Final answer:
To create 256 subnets on a Class B network, you need to use a subnet mask of 255.255.255.0, also referred to as /24 in CIDR notation. This involves borrowing 8 bits from the host part of the address to add to the network prefix for a total of 24 bits.
Step-by-step explanation:
To create 256 subnets on a Class B network, you would need to use a subnet mask that provides enough bits to accommodate the number of desired subnets. A Class B network has a default subnet mask of 255.255.0.0, which provides for no subnets with the standard 16-bit network prefix. To create additional subnets, we must extend this prefix by borrowing bits from the host part of the address.
To figure out how many bits we need to borrow, we can use the formula 2^n where n is the number of bits borrowed, and the result is the number of subnets. For 256 subnets, we would solve 2^n = 256 which gives us n = 8 because 2^8 = 256. Borrowing 8 bits for subnetting from the host part of the Class B address means that the subnet mask would be extended by 8 bits beyond the default 16 bits, for a total of 24 bits for the network prefix.
Therefore, the subnet mask for creating 256 subnets in a Class B network is 255.255.255.0, which is often represented in CIDR notation as /24.