In
this article we will explain how a basic sequential circuit works and
how its output is dependent on the previous inputs.Consider
the figure below
In
the figure we have two NOR gate connected such that the output of one
NOR gate becomes one of the input of the other gate. The two inputs R
and S are the primary inputs and can be changed when we need. But
this circuit shown above is not a practical one because it has no
delay. In real world every nor gate will be associated with some
delay . The diagram along with delay is shown in figure below.
Here
the two gates have a delay of “d”. Their outputs x and y becomes
X and Y after a delay of d. By the examination of equivalent circuit
we found that the output x and y follow changes in input R,S,X and Y
instantaneously. From this observation we write the combinatorial
relationships as
X
and Y are nothing but x and y delayed for some time. So we can write
X(t)
=x(t-d) Y(t) =y(t-d)
We
can represent x and y (eq.1) in K-maps as shown below.
For
simplicity we combine the two k-map into one as shown below.
With
K-map we cannot find the sequence of events ,but we can find out the
state of the circuit at a particular time using K-Map. Ie we can
determine what happens after a time delay d just by saying X becomes
x and Y becomes y after a time delay d.
The
circuit is stable when x= X and y=Y. In all other cases the circuit
is unstable and further changes must be take place to make the
circuit stable . In a K- map stable states can be identified by
comparing the XY values of each row and the entries of xy in the same
row.
Sequence of
events or cycles by which the sequential switching circuit come to a stable state.
Consider
that the circuit is in a unstable condition where RS= 10 and XY =11
(4th column 3rd row). We can see that the value
of xy at this position 00 and is not equal to the value of XY. But XY
assumes the value of xy(as it is given as feed back) after some time
and now becomes 00. So our point of attention moves to 4th
column 1st row . Here also its unstable since xy =01 and
is not equal to XY. So after some time XY becomes 01 and our point of
attention moves to 2nd row 1st column. Here xy
= 01 which is equal to XY . This is a stable situation.
Proving that
sequential switching circuit exhibit memory.
When
the primary input RS has value 00 it can assume two stable states
where XY=01(A) or 10 (B). But what was RS before it became 00. It
could have been 01 or 10 from which they changed one digit to become
00.
Suppose
that RS was equal to 01 and the circuit was in stable state C. We now
make S=0 making RS=00 making us move to the first column to reach the
stable state B.
Suppose
RS was equal to to 10 and the circuit was in stable state E. We now
make R=0 making RS=00 making us move to the first column to reach the
stable state A.
Thus
we clearly prove that sequential switching circuit ie it outputs
depend on previous inputs.
