What subnet mask is needed if an IPv4 network has 40 devices that need IP addresses and address space is not to be wasted?

To determine the correct subnet mask for a network with 40 devices, the necessary subnetting needs to accommodate at least that many usable IP addresses. The subnet mask defines how many bits are used for the network portion and how many bits are designated for host addresses.

A subnet mask of 255.255.255.192 provides a total of 64 addresses (2^6 = 64, since the last 6 bits are for host addresses). However, this includes network and broadcast addresses, which cannot be assigned to devices. Thus, with 64 total addresses, there are 62 usable addresses (64 - 2 = 62), adequately covering the requirement for 40 devices without wasting address space.

In contrast, the other subnet masks provided would allow either too few usable addresses or would represent an unnecessary allocation of IP space:

• A mask of 255.255.255.128 only supports 126 total addresses, hence 124 usable addresses, but for a smaller number of hosts, it includes too much space.

• A mask of 255.255.255.224 would provide only 30 usable addresses (32 total - 2), which is insufficient for 40 devices.

• A mask of 255.255.255