You have Class A network 10.0.0.0. There are already 40 subnets and 60 more will be added soon (total ≥ 100). To maximize host IDs per subnet, which subnet mask should you choose?

Introduction / Context:
Subnetting trades bits between the subnet field and the host field. Here, you must support at least 100 subnets while keeping the host space per subnet as large as possible. The address is a Class A (default /8) private block: 10.0.0.0.

Given Data / Assumptions:

• Base: Class A ⇒ default mask /8 (255.0.0.0).
• Required subnets: at least 100 (40 existing + 60 new).
• Maximize hosts per subnet.
• Assume traditional subnet count uses 2^b - 2 (for historical reserved all-0/all-1), but even with modern practice, choosing the smallest b meeting ≥100 is optimal.

Concept / Approach:

Let b = subnet bits needed. Need 2^b - 2 ≥ 100 ⇒ b = 7 (since 2^7 = 128, 128 - 2 = 126).New prefix length = 8 + 7 = /15./15 in dotted decimal is 255.254.0.0.

Step-by-Step Solution:

Verification / Alternative check:

Any mask longer than /15 (e.g., /16+/) would reduce hosts per subnet without increasing needed subnets beyond the minimum. /15 is the smallest prefix that meets ≥100 subnets from a Class A block while maximizing hosts.

Why Other Options Are Wrong:

255.240.0.0 (/12), 255.248.0.0 (/13), 255.252.0.0 (/14): Provide fewer than 100 usable subnets under 2^b − 2 convention.

255.255.255.255: /32, no host space.

Common Pitfalls:

Forgetting to add subnet bits to the classful /8 or confusing the requirement (≥100) with exactly 100. Choosing /15 satisfies with maximum host space.

Final Answer:

255.254.0.0