In Section 6.2 we stated that trying all possible state assignments in order to find the best one is impractical. Determine the number of possible state assignments for an FSM that has n states and for which k = log₂n state variables are used.

Data From Section 6.2

Having introduced the basic concepts involved in the design of sequential circuits, we should  revisit some details where alternative choices are possible. In Section 6.1.6 we suggested  that some state assignments may be better than others. To illustrate this we can reconsider  the example in Figure 6.4. We already know that the state assignment in Figure 6.6 leads  to a simple-looking circuit in Figure 6.8. But can the FSM of Figure 6.4 be implemented  with an even simpler circuit by using a different state assignment?Figure 6.16 gives one possible alternative. In this case we represent the states A, B,  and C with the valuations y₂y₁ = 00, 01, and 11, respectively. The remaining valuation, y₂y₁ = 10, is not needed, and we will treat it as a don’t-care condition. 

 

W Clock D D D Y Y O Q 10 Q D Q 10 MI 32 31 Y1 D E Rlin R3 out Done Rout R2 in R2 out R3 in