What is the maximum number of usable host IP addresses that can be assigned on a local subnet using the subnet mask 255.255.255.224?

Introduction / Context:
This question evaluates your ability to calculate the number of usable host IP addresses available in a subnet given its subnet mask. This is a basic but essential subnetting skill that you will use when planning VLANs, allocating addresses to departments, or designing WAN segments.

Given Data / Assumptions:
- The subnet mask is 255.255.255.224.
- We are concerned with the maximum number of IP addresses that can be assigned to hosts on a single subnet using this mask.
- Network and broadcast addresses cannot be assigned to hosts.
- We are working in a traditional IPv4 context where each subnet reserves two addresses (network and broadcast).

Concept / Approach:
The subnet mask 255.255.255.224 corresponds to a /27 prefix, because the first 27 bits are set to 1. That leaves 5 bits for host addresses in the last octet (since 32 - 27 = 5). The total number of addresses in a subnet equals 2^(number of host bits). To find the number of usable host addresses, you subtract 2 from this value to account for the network address (all host bits 0) and the broadcast address (all host bits 1).

Step-by-Step Solution:
Step 1: Convert the subnet mask 255.255.255.224 to prefix notation: 224 in binary is 11100000, so we have 8 + 8 + 8 + 3 = 27 network bits, which is /27.Step 2: Calculate the number of host bits as 32 - 27 = 5.Step 3: Find the total number of addresses by computing 2^5 = 32.Step 4: Subtract 2 addresses for the network and broadcast addresses, leaving 32 - 2 = 30 usable host addresses.Step 5: Confirm that this count matches typical subnetting tables, where a /27 network supports 30 hosts.

Verification / Alternative check:
Many subnetting cheat sheets or memorized patterns show that common masks have known host capacities: /24 supports 254 hosts, /25 supports 126, /26 supports 62, and /27 supports 30. This pattern confirms that a /27 (255.255.255.224) subnet can indeed host 30 devices. You could also quickly verify by picking an example subnet, such as 192.168.1.32/27, and listing addresses from 192.168.1.32 to 192.168.1.63. The first is the network address, the last is broadcast, leaving 30 usable IPs in between.

Why Other Options Are Wrong:
15 and 16 usable hosts correspond to a /28 mask (16 total addresses, 14 usable) or a miscalculation. 31 usable hosts would imply 33 total addresses, which does not align with any power of two. The option 32 usable host addresses incorrectly counts the network and broadcast addresses as assignable, which is not allowed in standard IPv4 subnetting practice.

Common Pitfalls:
A common error is to forget to subtract 2 for network and broadcast, resulting in the total number of addresses instead of usable hosts. Another pitfall is miscounting the number of host bits when converting from dotted decimal mask to prefix length. Practicing quick binary conversions for common masks like 224 (11100000) and 240 (11110000) helps avoid these mistakes.

Final Answer:
A subnet using the mask 255.255.255.224 has 30 usable host IP addresses.