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 subnet mask needed for a network with 40 devices, you need to calculate the subnet size that can accommodate at least 40 hosts. Remember that in a subnet, two IP addresses are reserved: one for the network address and one for the broadcast address. So, you need a subnet with at least 42 addresses.

Here’s how the subnet masks correspond to the number of addresses they provide:

• 255.255.255.224 – This is a /27 subnet mask, which provides 32 addresses (30 usable for hosts).
• 255.255.255.240 – This is a /28 subnet mask, which provides 16 addresses (14 usable for hosts).
• 255.255.255.192 – This is a /26 subnet mask, which provides 64 addresses (62 usable for hosts).
• 255.255.255.128 – This is a /25 subnet mask, which provides 128 addresses (126 usable for hosts).
• 255.255.255.0 – This is a /24 subnet mask, which provides 256 addresses (254 usable for hosts).

The smallest subnet mask that can accommodate at least 42 addresses is 255.255.255.192, which is a /26 subnet mask. This will allow for 62 usable IP addresses, which is more than enough for 40 devices without wasting too much address space.