Download e-book for kindle: Digital Electronics, Volume 3: Finite-state Machines by Tertulien Ndjountche

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 common sense Circuits (1848219857) electronic Electronics, quantity three: Finite-state Machines (1848219865)

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

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For the pair of states, S0 and S1 , the outputs are different when X = 1. Thus, states S0 and S1 are not equivalent and a cross cannot be inserted in the cell (0, 1). By examining the pair of states, S0 and S2 , we can see that the outputs are identical and that the NSs are S3 32 Digital Electronics 3 and S1 , regardless of the value of X. The cell (0, 2) now contains the pair of states, S3 and S1 . A cross can also be inserted in cells (0, 3), (1, 2) and (2, 3) because the outputs are different in each of these cases when X = 1.

60. 58. 59. 60. Reduced state table In order to simplify incompletely specified machines, the concept of compatibility is used instead of the concept of equivalence. Two states that are equivalent to a third state are also equivalent to one another. However, two states that are compatible with a third state are not necessarily compatible with each other. As a result of this difference, the simplification of incompletely specified machines can appear to be complicated and, in general, does not yield a unique solution.

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. For other partitions, Pk , k = 2, 3, · · · , the PSs are placed in the same block if and only if the NSs of the state machine for each input combination are in the same block of the partition, Pk−1 .

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

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