Created it, 06/09/09
Update it, 06/09/16
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In this theory, we will examine the sequential systems which are at the base of the circuits used in the automatisms and the computers.
1. - INTRODUCTION TO THE SEQUENTIAL SYSTEMS
1. 1. - SEQUENTIAL SYSTEMS
The logical circuits examined until now have the property to provide in exit and to a given moment, of the logical values which depend only on the combination of the logical values applied to this same moment at the entries (by naturally neglecting the delays which had at the travel times).
For this reason, these circuits are called combinative because their output east function of the combination of the logical states applied to their entries.
In addition to the circuits considering previously, there is the different one which have faculty to memorize the signals. Their exit is then a function not only of the instantaneous combination of the input signals, but also, because of their property of memory, of the combinations of the logical signals applied before to their entries.
These circuits in which the exit depends on the former logical states of the entries are usually called sequential circuits.
1. 2. - SYNCHRONOUS SYSTEMS
A sequential system is known as synchronous when the change of state of the exits is controlled in time or is synchronized. It can be it by the entries themselves or a signal single and common to all the assembly. This particular signal is called clock. We will reconsider later on the concept of clock.
1. 3. - ASYNCHRONOUS SYSTEMS
A system is known as asynchronous when the change of state of the exits is controlled by no particular entry contrary to a synchronous circuit.
1. 4. - CONCEPTS OF “TIMING” OR CHRONOGRAM
In order to obtain a representation of the evolution of the signals generated by a system and to compare them, one uses graphs in which the horizontal axis or x-axis is graduated according to the time expressed in milliseconds (thousandths of second) or in microseconds (millionth of second) for example.
The vertical axis or y-axis is graduated in levels of tension varying between the high level and the bottom grade (H and L).
Figure 1 represents the simplified “timing” of a bistable rocker which we will examine further.
The signals obtained in this figure being regular and periodic, one can define for each signal the period (or time) separating two successive impulses.
1. 5. - LEVELS AND FACES
The concept of levels is from now on familiar for us, we know two types : the bottom grade and the high level which are materialized by horizontal segments of right-hand sides on the chronogram.
We will call face, the passage of a level to another; it will be materialized on the chronogram by a segment of right-hand side vertical or at least very tilted, bus in reality the time of passage from one level to another is not null and can vary, according to the systems, of a few tens of milliseconds to some tenth of nanoseconds (1 nanosecond = 10-9 second).
There are rising faces, red arrow of the “timing” of figure 1, and downward faces green arrow on the same figure.
1. 6. - STATES ASSOCIATED WITH THE CONCEPT OF MEMORY
1. 6. 1. - RELAY OR MEMORY
Although this device is hardly any more used in the modern systems taking into account its consumption, its high response time and its obstruction prohibitory, this one has the advantage of being simple. Moreover, its mechanical operation is easily displayable from where its teaching interest.
A relay consists of a metal reinforcement and an electromagnet as represented figure 2.
When the reel of this electromagnet is fed, the reinforcement is attracted and comes by means of a scale or fixes insulating to close normally-open contacts or to open normally-closed contacts (on figure 2, it is about a normally-open contact).
The displacement of the reinforcement is not instantaneous, also closing or the opening of a contact is carried out it with a certain delay q compared to the establishment of current I traversing the reel (figure 3).
This system allows a rétrocouplage: the reel of the relay commonly called X (capital letter indicating that it is about a variable of exit) is a variable of exit generating a new variable of dependant entry : x, consisted one of the contacts of this same relay.
The chart of a relay adopted in this lesson is that of figure 4.
1. 6. 2. - STABLE STATES
One calls stable states the states during which the reel of a relay X, or excitation, is in the same state as its contact X, or transfer.
By convention, the number indicating a stable state is always surrounded by a circle.
Example: X
= 0 x = 0
stable state rest 
X = 1 x
= 1 stable state work
1. 6. 3. - TRANSITORY OR UNSTABLE STATES
In the two preceding states, there was identity between the excitation and the transfer. However, the delay of x conditions intermediate or transitory states for which excitation and transfer are in complementary states.
Example :
Transitory state 2 (by convention not to ring the number), we have :
X = 1 and x = 0.
The transfer is not instantaneous.
Transitory state 1 : we have X = 0 and x = 1
Note :
For a transitory state, the transfer is late on the excitation.
Regulate :
a) For a stable state, the reel of the relay and its contact of transfer are in the same state.
b) For a transitory state, the contact of store transfer the state which it had preceding in the stable state the transition.
The reel of the relay takes the binary value of the stable state to which the transitory state evolves.
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