You are given the IP block 172.16.0.0/24 and you need to subnet it into four smaller networks with the following host requirements:Network A: 40 hosts Network B: 20 hosts Network C: 10 hosts Network D: 5 hosts What is the subnet mask of the Network A in dotted decimal notation?

Question

BlackTom AI · Accepted Answer

To support 40 hosts you need at least 42 IP addresses (40 hosts + 1 network + 1 broadcast). Determine how many host bits are required: 2^n - 2 ≥ 40.

1) Relevant concepts
- IPv4 subnetting: number of usable hosts per subnet = 2^(host bits) − 2 (network and broadcast).
- Prefix length = 32 − host bits. Convert prefix to dotted-decimal mask by setting prefix number of leading 1 bits.

2) Step-by-step reasoning and calculations
- Try n = 5 host bits: usable = 2^5 − 2 = 32 − 2 = 30 → insufficient for 40 hosts.
- Try n = 6 host bits: usable = 2^6 − 2 = 64 − 2 = 62 → sufficient for 40 hosts.
- Therefore you need 6 host bits for Network A.
- Prefix length = 32 − 6 = /26.

3) Convert /26 to dotted decimal
- A /26 mask has 26 one-bits: first three octets are all ones (8+8+8 = 24), last octet has 2 ones then six zeros: 11000000 (binary) = 128 + 64 = 192.
- So the mask is 255.255.255.192.

4) Why this is correct
- /26 provides 64 total addresses (62 usable), which meets the required 40 hosts with room for growth while using the minimal host-bit allocation that satisfies the requirement.
- From the original 172.16.0.0/24 you can create four /26 subnets (172.16.0.0/26, .64/26, .128/26, .192/26), so /26 is an appropriate allocation for the largest required network.

5) Why other common masks are not appropriate
- /27 (255.255.255.224) gives 30 usable hosts → too small.
- /25 (255.255.255.128) gives 126 usable hosts → works but is larger than necessary (more waste).
- /28 (255.255.255.240) gives 14 usable hosts → too small.

Conclusion: The correct subnet mask for Network A is 255.255.255.192, matching the provided answer.

You are given the IP block 172.16.0.0/24 and you need to subnet it into four smaller networks with the following host requirements:Network A: 40 hosts Network B: 20 hosts Network C: 10 hosts Network D: 5 hosts What is the subnet mask of the Network A in dotted decimal notation?Short answer

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