Address Resolution with closed form computation: As all we know that many network technologies use static physical addresses, some technologies use configurable addressing in which a network interface can be assigned a specific hardware address. For such type of networks it is possible that we can choose addresses that make closed form address resolution possible.A resolver that uses a closed form method computes a mathematical function that maps an IP address to its equivalent hardware address. If the relationship between the IP address and its coprresponding hardware address is straightforward, the computation requires only a few arithmetic operations.Infact,the host portion of a computer’s IP address can be chosen such that it is identical to the computer’s hardware address.
Let’s understand this situation with the help of a example, suppose a configurable network has been assigned the network address 220.123.152.xxx and its suffix ranging from 0-24. As computers are added to the network, each computer is assigned an IP address from this range and a matching hardware address.The first host is assigned an IP address 18.104.22.168 and hardware address 1. The second host is assigned an IP address 22.214.171.124 and hardware address 2. The suffixes need not be sequential, if a router attached to a network assigned IP address126.96.36.199,then the router is assigned an IP address of 121.Given the IP address of any computer on the network, the computer’s hardware address can be computed by a single Boolean ‘and’ operation.
Hardware Address=IP Address & 0xff
As I think it is clear from the example that why closed form resolution is often used with configurable networks.