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Difficulty: HardIPv4 Addressing and Subnetting

A network architect is assigned the IPv4 address block 172.24.160.0/19172.24.160.0/19 to provision subnets for a new regional data center. To optimize routing and broadcast domain sizes, the architect must partition the entire block into equal-sized subnets such that each subnet can accommodate a minimum of 120120 usable host IP addresses. Using the longest possible CIDR prefix mask that satisfies this host requirement, what is the total maximum number of usable host IP addresses available across all subnets created?

Answer: 8064 host IP addresses

Answer

8064 usable host IP addresses
To support at least 120 usable host IP addresses per subnet while utilizing the longest possible CIDR prefix, a /25 subnet mask (7 host bits) is required, providing 27−2=1262^7 - 2 = 126 usable host addresses per subnet. Partitioning the parent 172.24.160.0/19172.24.160.0/19 block into /25 subnets yields 225−19=26=642^{25-19} = 2^6 = 64 subnets. Multiplying 64 subnets by 126 usable host IP addresses per subnet results in 8064 total usable host IP addresses.

Step-by-Step Solution

1
Determine the host bit requirement (hh) for at least 120 usable hosts per subnet.
7 host bits are required because 27−2=126≥1202^7 - 2 = 126 \ge 120 usable host addresses.
6 host bits (26−2=622^6 - 2 = 62) are insufficient to meet the 120 host requirement.
2
Calculate the subnet prefix length (CIDR notation).
Prefix length is /25/25 (32−7=2532 - 7 = 25).
Subtracting 7 host bits from the 32 total IPv4 bits leaves a 25-bit network prefix.
3
Calculate total /25/25 subnets created from the parent /19/19 block.
64 subnets (225−19=26=642^{25 - 19} = 2^6 = 64).
The difference between the new prefix (/25) and parent prefix (/19) is 6 subnet bits.
4
Calculate total usable host IP addresses across all 64 subnets.
8064 usable host IP addresses (64×126=806464 \times 126 = 8064).
Each of the 64 subnets reserves 2 IP addresses (network ID and broadcast address) out of 128 total addresses.

Key Concept

Partitioning IPv4 CIDR blocks using VLSM/subnetting and calculating total aggregate usable host space.
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Topics

IPv4 Addressing and Subnetting

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