Question

A router has just received the following new IP addresses: \(57.6 .96 .0 / 21,57.6 .104 .0 / 21\), \(57.6 .112 .0 / 21\), and \(57.6 .120 .0 / 21\). If all of them use the same outgoing line, can they be aggregated? If so, to what? If not, why not?

Short answer

Yes, aggregate to 57.6.96.0/19.

Step-by-step solution

Convert IPs to Binary

We start by converting each of the given IP addresses to their binary form. The first two octets (57.6) are the same for all addresses. Let's focus on the third octet. - 96 = 01100000 - 104 = 01101000 - 112 = 01110000 - 120 = 01111000 We keep the network portion (first 21 bits) constant and consider the rest.

Check Common Network Prefix

To aggregate these IP addresses, the network portion must be identical. We look for the longest common prefix in binary: - 96 -> 01100 - 104 -> 01101 - 112 -> 01110 - 120 -> 01111 They share the prefix '011', and in binary that represents the range covering all addresses.

Determine Aggregated Network Address

Trying to aggregate to a /19 since it covers more addresses: First we create the range from 96 (01100000) to 127 (01111111) Combining the addresses into a single route, we take: IP: 57.6.96.0/19, binary: 01100 This covers all IPs from 57.6.96.0 to 57.6.127.255.

Verify the Aggregation

A /19 CIDR block includes all four addresses under its range. - Range: 57.6.96.0 to 57.6.127.255 This confirms all the given addresses are within this range.

Key concepts

Binary Conversion

To understand IP address aggregation, it's essential to grasp binary conversion, which involves translating decimal numbers into the binary number system used in computing. Our decimal system is base-10, while binary is base-2, consisting only of 0s and 1s.
IP addresses are typically displayed in a "dotted-decimal" format, like 192.168.1.1, but in reality, computers read them in binary. Let's break down the conversion process using the third octet of the IP address (e.g., 96):

• Find the largest power of 2 less than or equal to the number. For 96, it's 64.
• Write a 1 for 64 and subtract it from 96, leaving 32. The binary so far is 1xxxxxx.
• Continue this process, writing 1s for each power of 2 (32, in this case) that fits into the remaining number, and 0s otherwise, until you reach 0.

For 96, this looks like: 01100000 in binary. Understanding this conversion is crucial as it helps break down IP addresses into bits, making it easier to identify network prefixes.

Network Prefix

The network prefix of an IP address is a fundamental component used to identify the network portion shared by all systems in a subnet. It's crucial when aggregating addresses, as it defines how devices communicate within and outside the local network.
Think of the network prefix like a street address but for computers. If several houses (or devices) share the same street name (network prefix), they belong to the same area. For IP addresses, this prefix is determined by the binary sequence shared by all addresses within a range.
To aggregate, all addresses must have an identical prefix. In binary terms, if you have IPs like 57.6.96.0/21 and 57.6.104.0/21, their prefix 011 aligns, indicating they can be grouped together. This shared beginning alters which part of the IP addresses are included or excluded in the aggregation.

CIDR Notation

CIDR stands for Classless Inter-Domain Routing, a method for allocating IP addresses and IP routing. CIDR notation helps in denoting the network prefix length by appending a slash and a number to an IP address; for example, 192.168.1.0/24.
This notation simplifies IP address management by not sticking strictly to the traditional class systems for networks (like Class A, B, C). Instead, CIDR allows more flexible networking by indicating precisely how many bits are used for the network part of the address.
In our aggregation example, 57.6.96.0/19 indicates that the first 19 bits are the network portion, allowing us to include all addresses from 57.6.96.0 to 57.6.127.255 in a single route. The short notation is efficient, helps conserve IP address space, and optimizes the routing process.

Routing

Routing is the process by which data packets are forwarded from one network to another. Think of it as a digital map, guiding data from its source to its destination.
In the context of IP address aggregation, efficient routing is achieved by combining multiple IP addresses into a single aggregated address. This minimizes the number of routes that need to be managed, simplifying the routing table. Instead of managing each address individually, networks can now be handled as a collective block using CIDR notation.
Routing benefits from aggregation because it reduces the complexity of routing decisions and conserves bandwidth. A single entry in the routing table can replace many smaller ones, making data processing faster and more efficient for routers, leading to improved network performance.