A LAN with the network address 172.16.0.0/20 is connected to the Router, which has a default gateway IP of 172.16.0.1 and a subnet mask of 255.255.240.0. How many subnets are available within this LAN?

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Let's restate the scenario to ensure clarity: a LAN has the network address 172.16.0.0/20, connected to a Router with a default gateway of 172.16.0.1 and a subnet mask of 255.255.240.0. The question asks how many subnets are available within this LAN.

First, identify the default classful boundary for the given address. The 172.16.0.0 range falls within Class B, whose default subnet mask is 255.255.0.0 (or /16). When we subnet this network further to 172.16.0.0/20, we are borrowing bits from the host portion of the default /16 network.

Next, determine how many bits were borrowed. A /20 mask means 4 bits have been borrowed from the original 16 host bits (since 20 = 16 + 4).

Now calculate the number of subnets created by borrowing 4 bits. The formula is 2^n, where n is the number of borrowed bits. Here, n = 4, so 2^4 = 16 subnets.

Proceeding to evaluate the answer choices:
- Option a: 16 — This matches the calculation of borrowing 4 bits from a /16 to reach /20, yielding 16 subnets.
- Option b: 64 — This would correspond to borrowing 6 bits (2^6 = 64), which would imply a /22 network from a /16, not /20.
- Option c: 32 — This would correspond to borrowing 5 bits (2^5 = 32), which would be a /21, not /20.
- Option d: 8 — This would correspond to borrowing 3 bits (2^3 = 8), which would be a /19, not /20.

So the structure of the answer choices reflects different possible subnetting schemes, but only the /20 boundary fractures the /16 into 16 subnets.

In summary, because the LAN uses 172.16.0.0 as a /20 subnet within the Class B 172.16.0.0/16 space, the number of subnets available is 16. The reasoning hinges on recognizing the classful default, the subnet mask used, and applying the 2^n rule for borrowed bits.

Introduction to Networking (032025-TGK)

A LAN with the network address 172.16.0.0/20 is connected to the Router, which has a default gateway IP of 172.16.0.1 and a subnet mask of 255.255.240.0. How many subnets are available within this LAN?

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