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14.3 FUNCTIONAL RELATIONSHIPS AND THE STABILITY CRITERIA 687

The model of Fig. 14.2 is the most degenerate (fundamental) form of the Mealy model
depicted in Fig. 10.5. This model can be broken down into the more rudimentary forms
similar in appearance to those in the development of the basic model in Fig. 10.3 or to the
Moore model in Fig. 10.4, but always with a memory stage composed of fictitious LPD
memory elements. Regarding the memory stage, it will be recalled that the memory for
the basic model in Fig. 10.3(c) is interpreted as basic cells in Fig. 10.22 or as a flip-flop in
the case of Fig. 10.36. In fact, the more general models given in Figs. 13.1 and 13.47 can
be used in synchronous systems where the memory is interpreted as discrete flip-flops, or
flip-flops in a register or counter. Now, the reader should consider that memory in all these
models can be interpreted as any one of the following forms given in the order of increasing
degeneracy:

{Flip-flops -> BasicCells -> LPD Memory Elements}

Thus, if the memory is composed of flip-flops and clocked, the FSM is called synchronous.
But if the more degenerate forms are used for the memory (e.g., basic cells or LPD memory
elements) the FSM becomes asynchronous. In this text, the nested cell model is character-
ized by the use of basic cells as the memory elements, while the LPD model is characterized
by the use of fictitious LPD memory elements.

1 4.3 FUNCTIONAL RELATIONSHIPS AND THE STABILITY CRITERIA

The parameters used in Fig. 14.2 are defined by

jc, = jc n _i , ...X2,x\,X Q = Input State (IP)
Y k = 7 m_! , . . . Y 2, Yi,Y 0 = Next State (NS)
(14.1)
yj = y m-i, ...yi,yi,yo = Present State (PS)
Z/ = Z r-i, . . . Z 2, Zj , Z 0 = Output State (OP),

all of which have been arranged in positionally weighted form to represent binary words.
These parameters are functionally related to each other and to the inputs and outputs by the
following set of logic equations written in subscript notation:

(14.2)

or simply

7 = /(IP, PS)

Z = /'(IP, PS).