Download PDF by Tertulien Ndjountche: Digital Electronics, Volume 3: Finite-state Machines

By Tertulien Ndjountche

ISBN-10: 1848219865

ISBN-13: 9781848219861

Трёхтомный курс по цифровой электронике от издательства Wiley. В первых двух томах рассматриваются логические схемы, в третьем - конечные автоматы electronic Electronics, quantity 1: Combinational good judgment Circuits (1848219849 electronic Electronics, quantity 2: Sequential and mathematics good judgment Circuits (1848219857) electronic Electronics, quantity three: Finite-state Machines (1848219865)

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Additional resources for Digital Electronics, Volume 3: Finite-state Machines

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A compatibility class is said to be maximal if it is strictly not a subclass of another compatibility class. A set of compatibility classes forms a cover of the state machine if each of the states of this machine belongs to at least one of these compatibility classes. A set of compatibility classes is said to be closed and constitutes a closed cover if any compatibility class implied by one of the compatibility classes of this set is also contained in this set. 52, the pairs of states, (S0 , S1 ) and (S1 , S2 ), are compatible.

As there are no more marking possibilities, the states S0 , S4 and S6 are equivalent: (S0 ≡ S4 ≡ S6 ), as are the states S3 and S5 (S3 ≡ S5 ). 42. 42. 2. Partitioning method The partitioning method is used to determine the equivalent states of a finite state machine and can also be considered as an approach to reduce the number of states. It consists of successively forming partitions, Pk , k = 1, 2, 3, · · · , which are composed of a certain number of blocks that group one or more states. The PSs are placed in the same partition block P1 if and only if the corresponding outputs of the state machine are identical for each input combination.

It thus appears that the block grouping the states S0 , S2 , S4 and S6 must be split into two. Starting from the states S3 and S5 , the state machine proceeds to the states S0 and S6 , when X = 0, or S1 and S1 , when X = 1. The states S0 and S6 are in the same block of the partition P2 , and the state S1 is the only element in one of the blocks of P2 . 26] As P4 is identical to P3 , it follows that the states in each block are equivalent: S0 ≡ S4 ≡ S6 and S3 ≡ S5 . 44 lists the different steps to follow in order to determine the equivalent states.

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Digital Electronics, Volume 3: Finite-state Machines by Tertulien Ndjountche


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