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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: May 2015

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Present,State X = 0 - X = 1 -
- NS O/P NS O/P
A A 0 A 0
B A 1 F 1
C D 0 E 0
D A 1 G 0
E B 0 C 0
F D 0 D 0
G B 0 C 0
  • 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, C, E, F, G) (B, D)

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

  • $P_3$ = (A)(C, E, F, G) (B, D)

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

    $P_5$ = (A)(C)(E,G) (F)(B)(D)

  • 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, E = G

    Unique states are (A,B,C,D,E,F).

  • Reduced state table is:

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  • State diagram of the reduced state table is:

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