IPv4 subnetting design: for the private Class B network 172.16.0.0, you want each subnet to support approximately 600 usable hosts. Which single subnet mask should you assign?

Introduction / Context: When choosing a subnet mask, two requirements must be met: the number of hosts per subnet and the number of subnets available. Here, we focus on host capacity per subnet for 172.16.0.0 (a Class B private block with default /16). We must select a mask that provides at least ~600 usable addresses per subnet.

Given Data / Assumptions:

• Base network: 172.16.0.0/16.
• Target: ≈600 usable hosts per subnet.
• Usable hosts per subnet = 2^(host_bits) - 2.

Concept / Approach: Borrow s bits from the /16 host space, leaving (16 - s) host bits. The number of usable addresses is 2^(16 - s) - 2. We need this to be ≥ 600. Compute for successive masks until the requirement is satisfied, choosing the smallest mask length that still meets the host count to conserve address space.

Step-by-Step Solution:

Verification / Alternative check: Cross-check neighboring options: /21 (255.255.248.0) yields 2^11 - 2 = 2046 usable (more than enough but wastes addresses). /23 is too small (only 510). Hence /22 is the optimal choice.

Why Other Options Are Wrong:

Common Pitfalls: Forgetting to subtract 2 addresses for network/broadcast, or misreading the host requirement as ‘‘exactly 600’’ rather than ‘‘at least 600’’.

Final Answer: 255.255.252.0.