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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

1 Answer
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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:

enter image description here

  • State diagram of the reduced state table is:

enter image description here

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