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Difficulty: HardIPv4 Addressing and Subnetting

An enterprise operations team is allocated the network block 172.28.64.0/21172.28.64.0/21 to deploy microservices within a private cloud environment. To satisfy security policies, the administrator must divide this entire block into equal-sized subnets such that each subnet can accommodate at least 100100 usable host IP addresses while reserving as much space as possible for maximum subnetting density (using the longest possible subnet mask that meets the requirement). What is the total number of usable host IP addresses available across all created subnets combined?

Answer: 2016 hosts

Answer

2016 usable host IP addresses
To host at least 100100 usable IP addresses, each subnet requires 77 host bits (27−2=1262^7 - 2 = 126 usable hosts), which corresponds to a /25/25 prefix (32−7=2532 - 7 = 25). Subnetting a /21/21 network block into /25/25 subnets yields 225−21=24=162^{25-21} = 2^4 = 16 distinct subnets. Because each /25/25 subnet reserves 11 network address and 11 broadcast address, each subnet has 126126 usable host IPs. Across all 1616 subnets, the total usable host capacity is 16×126=201616 \times 126 = 2016.

Step-by-Step Solution

1
Determine the required subnet mask for each subnet to support at least 100 hosts
A /25/25 prefix (255.255.255.128255.255.255.128) providing 126 usable host IP addresses per subnet
The formula for usable hosts is 2h−2≥1002^h - 2 \ge 100. For h=6h = 6, 26−2=622^6 - 2 = 62 (insufficient). For h=7h = 7, 27−2=1262^7 - 2 = 126 (sufficient). The subnet prefix length is 32−7=2532 - 7 = 25.
2
Calculate how many /25/25 subnets fit into the parent /21/21 block
16 subnets
The difference between the new subnet prefix (/25/25) and the parent prefix (/21/21) is 25−21=425 - 21 = 4 bits. The number of subnets is 24=162^4 = 16.
3
Calculate the total aggregate usable host capacity
2016 aggregate usable host addresses
Multiplying the total subnets (1616) by the usable hosts per subnet (126126) yields 16×126=201616 \times 126 = 2016.

Key Concept

Subnet partitioning and usable host capacity calculation under CIDR constraints
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Topics

IPv4 Addressing and Subnetting

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