**From the last
lecture we have the design and construction of a synchronous sequential system,
the Diver of sequences. Usually when designing a sequential system, solving the
problem can lead to**

**the appearance of
excessive internal states. So the diagram or table of states can contain**

**more condition
than the real solution to the problem really requires.**

**The number of
internal states is a key parameter that affects performance and cost**

**of the sequential
system. As the number of states determines the amount of material (logic gates)
needed to build the system and get the desired output. In the last lecture we
showed the realism that exists between the number of bistables and states system
interiors: From the above formula we can say that r ≤ 2 ****∗ n, so if we reduce the number of
states then we also reduce the number of bistables that the system uses, which
leads us to a more simplified system. But,** **The basic blocks that form a computer (physically) are called logic
gates or only the gate. Gates are basic circuits that have at least one (and
usually several) inputs and exactly one output. The input and output values are
the logical values TRUE (1) and FALSE (0). In computer architecture it is
common**

**use 0 for false
and 1 for true. The gates have no memory. The output value depends**

**only by the actual
value of the inputs. A useful way to describe the relationship between the
input values of the ports and the output is the table of that stalkers Synchronous
sequential systems are otherwise known as systems with hours after input,
output state this does not mean that the sex system has a lower cost, as reducing
the number of states of interiors and bistables can lead to increased input and
output variables, which increases more system cost.**

**In this lecture we
will examine some methods for simplifying the excessive states it contains**

**system.Two
internal states are equivalent when they for the same input sequences have the
same**

**value of output
functions and future state. In cases where we have two in the state table**

**states which are
equivalent, they can be merged into a single state.Table 1, we see that the
internal states D and E have the same future states, state A**

**for input X = 0
and state B for input X = 1. They also have the same output, ‘0’ for input X =
0**

**and ‘1’ for input
X = 1. Then, we can say that these two states are equivalent in order**

**straight and they
can be simplified to a single state, state D. We see that we no longer have**

**condition that can
be simplified.**

**We reconstruct once
again the table of states but already without the state E which has been
replaced by condition D (table 2) and then reconstruct the diagram of
simplified statesThe example given above, showed how we can simplify two
equivalent states. Usually equivalence cannot be easily found. Definition given
that two internal states are equivalent when they for the same input sequences
have the same value of output functions and future condition, not always is
easily evident from the analysis of the table of conditions. From this arises a
necessary but not sufficient condition: that two states may be when the values
of the output function are the same regardless of future states, but provided
that the states the future to be equivalent. This condition is based on the
transient property: If state A is equivalent to state B and state B is
equivalent to state C, then state A is equivalent to state C. From Table 3, we
see that states B and C are equivalent, as for both the next state is found.**

**is H and the
output ‘0’ for the input X = 0 and the next state is E and the output ‘0’ for
the input X = 1;**

**so B ≡ C. Also,
state I is equivalent to state J, as the next state is**

**A as for input X =
0 (output is ‘0’) and for input X = 1 (output is ‘1’), so I ≡ J.**

**If we look closely
at the other states in Table 3, we see that the state G for the input X = 0**

**has as its future
state the state J (which is equivalent to state I) and for the input X = 1**

**the next state is
state C (which is equivalent to state B). While condition H for**

**the input X = 0
has as its future state state I (which is equivalent to state J) and for**

**input X = 1 the
next state is state B (which is equivalent to state C). Starting and**

**from the transient
property, we can say that the state G is equivalent to the state H, i.e.: G ≡
H.The table method of simplifying the internal states of a sequential system is
based on a**

**the algorithm that two states can merge (combine) with each other if it is shown to exist**

#### a transient property of equivalence between them. As mentioned above, two conditions

**are equivalent if
for each input they give the same output and go to state**

**same or equivalent
futures between them.**

**To explain the tabular method we will rely on the table of the following states.**