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Difficulty: MediumIPv4 Addressing and Subnetting

A network administrator is provisioning a dedicated subnet for a newly established server cluster that requires static IP assignments for exactly 3131 usable host devices. To conserve address space, which of the following is the most efficient subnet mask that satisfies this requirement?

  1. A
    255.255.255.224
  2. 255.255.255.192Answer
  3. C
    255.255.255.240
  4. D
    255.255.255.128

Answer

The subnet mask 255.255.255.192 is the most efficient subnet mask because a /26 network provides 62 usable host IP addresses, satisfying the 31 host requirement with minimal wasted IP addresses.
The option specifying '255.255.255.192' corresponds to a prefix length of /26/26. A /26/26 subnet contains 66 host bits, yielding 26=642^6 = 64 total IP addresses. Subtracting 22 for the reserved network and broadcast addresses yields 6262 usable host IPs, which is the smallest standard subnet capable of housing 3131 hosts.

Step-by-Step Solution

1
Determine the required number of usable host IP addresses.
The scenario specifies a requirement of 3131 usable host IP addresses.
Subnet capacity must accommodate all host interfaces plus non-usable network and broadcast addresses.
2
Calculate required host bits using the formula 2h−2≥312^h - 2 \ge 31.
For h=5h = 5 bits: 25−2=302^5 - 2 = 30 usable IPs (insufficient). For h=6h = 6 bits: 26−2=622^6 - 2 = 62 usable IPs (sufficient).
Two IP addresses per subnet are reserved for the network ID and broadcast address.
3
Convert the required host bits to a subnet mask.
The prefix length is 32−6=/2632 - 6 = /26. Converting /26/26 to dotted-decimal yields 255.255.255.192255.255.255.192.
A /26/26 prefix uses 2626 network bits (11111111.11111111.11111111.110000002=255.255.255.19211111111.11111111.11111111.11000000_2 = 255.255.255.192).

Key Concept

IPv4 Subnetting & Usable Host Calculation
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Topics

IPv4 Addressing and Subnetting

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