Microsoft Word - Digital Logic Design v_4_6a

5.4. Inspection Design Methods for Finite State Machines

The classical design methods are limited to a small number of inputs, states and outputs since the K-
maps required become too difficult to draw and work with.

The Inspection Design Method provides ways to write the excitation equation for flip-flops by inspection
from a timing diagram, a state diagram, or ASM chart of a synchronous Finite State Machine. By
observing or inspecting the present state (PS) and next state (NS) for each state variable, the D, T and J-
K excitation equations can be written.

The equations derived using inspections are not typically minimum equations. There are two inspection
methods:
 Set-Hold 1 Method
or
 Clear-Hold 0 Method

 Set - Hold 1 Method for obtaining D excitation-input equations
We use the following table to write D excitation equations directly from a state diagram, ASM chart or
timing diagram.

Present State

(PS/NS)

Yi Yi+

Di

Comment

User for 1s

(Set-Hold 1)

Use for 0s

(Clear-Hold 0)

0 0

0 1

1 0

1 1

0

1

0

1

Hold 0 transition

Set transition

Clear transition

Hold 1 transition

Di

Di

Di’

Di’

 The “Set-Hold 1 Method” can be used to obtain the D excitation equations for the 1s of each

state variable (flip-flop outputs)

Di = ∑ (PS .external input conditions for set) + ∑ (PS .external input conditions for hold 1)

for i=1, 2, 3...

Note: This method solves for the 1’s of the function.

 We could also apply the “Clear-Hold 0 Method” to obtain the D excitation equations for the 0s

of each state variable (flip-flop outputs)

Di’ = ∑ (PS .external input conditions for clear) + ∑ (PS .external input conditions for hold 0)

for i=1,2,3,...

Note: This method solves for the 0’s of the function and it is equivalent to the first method.

For both of the methods, if we have not completely specified FSM meaning and some state

values are don’t care, enter them as such so that we can use them in later reduction processes.

 Example - Obtaining the D excitation-input equations from a state diagram

Obtain the excitation equations for the following state diagram of a mixed (Mealy-Moore)

machine.

State  Y1Y2

Input  STOP