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Difficulty: MediumIPv4 Addressing and Subnetting

A network administrator is provisioning a dedicated IPv4 subnet for a smart building automation system that requires static IP addresses for 5858 environmental sensors. To conserve address space, which of the following CIDR prefix lengths represents the smallest subnet that accommodates this requirement?

  1. /26/26Answer
  2. B
    /27/27
  3. C
    /25/25
  4. D
    /28/28

Answer

The prefix length /26/26 provides 6262 usable host IP addresses, which is the smallest subnet that can accommodate 5858 sensors.
The prefix length /26/26 allocates 6 host bits (26=642^6 = 64 total IP addresses). Subtracting 2 reserved addresses (one for network ID and one for broadcast) yields 6262 usable host IP addresses. This is the smallest subnet size that accommodates all 5858 required hosts without unnecessary address wastage.

Step-by-Step Solution

1
Determine required host capacity including overhead
58 hosts needed + 2 overhead addresses (network ID and broadcast address) = 60 total IP addresses minimum.
Every IPv4 subnet requires one address for the network ID and one address for the subnet broadcast.
2
Calculate the required host bits (h)
2^h >= 60 total addresses. For h = 5, 2^5 = 32 (too small). For h = 6, 2^6 = 64 (sufficient).
We need the smallest power of 2 that is greater than or equal to 60.
3
Calculate prefix length
32 total IPv4 bits - 6 host bits = /26.
Subtracting host bits from 32 gives the network prefix length.

Key Concept

Determining Minimum IPv4 Subnet Mask / CIDR Prefix for Host Requirements
Estimated Time:1m 0s
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Topics

IPv4 Addressing and Subnetting

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