Logical Addressing: IPv4

1. Fundamentals of IPv4 Addressing

An IPv4 Address is a 32-bit logical identifier that uniquely and universally defines the connection of a host or router interface to the global Internet.

• Address Space: Total possible addresses = $2^{32} = 4{,}294{,}967{,}296$ ($\approx 4.3\text{ billion}$).
• Notations:
  • Binary Notation: 32 bits divided into four 8-bit octets:
    11000000.10101000.00000001.00000001
  • Dotted-Decimal Notation: Each octet is converted to decimal ($0 - 255$) separated by dots:
    192.168.1.1

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2. Classful Addressing

Originally, the IPv4 address space was divided into 5 discrete classes (Classes A through E):

Detailed Breakdown of Classes:

Class	Leading Bits	1st Octet Range	Default Subnet Mask	Max Networks	Hosts per Network	Primary Use Case
A	0...	$1 - 126$	$255.0.0.0$ (/8)	$128$ ($2^7$)	$16{,}777{,}214$ ($2^{24} - 2$)	Massive global organizations
B	10...	$128 - 191$	$255.255.0.0$ (/16)	$16{,}384$ ($2^{14}$)	$65{,}534$ ($2^{16} - 2$)	Universities & mid-size enterprises
C	110...	$192 - 223$	$255.255.255.0$ (/24)	$2{,}097{,}152$ ($2^{21}$)	$254$ ($2^8 - 2$)	Small businesses & home LANs
D	1110...	$224 - 239$	None	—	—	Multicasting
E	1111...	$240 - 255$	None	—	—	Experimental & Research

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3. Special-Purpose IPv4 Addresses

1. Network Address (Network ID): Host bits all zeros (0). Represents the entire subnet (e.g., 192.168.1.0/24). Cannot be assigned to any host.
2. Directed Broadcast Address: Host bits all ones (1). Delivers a packet to all hosts in a specific subnet (e.g., 192.168.1.255).
3. Limited Broadcast Address: 255.255.255.255. Broadcasts to all local hosts on the immediate physical wire; never forwarded by routers.
4. Loopback Address: 127.0.0.0/8 (typically 127.0.0.1 = localhost). Used to test local network stack software without generating physical network traffic.
5. Private IP Addresses (RFC 1918): Unroutable on the public Internet, reserved for internal intranets behind NAT:
   • Class A: 10.0.0.0 to 10.255.255.255 (10.0.0.0/8)
   • Class B: 172.16.0.0 to 172.31.255.255 (172.16.0.0/12)
   • Class C: 192.168.0.0 to 192.168.255.255 (192.168.0.0/16)
6. APIPA (Automatic Private IP Addressing): 169.254.0.0/16. Auto-configured by Windows/Mac clients when a DHCP server cannot be reached.

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4. Subnetting & CIDR (Classless Inter-Domain Routing)

Due to rapid exhaustion of Class A and B blocks, CIDR (Classless Inter-Domain Routing) replaced rigid classful boundaries in 1993:

• An arbitrary number of contiguous bits ($n$) define the Network Prefix (written as /n slash notation).
• Subnet Mask: A 32-bit number where the first $n$ bits are 1s and the remaining $(32 - n)$ host bits are 0s.

Fundamental Subnetting Formulas:

For a subnet borrowing $s$ bits from the host field with $h$ remaining host bits:

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5. Solved Step-by-Step Subnetting Numerical

Problem:

Given the IP address 200.10.20.75 with subnet mask 255.255.255.224 (/27):

1. Find the Network Address.
2. Find the Directed Broadcast Address.
3. Find the range of usable host addresses.
4. Calculate the total number of usable hosts in this subnet.

Solution:

• Last octet of IP: $75_{10} = \mathbf{01001011}_2$.
• Last octet of Mask: $224_{10} = \mathbf{11100000}_2$ ($n = 27$, remaining host bits $h = 32 - 27 = 5$).

1. Network Address: Perform bitwise AND between IP and Mask:

2. Directed Broadcast Address: Set all 5 host bits to 1:

3. Usable Host Range: From (Network ID $+ 1$) to (Broadcast $- 1$):

4. Usable Hosts:

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