What class does the Host IP Address belong to?

Steps to Solve

1. Identify the New Subnet Mask Prefix

To find the subnet mask prefix for the new subnet mask $255.255.255.128$, we convert it to binary:
$$ 255.255.255.128 = 11111111.11111111.11111111.10000000 $$
The prefix length is 25 because there are 25 ones in the binary representation.

2. Calculate Number of Subnet Bits

The number of subnet bits is calculated as the difference between the new prefix and the original prefix. The original subnet mask of $255.255.255.0$ corresponds to /24.
Number of subnet bits = $25 - 24 = 1$

3. Determine Number of Subnets Created

The number of subnets created can be calculated using the formula:
$$ \text{Number of Subnets} = 2^{\text{Number of Subnet Bits}} $$
Substituting the value:
$$ \text{Number of Subnets} = 2^1 = 2 $$

4. Calculate Number of Host Bits per Subnet

The number of host bits per subnet is calculated by subtracting the subnet bits from 32 (the total number of bits in an IPv4 address):
$$ \text{Number of Host Bits} = 32 - 25 = 7 $$

5. Calculate Number of Hosts per Subnet

The number of hosts per subnet can be found using the formula:
$$ \text{Number of Hosts} = 2^{\text{Number of Host Bits}} - 2 $$
(We subtract 2 for the network and broadcast addresses.)
$$ \text{Number of Hosts} = 2^{7} - 2 = 128 - 2 = 126 $$

6. Determine the Network Address of this Subnet

The network address is found by performing a bitwise AND operation between the IP address and the subnet mask:
$$ 195.167.1.245 \land 255.255.255.128 = 195.167.1.128 $$

7. Identify the IPv4 Address of the First Host in this Subnet

The first usable host address is one more than the network address:
$$ \text{First Host} = 195.167.1.128 + 1 = 195.167.1.129 $$

8. Identify the IPv4 Address of the Last Host in this Subnet

The last usable host address is two less than the broadcast address. First, we find the broadcast address, next step.

9. Determine the IPv4 Broadcast Address of this Subnet

The broadcast address is the highest address in the subnet:
$$ \text{Broadcast Address} = 195.167.1.255 $$

10. Identify the IPv4 Address of the Last Host in this Subnet

The last usable host address is one less than the broadcast address:
$$ \text{Last Host} = 195.167.1.255 - 1 = 195.167.1.254 $$

11. Determine Which Class the Host IP Address Belongs To

Classes of IP addresses can be identified as follows:

• Class A: $1.0.0.0$ to $126.255.255.255$
• Class B: $128.0.0.0$ to $191.255.255.255$
• Class C: $192.0.0.0$ to $223.255.255.255$

Since $195.167.1.245$ falls in the range of Class C, it belongs to Class C.