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Identify indistinguishable state in following state table and obtain minimized state diagram

Mumbai University > ELECTRO > Sem 3 > Digital Circuits and Designs

Marks: 10M

Year: Dec 2014

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• Equivalent states are identified and merged to reduce the number of states by using the method of partitioning.

• First partition consists of all the states. $P_1$ = (A, B, C, D, E, F, G)

• Second partition is done by observing outputs for each state and separating dissimilar output states. $P_2$ = (A, B, D) (C, E, F, G)

• All the further partitions are done by separating states on the basis of their respective next states.

• $P_3$ = (A, B, D) (C, E, G) (F)

$P_4$ = (A, D) (B) (C, E, G) (F)

No further partitions are possible.

• The states in the same partition are indistinguishable. These redundant states can be merged to reduce the number of states. Thus, A = D, and C = E = G

Unique states are (A, B, C, F)

• Reduced state table is:

• State diagram of the reduced state table is: