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

Marks: 10M

Year: May 2015

• 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:

• State diagram of the reduced state table is: