Final answer:
The default subnet mask for a network that requires 100 usable hosts is 255.255.255.128, which provides enough IP addresses for the hosts by using 25 bits for the network address and 7 bits for host addresses.
Step-by-step explanation:
To calculate the default subnet mask for a network that requires 100 usable hosts, you need to consider the number of bits necessary to support at least 100 hosts. Every device on the network requires a unique IP address, and the subnet mask dictates how many addresses are available within a subnet.
A traditional IPv4 address consists of 32 bits, grouped into four octets (e.g., 192.168.1.0). A subnet mask is used to divide the IP address into network and host portions. The formula to calculate the number of hosts is 2n - 2, where n is the number of bits available for hosts after the network portion of the mask is defined.
Given that we need 100 usable hosts, we need to solve for n in the equation 2n >= 102 (100 for the hosts plus 2 for the network and broadcast addresses which are not usable for hosts). Solving the equation gives us n >= 7, but since 27 is 128 and we need at least 102 addresses, we will use 7 bits for the host addresses. Therefore, we would use 25 bits for the network address (32 - 7 = 25). The subnet mask for 25 bits is 255.255.255.128.