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Difficulty: MediumIPv4 Addressing and Subnetting

A network engineer is allocated the IPv4 block 198.51.100.0/24198.51.100.0/24 and needs to provision subnets for departmental networks. Each departmental network must support a minimum of 2525 usable host IP addresses. Using the longest prefix length (smallest subnet size) that satisfies this host requirement, what is the maximum number of usable host IP addresses available on each generated subnet?

Answer: 30 usable hosts

Answer

Each subnet supports a maximum of 30 usable host IP addresses.
To support at least 2525 usable host IP addresses, 55 host bits are required (25−2=302^5 - 2 = 30). This corresponds to a /27/27 subnet prefix length (32−5=2732 - 5 = 27). Each /27/27 subnet contains 3232 total IP addresses. Subtracting 22 reserved addresses for the network identifier and broadcast address leaves 3030 usable host IP addresses per subnet.

Step-by-Step Solution

1
Determine the minimum number of host bits (hh) required to accommodate 2525 usable host IP addresses using the formula 2h−2≥252^h - 2 \ge 25.
h=5h = 5 host bits are needed because 24−2=142^4 - 2 = 14 (too small) and 25−2=30≥252^5 - 2 = 30 \ge 25.
Host bits determine the size of the host portion of the IPv4 address space for the subnet.
2
Calculate total usable host IP addresses per subnet created with 55 host bits (a /27/27 subnet mask, or 255.255.255.224255.255.255.224).
25−2=302^5 - 2 = 30 usable host IP addresses.
Two IP addresses in every block are reserved for the network ID and the broadcast address, leaving 3030 addresses available for host assignment.

Key Concept

IPv4 Subnet Mask and Usable Host Capacity Calculation
Estimated Time:1m 30s
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Topics

IPv4 Addressing and Subnetting

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