Going beyond the fundamental mode of operation

• SIC and MIC with the fundamental mode of operation are restrictive
• Burst mode allows inputs to change in any order and over any span of time
• In the graph representation of the FSM, arcs are labelled with the input bursts (and corresponding output bursts)
• Note, that unlike synchronous m/c, asynchronous m/c change state immediately after the state transition condition is satisfied
• Therefore, these are better modelled as Moore m/cs
• Every input burst must be non-empty
• If no inputs change, the system is stable
• No input burst in a given state can be a subset of another, since otherwise the behavior may be ambiguous (maximal set property)

A sample specification follows; also a few observations are in order

• The edge label: a+b+/x+y+ means the input burst a+b+ (+ve pulses on a and b) results in the output burst x+y+ (+ve pulses on x and y)
• Of course for a +ve pulses to come on a, it must have been at a low value
• So, on any traversable trace, the +ve and -ve pulses on any variable (input or output) must be in strict alternation -- otherwise it won't be traversable
• Thus, on any closed traversable trace the sum total of the alternations must be zero -- otherwise it won't be traversable
• The original flow graph has been modified to indicate the maximal conditions on the input states that must be checked to trigger transitions; 11(0) indicates +ve pulses for a and b while c=0
• The complete outputs are also shown

• The given m/c must be transformed to a Moore m/c to produce the outputs in stable states
• Evidently states C and E can be merged (all other states have incompatible outputs)
• The modified flow table is shown below
• Note that the loop CE → D → CE is not traversable more than once
• However, the trace A → B → CE → D → CE → A is traversable

• Next, state assignment through hypercube embedding needs to be done
• Resulting m/c is shown below

Questions

• The initial state of the m/c is not indicated
• Which state may not be designated as the initial state?
• What must be done to designate A (say) as the initial state?
• What would be the hypercube embedding if states C and E had not been merged?

Exercises

• For the given FSM construct the next state function
• Obtain a hazard free realisation for the next state function
• Based on the discussion above, present a non-deterministic algorithm for state assignment for burst mode design with the provision for state minimisation