Final answer:
The default subnet mask for a network requiring 100 usable hosts is 255.255.255.128. This calculation is based on the formula for determining usable hosts in a subnet, accounting for the network and broadcast addresses.
Step-by-step explanation:
When calculating the default subnet mask for a given number of usable hosts, in this case, 100, we need to determine the appropriate subnet mask that allows at least that many hosts on a single network. The formula to calculate the number of usable hosts for a given subnet mask is 2(32 - CIDR notation bits) - 2 = number of usable hosts. This accounts for the network and broadcast addresses that are not used for host assignments.
To find the smallest subnet which supports 100 hosts, we need to find the smallest power of 2 which is greater than or equal to 102 (100 hosts plus 2 for network and broadcast addresses). The smallest power of 2 that meets this requirement is 128 (27). Therefore, we need 7 bits for host addresses, leaving us with 32 - 7 = 25 bits for network addressing, which corresponds to a subnet mask of 255.255.255.128.