English:IP Addresses and Subnetting
IP Addresses and Subnetting
Introduction
Every device that communicates with Internet Protocol needs addressing information. In a workplace network, a laptop, printer, server, access point, programmable controller, camera, or router may have an IP address. To configure and troubleshoot these devices, you need to understand not only the address itself but also the network prefix: the part that tells a device which addresses are local and which must be reached through a router.
This aiMOOC is designed for apprentices, trainees, and vocational students in Information technology, Computer networking, IT support, systems integration, network administration, and related technical fields. You will learn how IPv4 addresses are structured, how subnet masks and CIDR prefixes work, how to calculate network and broadcast addresses, how to design subnets with fixed and variable sizes, and how to diagnose common addressing faults. A short section also transfers the ideas to IPv6.
The main goal is practical competence: by the end, you should be able to look at an address such as 192.168.10.70/26, determine the subnet to which it belongs, find the usable host range, recognize the broadcast address, and explain what a default gateway must do.
The diagram above shows an IPv4 address in dotted-decimal and binary form. Each decimal octet represents eight binary bits.
Learning Goals
After completing the course, you should be able to:
- IPv4: Explain the structure of a 32-bit IPv4 address and convert relevant octets between decimal and binary.
- Subnet mask: Explain how a subnet mask separates network bits from host bits.
- CIDR: Convert common prefix lengths into dotted-decimal subnet masks and back.
- Subnetting: Calculate network addresses, broadcast addresses, usable host ranges, and subnet sizes.
- Private network: Recognize private IPv4 ranges and distinguish private addressing from public addressing.
- VLSM: Allocate different subnet sizes efficiently for workplace requirements.
- Default gateway: Decide whether a destination is local or must be sent to a router.
- Network troubleshooting: Diagnose common faults involving addresses, masks, gateways, DHCP, and overlapping subnets.
- IPv6: Transfer the prefix concept to 128-bit IPv6 addressing and recognize important differences from IPv4.
Why Subnetting Matters at Work
Subnetting is not only an examination topic. It is used to organize real networks. A company may separate office computers, training-room devices, production equipment, voice systems, servers, management interfaces, and guest Wi-Fi into different IP networks. Those networks may also correspond to different VLANs and different security rules.
Good subnetting supports several practical goals. It creates clear address plans, limits IPv4 broadcast domains, helps routing and access-control policies stay understandable, and avoids wasting more address space than necessary. A technician who can read a prefix can also diagnose faults more quickly. For example, two devices may be connected to the same physical switch but still be unable to communicate directly if their IP configurations place them in different logical subnets.
The illustration shows one /24 address block being divided into two /25 subnets. The key idea is that a longer prefix creates smaller subnets because more bits are reserved for the network portion.
The video introduces the network ID, broadcast address, host range, subnet size, CIDR notation, and other core subnetting attributes.
IPv4 Address Basics
32 Bits and Four Octets
An IPv4 address contains 32 bits. It is usually written as four decimal octets separated by dots, for example:
192.168.10.70
Each octet contains eight bits and therefore has a decimal value from 0 through 255. The place values inside one octet are:
| Bit position | Value |
|---|---|
| First | 128 |
| Second | 64 |
| Third | 32 |
| Fourth | 16 |
| Fifth | 8 |
| Sixth | 4 |
| Seventh | 2 |
| Eighth | 1 |
To convert a binary octet to decimal, add the place values wherever the bit is 1. For example, 11000000 is 128 + 64 = 192. The octet 11111111 is 255, and 00000000 is 0.
A fast technician does not need to convert every address completely into binary every time. However, understanding the binary structure makes subnet masks predictable instead of mysterious.
Network Part and Host Part
An IP address alone does not tell you the subnet boundary. You also need a subnet mask or a CIDR prefix length. The prefix identifies the most-significant bits that belong to the network. The remaining bits are available for host addressing inside that subnet.
For example, in 192.168.10.70/26, the prefix length /26 means that the first 26 bits are network bits and the remaining 6 bits are host bits.
CIDR notation can describe address blocks of many sizes. A longer prefix represents a more specific and usually smaller block.
Subnet Masks and CIDR Prefixes
What a Subnet Mask Does
An IPv4 subnet mask is a 32-bit value with 1 bits in the network portion and 0 bits in the host portion. In dotted-decimal notation:
/24 = 11111111.11111111.11111111.00000000
= 255.255.255.0
For /26:
/26 = 11111111.11111111.11111111.11000000
= 255.255.255.192
The mask does not identify a particular host. It tells the device where the network-host boundary lies.
Common Prefixes
The following table is useful for daily IPv4 work. The conventional usable-host value subtracts the network and broadcast addresses. The /31 case is different on point-to-point links, and /32 represents a single address.
| Prefix | Subnet mask | Total addresses | Conventional usable host addresses |
|---|---|---|---|
| /16 | 255.255.0.0 | 65,536 | 65,534 |
| /20 | 255.255.240.0 | 4,096 | 4,094 |
| /22 | 255.255.252.0 | 1,024 | 1,022 |
| /23 | 255.255.254.0 | 512 | 510 |
| /24 | 255.255.255.0 | 256 | 254 |
| /25 | 255.255.255.128 | 128 | 126 |
| /26 | 255.255.255.192 | 64 | 62 |
| /27 | 255.255.255.224 | 32 | 30 |
| /28 | 255.255.255.240 | 16 | 14 |
| /29 | 255.255.255.248 | 8 | 6 |
| /30 | 255.255.255.252 | 4 | 2 |
| /31 | 255.255.255.254 | 2 | 2 on an RFC 3021 point-to-point link |
| /32 | 255.255.255.255 | 1 | One individual address |
A useful formula for an ordinary IPv4 subnet is:
host bits = 32 - prefix length total addresses = 2^(host bits) conventional usable hosts = total addresses - 2
Use the last line only for conventional subnets through /30. A /31 can use both addresses on a point-to-point link according to RFC 3021, and a /32 identifies one address rather than a multi-host subnet.
Converting a Prefix to a Mask
For a /27 prefix, 24 network bits fill the first three octets. Three additional 1 bits appear in the fourth octet:
11100000 = 128 + 64 + 32 = 224 /27 = 255.255.255.224
For a /20 prefix, the first 16 bits fill two octets and four additional 1 bits appear in the third octet:
11110000 = 128 + 64 + 32 + 16 = 240 /20 = 255.255.240.0
This method works for any valid IPv4 prefix length.
Calculating an IPv4 Subnet
Method 1: Binary AND
A device finds the network address by applying a bitwise AND between the IP address and the subnet mask. A result bit is 1 only when both input bits are 1.
Consider 192.168.10.70/26:
IP address: 192.168.10.70 Mask: 255.255.255.192 Network: 192.168.10.64
The fourth octet makes the calculation visible:
70 = 01000110 192 = 11000000 AND = 01000000 = 64
Therefore the network address is 192.168.10.64/26.
To find the broadcast address in a conventional IPv4 subnet, set all host bits to 1. With six host bits, the /26 block contains 64 addresses. The block beginning at 64 ends at 127, so the broadcast address is 192.168.10.127.
The conventional usable host range is therefore:
192.168.10.65 through 192.168.10.126
Method 2: Block Size
For common subnetting tasks, the block-size method is faster. Find the interesting mask octet and subtract it from 256.
For /26:
Mask octet = 192 Block size = 256 - 192 = 64
Subnets in the last octet begin at multiples of 64:
0, 64, 128, 192
Each block continues until one address before the next block. Therefore:
| Network | First conventional host | Last conventional host | Broadcast |
|---|---|---|---|
| 192.168.10.0/26 | 192.168.10.1 | 192.168.10.62 | 192.168.10.63 |
| 192.168.10.64/26 | 192.168.10.65 | 192.168.10.126 | 192.168.10.127 |
| 192.168.10.128/26 | 192.168.10.129 | 192.168.10.190 | 192.168.10.191 |
| 192.168.10.192/26 | 192.168.10.193 | 192.168.10.254 | 192.168.10.255 |
This worked-example video demonstrates a repeatable method for finding the network ID, broadcast address, host range, subnet size, and next subnet.
A Four-Step Workplace Routine
When you receive an IPv4 subnetting problem, use the same routine every time:
- Prefix length: Convert the prefix to a mask or determine the block size.
- Network address: Find the first address in the block containing the given host.
- Broadcast address: Find the final address in that conventional IPv4 block.
- Host address: The conventional usable range lies between the network and broadcast addresses.
Write the result down in an address plan. Consistent documentation prevents configuration errors when several technicians work on the same site.
Public, Private, and Special IPv4 Addressing
Private Address Space
RFC 1918 reserves three IPv4 blocks for private internets:
| Private block | Prefix | Typical use |
|---|---|---|
| 10.0.0.0 to 10.255.255.255 | 10.0.0.0/8 | Large private addressing plans |
| 172.16.0.0 to 172.31.255.255 | 172.16.0.0/12 | Medium or segmented private networks |
| 192.168.0.0 to 192.168.255.255 | 192.168.0.0/16 | Small networks, labs, and local devices |
Private addresses are not globally routed on the public Internet. Organizations commonly use them internally and use routing, firewalls, and often NAT at network boundaries. NAT is a separate function; it is not part of the definition of subnetting.
Other Addresses You Should Recognize
127.0.0.0/8 is reserved for IPv4 loopback. The address 127.0.0.1 is commonly used to test the local TCP/IP stack.
169.254.0.0/16 is IPv4 link-local address space. On many client systems, seeing a 169.254.x.x address when you expected a managed DHCP address is a reason to investigate cabling, wireless association, VLAN placement, and the DHCP path.
255.255.255.255 is the limited broadcast address in IPv4. It is not a normal host address.
Do not assume that any address beginning with 172 is private. Only the range 172.16.0.0 through 172.31.255.255 belongs to the RFC 1918 private block.
Default Gateways and Local Decisions
A host compares its own network prefix with the destination address. If the destination is inside the same subnet, the host can attempt local delivery on that link. If the destination is outside the local subnet, the host normally forwards the packet toward a default gateway, usually a router interface in the same local subnet.
Suppose a workstation has:
Address: 192.168.20.62/27 Gateway: 192.168.20.33
A /27 has a block size of 32. The workstation is in subnet 192.168.20.32/27, whose conventional host range is 192.168.20.33 through 192.168.20.62 and whose broadcast address is 192.168.20.63. The gateway address 192.168.20.33 is therefore local and valid for that design.
Now consider a server at 192.168.20.65/27. It belongs to subnet 192.168.20.64/27, so the workstation needs routing to reach it even if both cables happen to terminate on the same physical switch.
This distinction between physical connection and logical IP subnet is central to practical troubleshooting.
VLSM: Different Sizes for Different Needs
Variable-length subnet masking allows one address plan to contain subnets with different prefix lengths. This is useful because departments and device groups rarely need exactly the same number of addresses.
The illustration compares equal-size subnetting with multi-level subdivision. VLSM can use address space more efficiently when requirements differ.
Worked VLSM Example
Assume a training company receives 192.168.50.0/24 for an internal lab and needs these conventional host capacities:
| Group | Required hosts | Selected prefix | Capacity |
|---|---|---|---|
| Training lab | 100 | /25 | 126 conventional hosts |
| Office | 50 | /26 | 62 conventional hosts |
| Industrial devices | 20 | /27 | 30 conventional hosts |
| Guest Wi-Fi | 10 | /28 | 14 conventional hosts |
Allocate the largest requirement first:
| Group | Network | Conventional usable range | Broadcast |
|---|---|---|---|
| Training lab | 192.168.50.0/25 | 192.168.50.1 to 192.168.50.126 | 192.168.50.127 |
| Office | 192.168.50.128/26 | 192.168.50.129 to 192.168.50.190 | 192.168.50.191 |
| Industrial devices | 192.168.50.192/27 | 192.168.50.193 to 192.168.50.222 | 192.168.50.223 |
| Guest Wi-Fi | 192.168.50.224/28 | 192.168.50.225 to 192.168.50.238 | 192.168.50.239 |
The range 192.168.50.240 through 192.168.50.255 remains available as a /28 block for future use. A network designer could choose a different valid layout, but every assigned subnet must begin on a correct boundary and must not overlap any other subnet.
VLSM Design Rules
- Host capacity: Translate each requirement into the smallest subnet that provides enough usable addresses and reasonable growth.
- Address planning: Allocate larger blocks before smaller blocks to reduce fragmentation and mistakes.
- Network address: Start each subnet on a boundary valid for its prefix.
- Overlapping subnets: Check that no two ranges intersect.
- Documentation: Record network, prefix, mask, gateway policy, VLAN, purpose, and reserved addresses.
A gateway does not have to be the first usable address. Many organizations choose the first or last conventional host address as a policy because consistency helps technicians, but the protocol does not require that particular choice.
CIDR and Route Summarization
CIDR also supports route aggregation. Instead of advertising many individual networks, a router may sometimes advertise one shorter prefix that covers a set of contiguous, correctly aligned networks. This can reduce routing-table size.
For example, these four contiguous /24 networks:
192.168.0.0/24 192.168.1.0/24 192.168.2.0/24 192.168.3.0/24
can be summarized as:
192.168.0.0/22
The summary is valid because a /22 contains 1,024 addresses and starts on the correct boundary. Route summarization must be planned carefully: an overly broad summary can claim destinations that are not actually reachable through the summarizing router.
Routers use longest-prefix matching: when several routes match a destination, the most specific matching prefix is normally preferred. This is one reason a /27 route can override a less specific /24 or /16 route for addresses inside that /27.
Troubleshooting IP Configuration
Common Faults
A structured subnetting method helps you detect common problems:
- IP address conflict: Two devices are configured with the same IPv4 address.
- Subnet mask: A device has the correct-looking address but the wrong prefix or mask.
- Default gateway: The gateway is missing, incorrect, or outside the local subnet.
- DHCP: The client does not receive the expected address, mask, gateway, or DNS settings.
- VLAN: The switch port places the device in a different Layer 2 network than expected.
- Routing: No route exists between the source and destination subnets.
- Firewall: Addressing and routing are correct, but a security policy blocks the traffic.
- Overlapping subnets: Two parts of the network use address ranges that conflict.
Never change a production network simply because a calculation appears wrong. Verify the approved address plan, record the current configuration, and follow your workplace change procedure.
Useful Diagnostic Commands
On Windows, common commands include:
ipconfig /all route print ping 192.168.50.1 tracert 203.0.113.10
On Linux, common commands include:
ip address ip route ping -c 4 192.168.50.1 traceroute 203.0.113.10
Command availability can vary by system. A successful ping can confirm some connectivity, but a failed ping does not prove that the destination is offline because ICMP may be filtered. Combine command output with subnet calculations, switch/VLAN information, routing tables, and approved network documentation.
A Practical Troubleshooting Sequence
- Physical layer: Confirm power, link state, cabling, wireless association, and the intended switch port.
- IP configuration: Record the address, prefix or mask, default gateway, and DNS settings.
- Subnet calculation: Calculate the local network and check whether the gateway is inside it.
- Local connectivity: Test the local stack and, when allowed, a known local neighbor or gateway.
- Routing: Inspect the route table and the path toward remote networks.
- Name resolution: Separate DNS problems from raw IP reachability problems.
- Documentation: Compare your findings with the authorized address and VLAN plan.
This video focuses on IPv4 subnet calculations using binary math. Its certification-series title is historical, but the demonstrated network, broadcast, and host-address calculations remain useful for subnetting practice.
IPv6: Transfer the Prefix Idea
IPv6 addresses contain 128 bits and are normally written in hexadecimal. Prefix notation still uses a slash followed by the number of leading prefix bits, for example:
2001:db8:1234:10::/64
A /64 is the normal subnet size for many IPv6 LANs. Unlike IPv4, IPv6 has no broadcast address; multicast replaces broadcast functions. You also do not calculate a conventional IPv6 usable-host count by subtracting network and broadcast addresses as you often do in IPv4.
The transferable skill is the prefix concept: the prefix identifies the network portion, and routing decisions depend on matching prefixes. The practical details of address assignment, neighbor discovery, router advertisements, DHCPv6, and IPv6 security deserve separate study.
Vocational Case Study: Diagnose Before You Reconfigure
You are supporting a small training workshop. A PC reports:
IPv4 address: 192.168.40.78 Prefix: /27 Default gateway: 192.168.40.65
The target file server is configured as:
IPv4 address: 192.168.40.94 Prefix: /27
A /27 has a block size of 32. The block containing 78 begins at 64 and ends at 95. Therefore:
Network: 192.168.40.64/27 Hosts: 192.168.40.65 through 192.168.40.94 Broadcast: 192.168.40.95
Both devices are in the same IPv4 subnet, and the gateway is also a valid local host address. If the PC still cannot reach the server, changing the subnet mask is not the next logical action. You should investigate local switching, VLAN membership, ARP/neighbor information, host firewalls, the server state, and other evidence.
Now suppose the server were 192.168.40.96/27. That value is the network address of the next /27 block, not a conventional host address. The configuration would need review against the approved design.
This case shows why subnetting is a troubleshooting tool: it helps you eliminate incorrect explanations and choose the next test.
Standards and Reliable Reference Sources
For deeper study, use standards and maintained technical references:
- Private IPv4 addressing: RFC 1918 — Address Allocation for Private Internets
- CIDR: RFC 4632 — Classless Inter-domain Routing
- IPv4 /31 links: RFC 3021 — Using 31-Bit Prefixes on IPv4 Point-to-Point Links
- IPv6: RFC 4291 — IP Version 6 Addressing Architecture
- Subnetwork: English Wikipedia — Subnet
- IP address: English Wikipedia — IP address
Interactive Tasks
Quiz: Test Your Knowledge
How many bits are in an IPv4 address? (32 bits) (!16 bits) (!48 bits) (!128 bits)
Which subnet mask corresponds to a /24 prefix? (255.255.255.0) (!255.255.0.0) (!255.255.255.128) (!255.255.255.252)
What is the network address for 192.168.10.70/26? (192.168.10.64) (!192.168.10.0) (!192.168.10.70) (!192.168.10.128)
What is the broadcast address for the subnet containing 192.168.10.70/26? (192.168.10.127) (!192.168.10.63) (!192.168.10.126) (!192.168.10.255)
How many total IPv4 addresses are in a /27 block? (32) (!14) (!30) (!64)
Which block is private IPv4 address space defined by RFC 1918? (172.16.0.0/12) (!172.0.0.0/8) (!169.254.0.0/16) (!224.0.0.0/4)
How many host bits remain in an IPv4 /28 prefix? (4) (!8) (!24) (!28)
What should a host do when an IPv4 destination is outside its local subnet and a suitable default route exists? (Send the packet toward the default gateway) (!Send the packet directly without routing) (!Change its own subnet mask automatically) (!Replace the destination with a broadcast address)
What is the main purpose of VLSM in an address plan? (Use different subnet sizes for different requirements) (!Force every subnet to have the same size) (!Remove the need for routing) (!Convert IPv4 addresses into IPv6 addresses)
Which statement about IPv6 is correct? (IPv6 addresses are 128 bits long) (!IPv6 addresses are 32 bits long) (!IPv6 uses dotted decimal for every address) (!IPv6 requires an IPv4 broadcast address)
Memory Game
| Prefix length | Number of leading bits that identify the network portion |
| Subnet mask | IPv4 bitmask that separates network bits from host bits |
| Network address | Address that identifies the subnet itself |
| Broadcast address | Final address used for directed broadcast in a conventional IPv4 subnet |
| CIDR | Classless notation and allocation method based on variable prefix lengths |
| VLSM | Address-planning method that uses different prefix lengths in one design |
| Default gateway | Router address used to reach destinations outside the local subnet |
| DHCP | Service that can provide clients with IP configuration automatically |
Drag and Drop
| Match the correct terms. | Topic |
|---|---|
| Network address | Identifies the subnet itself |
| Broadcast address | Reaches all hosts on one conventional IPv4 subnet |
| Host address | Identifies an interface inside a subnet |
| Subnet mask | Separates network bits from host bits in IPv4 |
| Default gateway | Routes traffic toward other networks |
...
Crossword Puzzle
| Subnet | What is a logical subdivision of an IP network called? |
| Gateway | Which device address is commonly used to reach remote networks? |
| Prefix | What word describes the leading network bits in CIDR notation? |
| Broadcast | What is the final special address called in a conventional IPv4 subnet? |
| Netmask | What single word is another common name for an IPv4 subnet mask? |
| Routing | What process forwards packets between different IP networks? |
LearningApps
Cloze Text
Open-Ended Tasks
Easy
- Binary octet: Create a one-page reference card showing the values 128, 64, 32, 16, 8, 4, 2, and 1, then add at least six decimal-to-binary examples that you calculate yourself.
- IP configuration: On an approved lab computer, record the IP address, prefix or mask, default gateway, and DNS information, then produce an annotated screenshot or diagram that explains what each field means without exposing sensitive workplace data.
- Subnet poster: Design an image that shows the network address, first host, last host, and broadcast address for one /27 subnet and explain how you found each boundary.
- Subnetting tutorial: Produce a two-minute video or narrated screen recording that teaches another trainee how to find the block size of a /26 subnet.
Standard
- Help desk troubleshooting: Write a short support procedure for a workstation that can reach local devices but not remote networks, including checks for the subnet, gateway, route table, and firewall evidence.
- Small office network: Design an IPv4 addressing plan for three workplace groups with different host requirements, calculate every subnet, and present the result as a clear table.
- Packet capture: In an authorized lab, capture ARP and ICMP traffic while communicating with a local host and then with a remote host; explain how the observed frames and packets support the local-versus-routed decision.
- Network technician interview: Interview a network technician, instructor, or systems administrator about how address plans are documented and changed, then summarize three practices that reduce configuration errors.
Advanced
- Variable-length subnet masking: Create a VLSM design for a /24 block that must support at least four groups of different sizes, include growth space, prove that the subnets do not overlap, and justify your allocation order.
- Network segmentation: Visit an approved training lab, server room, workshop network cabinet, or simulated site and produce a proposal that maps device groups to subnets or VLANs while explaining operational and security reasons for the separation.
- Subnet calculator: Write a small script or spreadsheet that accepts an IPv4 address and prefix and outputs the network, broadcast, first conventional host, last conventional host, and total address count; test it against at least ten manually verified cases.
- Route summarization: Build or simulate several contiguous networks, develop the shortest correct summary route, test what happens when an unrelated subnet falls inside an overly broad summary, and present the result as a technical report or demonstration video.
Learning Assessment
- Address diagnosis: Given a workstation address, prefix, gateway, and target server address, calculate both subnets and justify whether traffic should be local or routed before proposing any configuration change.
- Subnet design: Convert a set of realistic host requirements into an address plan, choose suitable prefix lengths, calculate the usable ranges, and explain how your design avoids overlap and unnecessary waste.
- Fault analysis: Analyze a case where two devices use the same IP address but different subnet masks and explain the different symptoms that could appear at Layer 2 and Layer 3.
- Troubleshooting evidence: Evaluate command output from an IP configuration tool, route table, ping, and traceroute, then rank possible causes and identify the next test that would produce the most useful evidence.
- CIDR reasoning: Decide whether four given networks can be summarized safely into one route, show the binary or prefix reasoning, and explain the risk of advertising a summary that is too broad.
- IPv6 transfer: Compare an IPv4 /24 subnet with an IPv6 /64 prefix and explain which subnetting ideas transfer directly and which IPv4-specific ideas such as broadcast handling do not.
Evidence of Learning
Knowledge: You can explain IPv4 address structure, binary octets, subnet masks, CIDR prefixes, private address ranges, network and broadcast addresses, VLSM, default gateways, longest-prefix matching, and basic IPv6 prefix concepts.
Skills: You can convert common prefixes and masks, calculate subnet boundaries, determine local versus remote destinations, design non-overlapping address plans, interpret workstation and route-table output, and verify calculations with a second method.
Products: Suitable evidence includes a subnetting reference sheet, annotated IP configuration, network diagram, VLSM plan, troubleshooting procedure, packet-capture explanation, script or spreadsheet, interview summary, and route-summarization report.
Transfer achievements: You can apply subnetting knowledge to unfamiliar workplace scenarios, explain your reasoning to another technician, distinguish addressing faults from VLAN, routing, DNS, or firewall faults, and adapt the prefix concept when moving from IPv4 to IPv6.
OERs on the Topic
The following English Wikipedia resources provide openly accessible background reading:
Linked Learning Areas
The topic connects directly with vocational learning in Computer networking, Information technology, Network administration, Cybersecurity, systems integration, technical support, and infrastructure operations. Subnetting is especially useful when you configure routers and switches, document VLANs, plan DHCP scopes, troubleshoot connectivity, or communicate with colleagues about network changes.
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