Question

Consider a datagram network using 8-bit host addresses. Suppose a router uses longest prefix matching and has the following forwarding table: \begin{tabular}{cc} \hline Prefix Match & Interface \\ \hline 1 & 0 \\ 10 & 1 \\ 111 & 2 \\ otherwise & 3 \\ \hline \end{tabular} For each of the four interfaces, give the associated range of destination host addresses and the number of addresses in the range.

Short answer

Interface 0: 64; Interface 1: 64; Interface 2: 32; Interface 3: 128 addresses.

Step-by-step solution

Understand Longest Prefix Matching

In the datagram network, the router forwards packets based on the longest prefix match. This means that the router will match the incoming host address with the longest prefix available in its table. In this table with 8-bit addresses, an address can be represented in binary as an 8-digit string (e.g., 11001011).

Analyze Interface 0

The entry '1' in the table indicates addresses beginning with '1'. Since longer matches ('10' and '111') exist, this entry covers all addresses starting with '1' that don't fall under those longer prefixes. These addresses can be written as '1XXXXXXX', where 'X' can be either 0 or 1. Thus, the range is binary '10000000' to '11111111'. The number of addresses is \(128\) (as there are \(2^7\) combinations for X).

Analyze Interface 1

The entry '10' specifies addresses starting with '10'. This takes precedence over any singular '1' prefixed address from interface 0. The addresses range from '10000000' to '10111111', represented in binary as '10XXXXXX'. The number of addresses is \(64\) (as there are \(2^6\) combinations for X).

Analyze Interface 2

For '111', it covers the addresses starting with '111', meaning '111XXXXXX'. Even though this is a subset of interface 0's '1' prefix, its longer match means it takes precedence. The addresses range from '11100000' to '11111111', covering \(32\) addresses (as \(2^5\) combinations for X).

Analyze Interface 3

The 'otherwise' entry captures all addresses that don't match the prefixes above. This includes all addresses starting with '0'. Thus, these addresses range from '00000000' to '01111111', giving \(128\) addresses (as there are \(2^7\) combinations for X).

Compile Interface Ranges and Counts

- Interface 0: Range from '10000000' to '10111111', 64 addresses - Interface 1: Range from '10000000' to '10111111', 64 addresses - Interface 2: Range from '11100000' to '11111111', 32 addresses - Interface 3: Range from '00000000' to '01111111', 128 addresses

Key concepts

longest prefix matching

In a datagram network, routers use a technique known as **longest prefix matching** to direct incoming data packets to the correct destination. This method helps routers decide which path to take by evaluating the initial bits of an IP address against its forwarding table entries. This concept can be likened to looking at the first few letters of a word to determine its category in a dictionary. The router will match the longest sequence of starting bits from the incoming address with the entries in its table. It ensures data packets follow the most accurate and appropriate route to their destination. To provide an example, consider a router with a forwarding table that includes prefixes like '1', '10', and '111'. When a packet with an address like '11001010' arrives, the router matches these initial bits with the table. In this case, '111' would be the longest matching prefix, leading the data packet through the corresponding interface.

router forwarding table

A **router forwarding table** is an essential component in any network where routers direct packets to their destinations. These tables consist of various entries known as prefixes along with corresponding networking interfaces. The role of the forwarding table within a router is to maintain the information required to make forwarding decisions efficiently. Each entry in the table associates a specific prefix with a designated interface. Here's a closer look at how this works: - The forwarding table is scanned for a match to the address prefix of every incoming packet. - Upon finding the longest match, it forwards the packet through the linked interface. In a practical scenario, suppose a router's table has the following entries: '1', '10', and '111'. When a packet with an address beginning with '10' arrives —despite being part of the broader '1' subnet— it will be sent through the more specific '10' interface.

binary address representation

Understanding **binary address representation** is key to grasping how routers process data in a network. In computer networks, addresses are typically expressed in binary form — a system that uses only two symbols: 0 and 1. Routers interpret each IP address as a sequence of bits. For example, an 8-bit address might look like '11001010'. This string has specific significance in routing, as routers identify the most extended prefix within the forwarding table that matches the address's initial bits. Binary representation allows routers to efficiently determine the specific paths for data flow based on the match quality against the entries in their forwarding tables. The use of binary numbers in this context optimizes computational efficiency and speeds up the decision-making process in routing.

networking interfaces

**Networking interfaces** play a pivotal role in the functioning of routers within a network. They act like ports where data packets enter or exit a router on their journey. A router's interface is essentially a network path for data packets that have a specific destination or requirements. In the context of the routers’ forwarding table, each interface corresponds to a particular prefix in the table, guiding packets to the next hop. For instance: - If the table has an entry with prefix '1' and it maps to interface 0, packets with addresses that match this prefix are routed through interface 0. - This ensures organized and route-efficient data transfer across the network. By having multiple interfaces, routers can connect to various networks or different segments of the same network, thereby facilitating broader and more intricate data flows.