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

By Tertulien Ndjountche

Трёхтомный курс по цифровой электронике от издательства Wiley. В первых двух томах рассматриваются логические схемы, в третьем - конечные автоматы electronic Electronics, quantity 1: Combinational common sense 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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Extra resources for Digital Electronics, Volume 3: Finite-state Machines

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31] As P4 is identical to P3 , it follows that the states S1 and S2 , which are in the same block, are equivalent. 47 lists out the different steps to be followed in order to determine the equivalent states. 48. 3. 49, where X and Y represent the inputs. 47. 50 summarizes the different steps to be followed in order to determine the equivalent states. From the last partition, P2 , it can be deduced that the states S0 and S3 are equivalent, (S0 ≡ S3 ), as are the states S1 and S4 (S1 ≡ S4 ), and the states S2 , S5 and S7 (S2 ≡ S5 ≡ S7 ).

A choice of maximal compatibility classes that covers all the states of the state machine consists of (ABCD) and (EF ). However, the closure conditions are not satisﬁed as the set (ABCD) implies (CF ) for XY = 01 and (BE) for XY = 10. 41, we can identify the closed cover that consists of the pairs of states (AB), (CD) and (EF ). 66 presents the reduced state table, obtained by assuming that S0 = (AB), S1 = (CD) and S2 = (EF ). – We can also determine the pairs of compatible or incompatible states by making use of the concept of compatibility in the construction of an implication table.

21. 14. 15. – By choosing a code to represent the states of a machine, a tradeoff is made between the size and electrical performance (power consumption, response time) of the circuit. 16. Gray code is used when the states are decoded asynchronously. For instance, if a machine must proceed from 01 to 10, as is the case with natural binary code, and the ﬂip-ﬂops do not switch exactly at the same instant, transient states may appear, taking the form of 11 or 00. This can affect the normal operation of the state machine.