Your router has the following IP address on Ethernet0: 172.16.2.1/23. ...
The router's IP address on the E0 interface is 172.16.2.1/23, which is 255.255.254.0. This makes the third octet a block size of 2. The router's interface is in the 2.0 subnet, and the broadcast address is 3.255 because the next subnet is 4.0. The valid host range is 2.1 through 3.254. The router is using the first valid host address in the range.
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Your router has the following IP address on Ethernet0: 172.16.2.1/23. ...
Explanation:
The given IP address on Ethernet0 is 172.16.2.1/23. Let's break down the IP address and subnet mask to understand the range of valid host IDs on the LAN interface.
IP address: 172.16.2.1
Subnet mask: /23
Binary representation of the IP address: 10101100.00010000.00000010.00000001
Binary representation of the subnet mask: 11111111.11111111.11111110.00000000
Network address: To find the network address, we perform a bitwise AND operation between the IP address and the subnet mask. This operation yields the network address.
10101100.00010000.00000010.00000001 (IP address)
11111111.11111111.11111110.00000000 (Subnet mask)
--------------------------------------
10101100.00010000.00000010.00000000 (Network address)
The network address in binary representation is 172.16.2.0.
Range of valid host IDs:
For a /23 subnet, the host bits available are 9 (32 - 23 = 9). This means that there are 2^9 - 2 = 510 valid host IDs in the subnet.
The range of valid host IDs will start from the network address + 1 and end at the network address + (2^9 - 2).
Network address: 172.16.2.0
First valid host ID: 172.16.2.1
Last valid host ID: 172.16.3.254
Broadcast address: 172.16.3.255
Determining the valid host IDs from the given options:
Let's analyze the given options:
1. 172.16.1.100 - This IP address is not within the range of valid host IDs for the given subnet. It is outside the range of 172.16.2.1 to 172.16.3.254.
2. 172.16.1.198 - This IP address is not within the range of valid host IDs for the given subnet. It is outside the range of 172.16.2.1 to 172.16.3.254.
3. 172.16.2.255 - This IP address is within the range of valid host IDs for the given subnet. It falls between 172.16.2.1 and 172.16.3.254.
4. 172.16.3.0 - This IP address is not within the range of valid host IDs for the given subnet. It is the network address.
Therefore, the valid host IDs on the LAN interface attached to the router are 172.16.2.255 only.
Conclusion:
Based on the given IP address and subnet mask, the valid host IDs on the LAN interface attached to the router are 172.16.2.255.