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Difficulty: MediumIPv4 Addressing and Subnetting

A network administrator is assigned the IPv4 address block 10.20.0.0/2210.20.0.0/22 for a new branch location. The administrator needs to partition this block into equal-sized subnets, where each subnet must support at least 5050 usable host IP addresses. What is the maximum number of such subnets that can be created from this address block?

Answer: 16 subnets

Answer

The maximum number of subnets that can be created is 16.
To accommodate at least 50 hosts, each subnet requires 6 host bits because 26−2=622^6 - 2 = 62 usable addresses (5 host bits only provides 30 usable addresses). A subnet with 6 host bits uses a /26/26 prefix (32−6=2632 - 6 = 26). Subnetting a /22/22 prefix into /26/26 subnets borrows 4 bits (26−22=426 - 22 = 4), resulting in 24=162^4 = 16 total subnets.

Step-by-Step Solution

1
Determine the required host bits for each subnet.
6 host bits are required.
The formula for usable hosts per subnet is 2h−22^h - 2. Setting h=6h = 6 yields 26−2=622^6 - 2 = 62 usable host IP addresses, satisfying the requirement of at least 50 hosts.
2
Determine the subnet CIDR prefix length.
The prefix length is /26/26.
Subtracting 6 host bits from the total 32 IPv4 bits gives 32−6=2632 - 6 = 26 network bits.
3
Calculate the total number of /26/26 subnets within the original /22/22 block.
16 subnets.
The difference between prefix lengths is 26−22=426 - 22 = 4 borrowed subnet bits. Calculating 242^4 gives 16 subnets.

Key Concept

IPv4 Subnetting and Host Capacity Calculation
Estimated Time:1m 30s
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Topics

IPv4 Addressing and Subnetting

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