The current method for maintaining the water level in a swimming pool is to connect a float to a valve. If the float is below a certain level, then the valve opens and water flows into the pool. Our company has won a contract to create an electronic pool filler that has two speeds. This specification details the requirements for the controller circuit. There are two inputs and two outputs: Inputs: L: $1$ means the pool level is low and should fill slowly; $0$ means pool level is normal V: $1$ means the pool level is very low and should fill quickly; $0$ means fast fill is not needed Outputs: R: $0$ means slow fill valve should be off; $1$ means the slow fill valve should allow water flow F: $0$ means fast fill valve should be off; $1$ means the fast fill valve should allow water flow There are rules that must be followed: $1.$ F may be asserted for no more than $2$ clocks and may not assert again until V$=0$ for at least one clock. $2.$ The design must have a minimum of $5$ states. There are some items that are not specified. For example, what should be done if both L and V are $1?$ Can V be asserted for less than $2$ clocks? What if V is asserted for more than $2$ clocks? During which states can V and F assert or negate? Come up with $3$ different ideas on how you$$d like to design the system.