (or privately) addressed
- Subnetting in cloud infrastructure (VPCs, security groups scoped to IP ranges)
- NAT (network address translation), letting many private devices share one public IP
- Understanding traceroute output as a sequence of routing hops
Projects
- Given an IP address and subnet mask, compute the network address, broadcast address, and usable host range by hand
- Run traceroute to a public website and interpret each hop as a routing decision getting progressively closer to the destination
Examples
- 192.168.1.0/24 has a 24-bit network portion, leaving 8 bits (256 addresses) for hosts on that local network
- A home router uses NAT so an entire household shares one public IP address for all outbound traffic
Resources
Mastery checklist
- I can compute a network address and usable host range from an IP address and subnet mask
- I can explain the difference between a public and a private IP address
- I can explain what NAT does and why it's necessary for most home networks
- I can interpret traceroute output as a sequence of routing hops