IPv4 addressing, subnetting, CIDR, LPM & VLSM

Chapter 3.1 gave our datagram its universal 32-bit hierarchical address. We traced the evolution from fixed classes (A–E) and special addresses (0.0.0.0, 255.255.255.255, 127.x.y.z) to subnetting (borrowing s bits for 2ˢ subnets of 2ʰ − 2 usable hosts), CIDR slash notation /n with its power-of-2 size and alignment rules, route aggregation, Longest Prefix Match (LPM) in router forwarding tables, and largest-first VLSM block design.

From 3.1.1 IPv4 address structure, dotted decimal, net-id vs host-id

• IPv4 address = 32 bits = 4 octets (0–255 each), total space = 2³².
• Split: Net-ID (left n bits) + Host-ID (right h = 32 − n bits).
• Identifies a network interface (routers have one IP per link).

From 3.1.2 Classful addressing (A–E) and special IPv4 addresses

• Classes by 1st octet: A = 0–127 (0, 8 net bits), B = 128–191 (10, 16 net bits), C = 192–223 (110, 24 net bits), D = 224–239 (1110, multicast), E = 240–255 (1111, reserved).
• Usable hosts = 2ʰ − 2 (exclude host all-0s = network address, host all-1s = directed broadcast).
• Specials: 0.0.0.0 = this host (src only); 255.255.255.255 = limited broadcast (local LAN only); 127.x.y.z = loopback.

From 3.1.3 Subnet masks, subnetting, network/broadcast & usable hosts

• Borrow s bits from host field, leaving h bits → 2ˢ subnets, each with 2ʰ − 2 usable hosts.
• Subnet address = IP AND Mask; Broadcast = host bits all 1s.
• Stride Δ = 256 − Mask octet: blocks start at 0, Δ, 2Δ, … and end at Δ−1, 2Δ−1, ….
• Valid mask octets: 128, 192, 224, 240, 248, 252, 254, 255.

From 3.1.4 CIDR notation (/n), block size, alignment & route aggregation

• CIDR a.b.c.d/n: n prefix bits, h = 32 − n host bits, block size N = 2ʰ.
• Alignment rule: first address must be divisible by 2ʰ (for /(24−k), 3rd octet must be divisible by 2ᵏ).
• Supernetting: 2ᵏ contiguous, aligned /n blocks merge into one /(n − k) block.

From 3.1.5 Forwarding tables & Longest Prefix Match (LPM)

• Match condition: Row N/n (mask M) matches destination D iff (D AND M) == N (i.e. D falls in [N .. N + 2³²⁻ⁿ − 1]).
• Longest Prefix Match (LPM): Among all matching rows, pick the one with the largest prefix length n.
• Default route 0.0.0.0/0: matches every address with n = 0 (used only if nothing else matches).

From 3.1.6 Variable-Length Subnet Masking (VLSM) & block allocation

• Block size for H usable hosts: smallest 2ʰ with 2ʰ − 2 ≥ H; prefix = /(32 − h).
• Largest-first rule: sort subnets by decreasing 2ʰ and allocate sequentially so every block is naturally aligned.
• Non-overlap: sum of block sizes ∑ 2ʰᵢ ≤ 2³²⁻ⁿ_parent, and every block starts on a multiple of its own 2ʰᵢ.

1. NAT · 1 mark

   A Class B network 172.16.0.0 is subnetted with subnet mask 255.255.252.0. How many usable hosts exist per subnet?

   Write your answer before opening the key.

2. MCQ · 2 marks

   What is the directed broadcast address of the subnet to which host 172.16.45.19 with mask 255.255.248.0 belongs?

   1. 172.16.47.255
   2. 172.16.45.255
   3. 172.16.48.255
   4. 172.16.255.255
3. MSQ · 2 marks

   Which of the following CIDR blocks are properly aligned (valid network prefixes)?

   1. 200.10.24.0/21
   2. 200.10.20.0/21
   3. 10.0.128.0/17
   4. 192.168.1.64/26
4. MCQ · 2 marks

   Two routers advertise 192.168.16.0/22 and 192.168.20.0/22 to an upstream ISP. What single aggregated CIDR prefix represents both blocks?

   1. 192.168.16.0/21
   2. 192.168.16.0/20
   3. 192.168.0.0/16
   4. They cannot be aggregated into a single prefix without extra addresses.
5. MCQ · 2 marks

   A router forwarding table has: (1) 128.75.43.0/25 → R1, (2) 128.75.43.64/26 → R2, (3) 128.75.43.0/24 → R3, (4) 0.0.0.0/0 → R4. Which next hop is chosen for 128.75.43.130?

   1. R1
   2. R2
   3. R3
   4. R4
6. NAT · 2 marks

   From 192.168.10.0/24, we allocate three subnets for 110 hosts, 55 hosts, and 25 hosts using largest-first VLSM. What is the 4th octet of the network address of the 3rd subnet (for 25 hosts)?

   Write your answer before opening the key.

7. MCQ · 1 mark

   Which IPv4 address is used by a booting host as its source IP before it knows its own address?

   1. 0.0.0.0
   2. 255.255.255.255
   3. 127.0.0.1
   4. 192.168.0.1
8. NAT · 1 mark

   How many bytes longer is an Ethernet MAC address than an IPv4 address?

   Write your answer before opening the key.