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Difficulty: MediumIPv4 Addressing and Subnetting

A systems deployment team is provisioning a dedicated IPv4 subnet for a smart office floor. The design plan requires static IP assignments for 4242 IoT sensors, 44 wireless access points, and 22 router interfaces configured for high-availability default gateway redundancy. What is the total number of usable host IPv4 addresses provided by the smallest standard subnet mask that accommodates all required devices?

Answer: 62 hosts

Answer

The smallest subnet that satisfies the requirement for 4848 IP addresses is a /26/26 subnet, which provides 6262 usable host IPv4 addresses.
To determine the total usable IPv4 host capacity of the smallest suitable subnet, first sum the required IP assignments: 42 (sensors)+4 (access points)+2 (gateways)=48 addresses42\text{ (sensors)} + 4\text{ (access points)} + 2\text{ (gateways)} = 48\text{ addresses}. The formula for usable host addresses is 2h−22^h - 2, where hh is the number of host bits. A /27/27 block (h=5h=5) yields 25−2=302^5 - 2 = 30 usable addresses, which is too small. A /26/26 block (h=6h=6) yields 26−2=622^6 - 2 = 62 usable host addresses, which fully supports the 4848 required addresses.

Step-by-Step Solution

1
Calculate total host IP addresses required
Total host requirement = 42+4+2=4842 + 4 + 2 = 48 usable IP addresses
Every connected device and default gateway interface requires a distinct usable IPv4 address.
2
Determine the required host bit count
h=6h = 6 host bits (CIDR prefix /26/26)
25−2=302^5 - 2 = 30 hosts is insufficient for 4848 addresses, whereas 26−2=622^6 - 2 = 62 hosts satisfies the requirement.
3
Calculate the usable host capacity of the subnet
6262 usable host addresses
Subtracting 22 reserved addresses (network ID and broadcast address) from total 26=642^6 = 64 block addresses yields 6262 usable host IPs.

Key Concept

Subnet Host Capacity Calculation (2h−22^h - 2 Rule)
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Topics

IPv4 Addressing and Subnetting

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