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Difficulty: HardIPv4 Addressing and Subnetting

A network architect is designing a Variable Length Subnet Mask (VLSM) addressing scheme for a enterprise branch using the allocated summary block 172.16.48.0/20172.16.48.0/20. Subnets must be allocated sequentially starting from the beginning of the block, prioritized from the largest host requirement to the smallest, to preserve contiguous unassigned space. The host requirements for the subnets are as follows:

- Department Alpha: 120120 hosts
- Department Beta: 6060 hosts
- Department Gamma: 2828 hosts
- Department Delta: 1212 hosts

Which IPv4 network address and subnet mask must be assigned to Department Gamma?

  1. 172.16.48.192172.16.48.192 with subnet mask 255.255.255.224255.255.255.224Answer
  2. B
    172.16.48.128172.16.48.128 with subnet mask 255.255.255.224255.255.255.224
  3. C
    172.16.48.192172.16.48.192 with subnet mask 255.255.255.240255.255.255.240
  4. D
    172.32.48.192172.32.48.192 with subnet mask 255.255.255.224255.255.255.224

Answer

Department Gamma should be assigned network address 172.16.48.192 with subnet mask 255.255.255.224.
The correct response identifies 172.16.48.192 255.255.255.224 as the network address and subnet mask. Calculating sequentially from the summary block 172.16.48.0/20: Department Alpha uses 172.16.48.0/25 (128 addresses, 126 usable), ending at 172.16.48.127. Department Beta uses 172.16.48.128/26 (64 addresses, 62 usable), ending at 172.16.48.191. Department Gamma requires 28 usable hosts, which fits in a /27 subnet (32 addresses, 30 usable, mask 255.255.255.224) starting at the next boundary: 172.16.48.192.

Step-by-Step Solution

1
Determine prefix length and block size for Department Alpha (120 hosts)
Requires 120 hosts. Formula 2n−2≥120  ⟹  n=72^n - 2 \ge 120 \implies n=7 host bits. Subnet mask /25 (255.255.255.128, block size 128). Range: 172.16.48.0 to 172.16.48.127.
Always allocate largest subnets first to optimize contiguous IP space.
2
Determine prefix length and block size for Department Beta (60 hosts)
Requires 60 hosts. Formula 2n−2≥60  ⟹  n=62^n - 2 \ge 60 \implies n=6 host bits. Subnet mask /26 (255.255.255.192, block size 64). Next available boundary is 172.16.48.128. Range: 172.16.48.128 to 172.16.48.191.
Department Beta starts immediately after Department Alpha's broadcast address.
3
Calculate network address and subnet mask for Department Gamma (28 hosts)
Requires 28 hosts. Formula 2n−2≥28  ⟹  n=52^n - 2 \ge 28 \implies n=5 host bits (25−2=302^5 - 2 = 30 usable hosts). Subnet mask /27 (255.255.255.224, block size 32). Next available boundary is 172.16.48.192.
Department Gamma starts at 172.16.48.192/27, providing 30 usable host IPs (172.16.48.193 - 172.16.48.222).

Key Concept

Variable Length Subnet Masking (VLSM) and Host Capacity Calculation
Estimated Time:2m 0s
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Topics

IPv4 Addressing and Subnetting

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