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Difficulty: MediumIPv4 Addressing and Subnetting

A network engineer is provisioning subnets from the assigned IPv4 block 10.150.12.0/2210.150.12.0/22 for an industrial automation network. Each production segment requires a subnet capable of accommodating at least 110110 usable IP addresses for automated controllers and monitoring sensors. What is the maximum number of subnets meeting this requirement that can be created from the allocated block?

Answer: 8 subnets

Answer

The maximum number of valid subnets that can be created is 8.
To host at least 110110 usable IP addresses per segment, 77 host bits are required because 27−2=1262^7 - 2 = 126 usable host IPs (66 bits only provide 26−2=622^6 - 2 = 62 usable IPs). A 77-bit host field corresponds to a /25/25 prefix length (32−7=2532 - 7 = 25). Subnetting a /22/22 block into /25/25 subnets yields 225−22=23=82^{25 - 22} = 2^3 = 8 subnets.

Step-by-Step Solution

1
Calculate the host bits needed for at least 110 usable IP addresses.
7 host bits are required because 27−2=1262^7 - 2 = 126 usable hosts (26−2=622^6 - 2 = 62 is insufficient).
Each subnet must accommodate 110 hosts, requiring 7 host bits.
2
Determine the required prefix length for each subnet.
Subnet prefix length is /25/25 (32−7=2532 - 7 = 25).
Subtracting host bits from 32 gives the network prefix length.
3
Determine the number of /25/25 subnets created from a /22/22 block.
2(25−22)=23=82^{(25 - 22)} = 2^3 = 8 subnets.
The difference between the new prefix length (/25) and original prefix length (/22) provides 3 subnet bits.

Key Concept

Subnet sizing and host capacity calculation using IPv4 CIDR notation
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Topics

IPv4 Addressing and Subnetting

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