how the last usable host address in this range in both binary and dotted decimal format

To determine the last usable host address in a given IP address range, we need to follow these steps:

1. Break Down the Problem

   • Identify the network address and subnet mask.
   • Calculate the total number of addresses in the subnet.
   • Identify the broadcast address.
   • Determine the last usable host address.

2. Relevant Concepts

   • The last usable host address is always one less than the broadcast address.
   • The total number of addresses in a subnet can be calculated using the formula $2^{(32 - n)}$, where $n$ is the number of bits in the subnet mask.

3. Analysis and Detail

   • Let's assume you have a subnet mask of $/24$ (which means 255.255.255.0):
     • Total addresses: $2^{(32 - 24)} = 256$
     • Network address: e.g., $192.168.1.0$
     • Broadcast address: $192.168.1.255$
     • Last usable host address: $192.168.1.254$

4. Verify and Summarize

   • Binary representation of the last usable host address (Dotted Decimal: $192.168.1.254$):
     • $192$ → $11000000$
     • $168$ → $10101000$
     • $1$ → $00000001$
     • $254$ → $11111110$
   • So, in binary format, the last usable host address is $11000000.10101000.00000001.11111110$.

Final Answer

The last usable host address in dotted decimal format is 192.168.1.254, and in binary format, it is 11000000.10101000.00000001.11111110.