Understanding Classless Addressing (CIDR)

The question provides a classless IP address in CIDR (Classless Inter-Domain Routing) notation: 167.199.170.82/27. This notation is a way to specify an IP address and its associated network mask efficiently. The number after the slash, /27 in this case, represents the number of bits used for the network portion of the IP address.

Analyzing the /27 CIDR Mask

An IPv4 address is 32 bits long. In the CIDR notation /N, the first N bits are dedicated to identifying the network, and the remaining bits are used for host addresses within that network. To find the number of bits available for hosts, we subtract the network bits from the total number of bits in an IPv4 address:

Total IPv4 bits = 32

Network bits (N) = 27

Host bits = Total IPv4 bits - Network bits

Host bits = $32 - 27 = 5$

So, there are 5 bits available for host addresses in this network.

Calculating the Total Number of Addresses in the Network

The total number of possible addresses within a network is determined by the number of host bits. If there are 'H' host bits, the total number of addresses is $2^H$. This count includes all possible combinations of the host bits, from all zeros to all ones.

In this specific network, we found that there are 5 host bits. Therefore, the total number of addresses in the network is calculated as:

Total addresses = $2^{\text{Host bits}}$

Total addresses = $2^5$

Let's calculate $2^5$:

$2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32$

Thus, the network defined by the address 167.199.170.82/27 contains a total of 32 addresses.

Network Address vs. Usable Host Addresses

It's important to distinguish between the total number of addresses and the number of usable host addresses. In a standard IP network (excluding special cases like /31 and /32), two addresses are reserved:

• The network address (where all host bits are 0). This identifies the network itself.
• The broadcast address (where all host bits are 1). This address is used to send data to all devices on the network simultaneously.

The number of usable host addresses is $2^H - 2$. However, the question specifically asks for the "number of addresses in the network," which refers to the *total* count, including the network and broadcast addresses. Our calculation of 32 represents this total count.

Conclusion

Given the classless address 167.199.170.82/27, we determined that there are 5 host bits ($32 - 27 = 5$). The total number of addresses in this network is $2^5$, which equals 32.

Revision Table: Key Concepts for Network Addressing

Additional Information: Subnet Mask for /27

While the question can be answered just by knowing the number of host bits, understanding the subnet mask is also useful. The subnet mask helps devices determine which part of an IP address is the network and which is the host. A /27 mask means the first 27 bits are '1's in the binary representation of the mask.

32 bits in total.

27 network bits (1s) + 5 host bits (0s).

Subnet mask in binary: $11111111.11111111.11111111.11100000$

Converting this binary to decimal gives:

• First octet: $11111111_2 = 255$
• Second octet: $11111111_2 = 255$
• Third octet: $11111111_2 = 255$
• Fourth octet: $11100000_2 = 128 + 64 + 32 = 224$

So, the subnet mask for /27 is 255.255.255.224.

This information confirms that the network portion occupies the first 27 bits, leaving 5 bits for the host portion, which aligns with our calculation for the number of addresses.