Question

Consider a router that interconnects three subnets: Subnet 1, Subnet 2, and Subnet 3. Suppose all of the interfaces in each of these three subnets are required to have the prefix \(223.1 .17 / 24\). Also suppose that Subnet 1 is required to support at least 60 interfaces, Subnet 2 is to support at least 90 interfaces, and Subnet 3 is to support at least 12 interfaces. Provide three network addresses (of the form a.b.c.d/x) that satisfy these constraints.

Short answer

Subnet 1: 223.1.17.0/26, Subnet 2: 223.1.17.64/25, Subnet 3: 223.1.17.192/28.

Step-by-step solution

Determine the Number of Host Bits for Each Subnet

First, calculate the number of host bits needed for each subnet. For Subnet 1, we need at least 60 interfaces. We know the formula for the number of hosts in a subnet is given by \(2^n - 2\), where \(n\) is the number of host bits. Solving \(2^n - 2 \geq 60\), we get \(n = 6\) (since \(2^6 - 2 = 62\)). Similarly, for Subnet 2 with at least 90 interfaces, \(n = 7\) (as \(2^7 - 2 = 126\)), and for Subnet 3 with at least 12 interfaces, \(n = 4\) (since \(2^4 - 2 = 14\)).

Calculate the New Subnet Masks

Determine the subnet mask required for each subnet by subtracting the number of host bits \(n\) from 32 (the total number of bits in an IPv4 address). For Subnet 1 needing 6 host bits, the mask is \(32 - 6 = 26\), so the notation is /26. For Subnet 2, the mask is \(32 - 7 = 25\), so /25. For Subnet 3 needing 4 host bits, the mask is \(32 - 4 = 28\), so /28.

Assign Network Addresses

Assign suitable network addresses starting with the given prefix \(223.1.17.0/24\). The first available address space is \(223.1.17.0 /26\) for Subnet 1, handling up to 62 addresses. Subnet 2, with a /25 mask, can start at \(223.1.17.64 /25\), covering the next 126 addresses. Subnet 3 begins at \(223.1.17.192 /28\), allowing for 14 addresses, leaving room for future expansion.

Verify Address Requirements and Ranges

Check each assigned network to ensure all interface requirements are met and there are no overlaps. Subnet 1 (/26) includes 223.1.17.0 to 223.1.17.63, Subnet 2 (/25) spans 223.1.17.64 to 223.1.17.191, and Subnet 3 (/28) covers 223.1.17.192 to 223.1.17.207. This distribution provides each subnet with the required interfaces without overlap.

Key concepts

IPv4 addressing

IPv4 addressing is essential for communication over a network. It provides a unique identifier to each device, known as an IP address. An IPv4 address is a 32-bit number, typically represented in a dotted decimal format such as 223.1.17.0.

Each IPv4 address is divided into two parts: the network prefix and the host identifier. The network prefix identifies a particular network, allowing devices within the same subnet to communicate directly. The host identifier is unique within this network, distinguishing each device.

This division allows efficient routing of data between networks and hosts. The structure of an IPv4 address means there is a limited amount of total addresses, though subnetting helps manage this by allowing large networks to be segmented into smaller networks.

Subnet masks

A subnet mask is crucial in defining the structure of a network by separating the network portion of an IP address from the host portion. It aids in the creation of subnets, which are smaller, manageable sections of a larger network.

The subnet mask tells us which portion of the address space is designated for network identification and which part is available for devices or hosts. For example, a /26 subnet mask indicates that the first 26 bits of the IP address are used for the network, leaving the remaining bits for host addresses.

Subnet masks are typically expressed in CIDR notation, such as /24 or /26, which denotes the number of bits in the network portion. Understanding the subnet mask helps in network planning by facilitating efficient use of IP addresses while minimizing unnecessary communication.

Network addressing

Network addressing is all about defining how devices communicate within a network as well as between networks. The network address is the first IP address in the range assigned to a subnet. It identifies the subnet rather than a specific device within the subnet.

For instance, in this exercise, the network address for Subnet 1 with a /26 mask could be 223.1.17.0, marking the beginning of that subnet's range. It's essential to correctly assign these addresses to avoid conflicts and overlaps, ensuring smooth communication.

The network address is crucial for routers, which use this designation to make routing decisions. Assigning network addresses efficiently means ensuring that each subnet has enough addresses for its devices and predicts future growth.

Host bits calculation

Host bits calculation helps determine how many devices can be supported within a subnet. The number of host bits is the difference between the total number of bits in an IPv4 address (32) and the number of bits used by the subnet mask.

The host bits calculation follows the formula: \(2^n - 2\). Here, \(n\) is the number of host bits, \(2^n\) represents all possible combinations of these bits, and subtracting 2 accounts for the network and broadcast addresses.

For example, if a subnet requires at least 60 devices, then solving \(2^n - 2 \geq 60\) gives \(n = 6\). This calculation ensures that subnets have adequate space for all their devices, preventing overcrowding and network issues.