Final answer:
In a network with a subnet mask of 255.255.255.240, there are (2^4) - 2, or 14, valid host addresses available. This calculation excludes the network and broadcast addresses. Option A is correct.
Step-by-step explanation:
To determine how many valid host addresses are available in the network 192.168.27.32 with a subnet mask of 255.255.255.240, we have to consider the number of bits used for the host portion in the mask. The subnet mask 255.255.255.240 corresponds to /28 in CIDR notation, meaning that 28 bits are used for the network portion, leaving 4 bits for the host portion.
Thus, the formula to calculate the number of valid host addresses is (2^number of host bits) - 2. The subtraction by 2 accounts for the network address and the broadcast address, which cannot be assigned to hosts. In this case:
Number of host bits: 4
Total number of addresses: 2^4 = 16
Valid host addresses: 16 - 2 = 14
Therefore, the correct answer is (2⁴) - 2, which equals 14 valid host addresses.
The subnet mask 255.255.255.240 means that the last 4 bits of the IP address are used to identify the host address. With 4 bits, there are 2^4 = 16 possible combinations. However, the first address in the network is reserved for the network address, and the last address is reserved for the broadcast address. Therefore, there are (2^4) - 2 = 14 valid host addresses in the network.