A network administrator is adding a new LAN to a branch office. The new LAN must support 200 connected devices. What is the smallest network mask that the network administrator can use for the new network?

To determine the smallest network mask that can support 200 connected devices, you need to calculate the subnet size that can accommodate at least 200 host addresses.

Here’s how to determine the required subnet size:

1. Each subnet has two addresses that cannot be used for hosts: the network address and the broadcast address.
2. The remaining number of addresses must be equal to or greater than the number of required hosts (200 in this case).

The formula to calculate the number of usable host addresses in a subnet is 2(32−�)−22(32−n)−2, where $n$ is the number of bits used for the network portion of the address (the subnet mask).

You will need to find the smallest subnet mask that provides at least 202 addresses (200 for the devices, plus 2 for the network and broadcast addresses).

• A /27 subnet mask (255.255.255.224) provides 2(32−27)−2=302(32−27)−2=30 usable host addresses, which is not enough.
• A /28 subnet mask (255.255.255.240) provides 2(32−28)−2=142(32−28)−2=14 usable host addresses, which is also not enough.
• A /26 subnet mask (255.255.255.192) provides 2(32−26)−2=622(32−26)−2=62 usable host addresses, which is still not enough.
• A /24 subnet mask (255.255.255.0) provides 2(32−24)−2=2542(32−24)−2=254 usable host addresses, which is sufficient for 200 devices.

Therefore, the smallest subnet mask that the network administrator can use for the new LAN to support 200 connected devices is 255.255.255.0.