IP address

[1] An IP (internet protocol) address is a unique numerical address assigned to each device using the Internet Protocol for communication, like 192.168.1.1 or 2001:0db8:0000:0000:0000:8a2e:0370:7334.

It assigns 2 main functions: network interface identification and addressing.

[1] Internet protocol version 4 (IPv4) was the first ever the IP address specification, being 32-bits numbers and has been used since 1983. It was til 2010 that it became too small to handle the number of devices as the internet grew and the Internet protocol version 6 (IPv6), 128 bits, was introduced, providing 2128 = 3.40282367e38 addresses. But both IPv4 and IPv6 are both still used as of 2025.

Thought IP address are often displayed as human-readable notations, systems can use them in many computer number formats.

CIDR notation can be used to decide how much of the address can be used as routing prefix. E.g., 192.0.2/24.1 means that 24 significant bits of the address are the prefix and the remaining 8 bits for host addressing for IPv4 addresses (which is 32 bits, 32-24 = 8 bits or 1 octet remaining), being historically equivalent as the subnet masking (255.255.255.0).

CIDR notation: way to show IP address and associated network mask, being an IP address followed by a slash and number (e.g., 192.0.2.1/24)

[1] IP addresses are assigned by the IANA (Internet Assigned Numbers Authority) and the 5 RIRS (regional Internet registeries). IANA blocks IP addresses to the RIRs, which are responsible for allocating them to local Internet registeries in their regions, like the internet service providers (ISPs) and big institutions.

An IP address is split into 2 parts: the network ID and the host ID. The network ID identifies the specific group of devices (the network). The host ID identifies the exact device (the host) within that group.

IPv4

An IP address consisting of 4 octets is a IPv4 (internet protocole version 4) (like 126.255.255.255), which was the first used IP address. IPv4 uses 32 bits, which provides 232 = 4,294,967,296 (4.3 B) addresses which ran out in 2011 and was replaced by IPv6.

The dots separates an addresses into octets for address to be easier for humans to read. IPv4 is fundamentally a string of binary of 32 binary number, like 01111110111111111111111111111111, which is what the system only understands.

; each converted to decimal values:

01111110 = 126
11111111 = 255
11111111 = 255
11111111 = 255

; Where the first bit of the first octet 126 is always set to 0, thus ranging from 1 to 126.

Note: Since each block is exactly 8 bits, the values are limited from 0 to 255, so IPv4 address is never 126.300.500.255.

1st, 2nd, 3rd, 4th octets

Addresses' octets locate and identify devices on a network.

1st octet identifies the network class and the country, major internet provider, or large network block.
2nd octet Identifies the network group/regional area in the 1st octet.
3rd octet identifies the sub-network (like a building/department).
4th octet identifies the device (host) on the sub-network.

IPv4 address classes

[3] IPv4 address classes (A, B, C, D, and E) are introduced to make managing IP addresses straightforward, routers can quickly identify the class from the first bits.
But classes led to address wastages:

If a firm needs 2,000 addresses, but if they chose Class C, it'd be too small (254 hosts), Class B is too large (65k hosts), and Class A is even larger (224 = 16 M). So Class B must be chosen but this wastes 63k addresses.

Solution for IPv4 class: CIDR As a result of this, the CIDR (Classless Inter-Domain Routing) was introduced to allow us to divide address space into any needed sizes via slash notations.

E.g., to provide exactly 21 address, "/21" is used.

[4] This diagram depicts how a (32-bit) IPv4 address is split into network and host parts per class. The key is the leading bits (white parts at the start), acitng as "flags" to tell the system which class the address belongs to.

The flag bits (white parts) in the diagram are leading bits that act as the identifiers per class (decides the address' class).

E.g., 192.168.1.11 is Class C, since its first octet "192" in binary is 11000000, which has 110 as the first 3 bits.
10.5.2.1 is Class A, since its first octet in decimal "10" is 00001010, whose first bit is 0. Same for 12.0.0.1.
172.16.0.1 is Class B, since its first octet "172" in decimal 10101100, whose first 2 bits are 10.

The 32-bit IP address is divided into 5 sub-classes: Class, A, B, C, D, E.

This diagram depicts the variable (host/network ID) part in green and the white parts (fixed prefix that identifies the class.

Class A addresses start as 0 bits flag, split into 8 bits/1 byte (as network ID) and 24 bits/3 bytes (as host ID).
Class B addresses start starts as 10 bits flag, split into 10 bits, split into 2 bytes (as network ID) and 2 bytes (as host ID)
Class C addresses start as 110 bits flag, split into 3 bytes (as host ID) and 1 bytes (as network ID). Since many network area available, but few hosts (254), so most often used in small offices.
Class D addresses start as 1110 bits flag, without network or host ID. These aren't for specific devices and are for addresses of Multicast groups (sending 1 message to many specific receivers simultaneously).
Class E addresses are experimental and starts as 1111 bits flag and also wityhou host and network ID. It's reserved for research and future use, and not for standard public networks.

[4]

- Class A

[2] Class A is the biggest IP addresses class, handling 8-bits, being 0.0.0.0 to 127.255.255.255. It allows 126 networks via the first network ID's octet.

126, since the octet's 1st bit is frozen as 0 and the remaining bits complete the network ID: First octet structure: 0xxxxxxx (where 'x' = 0 or 1); And the last digit is blocked others and only accessible by the local computer, so 127 is a still a valid Class A structure. I.e., the public (outside devices) have no access to it and only that specific device has access to it, being be used for loopback testing.

If we send traffic to a 127.x.x.x address, the computer's operating system routes the data right back to itself (communicating to itself) without sending it out over a physical network wire, meaning that the "127 network" is itself.

A network ID of 0 is a placeholder indicating it's a default route, so no firms/internet providers can assign addresses starting as 0.

As first bit is set as 0, 7 bits remain are left to change to create different networks: a combination of 27 = 128 possible networks, which cover the decimal range of 0 to 127.

To get the true usable range, we subtract 2 reserved network IDs that can't be assigned to public networks: 128 - 2 = 126 possible networks, so a usable Class A network range from 1 to 126 (e.g., 1.0.0.0 to 126.0.0.0).

IPv4 addresses

[1]

[1] An IPv4 address has a size of 32 bits, which limits the address space to 4294967296 (232) addresses, where some addresses are reserved for special purposes like private networks (≈18 million addresses) and multicast addressing (≈270 million addresses).

Types

IP addresses are mainly classified as either public or private, assigned by the Internet Service Provider (ISP).

Public IP address

A public IP address is the address everyone on the internet.

Private IP address

A private IP address is only used your home/office network, which can't be reached directly from the internet.

Other IP address types are static and dynamic, types based assignment.

Static IP address

A static IP address is manually configured and never changes. Servers, printers, and business websites often use static IPs so other devices always know their location.

Dynamic IP address

A dynamic IP address is temporarily assigned to a device by a DHCP (dynamic host configuration protocol) server. It changes overtime (e.g., whif you reboot your router or lease expires). Most home devices and standard internet connection uses dynamic IPs.

Subnet

A subnet/subnet network is a logical subdivision of IP network. Subnetting is the process to divide a network into many networks.

In IPv4 IPs, it's called a subnet mask.

Subnet mask

A subnet mask is a 32-bit number paired to an IP address to split it into 2 parts: the network ID and the host ID. It defines and creates a subnet, indicating to computers and routers which part of an IP address points to the local network and which part points to the individual device.

In a subnet mask, binary 1s is the network portion and binary 0s is the device (host) portion.

Block size

A block size (or the subnet increment) is the size or step interval per subnet, telling how many total IP addresses exist per subnet and how apart the subnet network addresses are from one another.

In any outlet, the block size is calculated as: Block size = 256 - mask's interesting octet = 2#h, where

#h = host bits
interesting octet: subnet mask's first octet not being 255 or 0 (octet where subnetting occurs). E.g., for 255.255.255. 192 the 4th octet is the interesting octet since 192 is neither 255 nor 0.

E.g., for an IP address 172.20.197.111 with subnet mask 255.255.255.192 (/26):

Borrowed bit

A borrowed bit refers to a host bit being taken ("borrowed") from an IP address' host portion and converted to network bits to create smaller subnets.

The number of borrowed bits is calculated by the IP address' network bits (1s), i.e., in CIDR notation substracted by the IPv4's default number network bits:
nborrowed bits = nactual network bits (in CIDR) - ndefault class' network bits

E.g., for the IP address 172.20.197.111 with subnet mask 255.255.255.192 (/26):

Default Class B prefix: /16 (16 default network bits or 16 logic 1s)
Custom subnet mask prefix: /26 (26 total network bits or 26 logic 0s)
The number borrowed bits is 26 - 16 = 10 bits, meaning that 10 bits can be borrowed, providing 210 = 1024 subnets.

DHCP

DHCP (Dynamic Host Configuration Protocol) is an network protocol automatically assigning an IP address to and other network settings (like subnet mask, default gateway, and DNS) to devices connected to network. Without DHCP, all devices' IP addresses must be given manually.

Default gateway

A default gateway is the network node or router that routes traffic from a local network to an external network like the internet, i.e., the main exit point for data when a device tries to reach an IP address outside its local subnet.

Its name refers to its act as the exit door ("gateway") the device automatically uses ("default") to send data outside your local network when it doesn't know a specific path.

DNS

DNS (domain name system) is the addresses used by websites (e.g., google.com, youtube.com), which translates names into IP addresses.

Network and host ID

Network ID identifies the network. Every device on the same local network shares this same ID.
Host ID identifies the device. Every device on a network has a unique host ID.

Variable length subnet masking

Variable length subnet masking (VLSM) is an IP subnetting method allowing network admins to divide IP addresses space into subnets of various sizes, preventing address waste and maximize efficiency.

[4] E.g., a firm buys the IP address range 37.1.1.0/24 (256 addresses). They have 5 offices, as figure 1 shows:

[4]

[4] We are tasked to subnet the 37.1.1.0/24 IP address block and assign each office an IP subnet. Let's see what the two ways to do this are.

The diagram's top shows the main IP address range the firm owns: 37.1.1.0/24 (256 total IP addresses), which marks this /24 block's boundary, starting at 37.1.1.0 and ending at 37.1.1.255.

The illustration connects 4 office subnets (SW2-4) to the central router. The key to VLSM is allocating IPs from the largest subnet requirement to the smallest:

Note: host formula (to accomodate the number of hosts, we need a block size of 2): 2h ≥ ("needed hosts" + 2), where
- 2 is the reserved net ID and broadcast address.
- h = hosts

Office 1 (50 users needed):

Allocated subnet/Block size:

- Addresses needed: 50 + 2 = 52
- Smallest power of 2 to fit addresses needed: 25 = 32 addresses is too small (only 30 hosts) and 26 = 64 addresses (holds 62, which fits 52) should be used.
- So 6 bits are needed for host addresses.
- Block size: 32 - 6 = /26

Range: 37.1.1.0/26 (IPs 37.1.1.0 to 37.1.1.63) (the block's total number of IP address minus 1 is added to last office's min range's octet to determine each its max range's last octet, in this case 64 - 1)

Office 2 (30 users needed):

Allocated subnet:
- Addresses needed: 30 + 2 = 32
- 5 bits (25 = 32 addresses) are needed for host addresses.
- Block size: 32 - 5 = /27

Range: 37.1.1.64/27 (IPs 36.1.1.64 to 36.1.1.95)

Office 3 (20 user needed):

Allocated subnet:

- Addresses needed: 20 + 2 = 22
- 5 bits (25 = 32 addresses) are needed for host addresses.
- Block size: 32 - 5 = /27

Range: 37.1.1.96/27 (IPs 36.1.1.96 to 36.1.1.127)

Office 4 (10 users needed):

Allocated subnet:

- - Addresses needed: 10 + 2 = 12
  - 4 bits (24 = 16 addresses) are needed for host addresses.
  - Block size: 32 - 4 = /28

Range: 37.1.1.128/28 (IPs 36.1.1.128 to 36.1.1.143)

FLSM

The first step is to divide the 256-address block into 4 same-sized subnets, a method called Fixed Lenght Subnet Mask (FLSM). The method's upside is that all subnets share the same subnet mask, making the process straightforward and less prone to errors, as Figure 2 shows.

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IP address

IPv4

1st, 2nd, 3rd, 4th octets

IPv4 address classes

- Class A

IPv4 addresses

Types

Public IP address

Private IP address

Static IP address

Dynamic IP address

Subnet

Subnet mask

Block size

Borrowed bit

DHCP

Default gateway

DNS

Network and host ID

Variable length subnet masking

FLSM

References

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