**So far we have seen
the definition and construction of logical systems in the form of a truth
table,**

**from which the
corresponding logical canonical expression was derived which was then minimized
through the algebra of**

**bool, karno tables or
and tabulation method of minimization. The systems built so far have**

**there was only one
output function, regardless of the number of input variables. But in many
applications we**

**we encounter problems
which have a certain number of output functions.**

**In general,
multi-output systems are based on the same single-output system concepts. Where
any**

**the output function
of the system, is treated as a single one and then all the results are
collected in a system of**

**only.**

**For example, suppose
we want to build a system with 3 inputs A, B, C and two outputs F and G. We**

# we can build two separate systems one for F output and one for G output, or we can build one

**single system by
assembling the output functions in a single logic circuit (see figure 1). The
latter**

**it is more preferable
as we can save more circuit, using the same ports**

**logical to
functions.Multi-output systems are based on the same single-output system
concepts. Where every output function**

**of the system, is
treated as a single system and then all the results are collected in a single
system. illustrated**

**minimizing
multi-output systems, through the following two examples. If we construct them
as two separate systems, then the whole circuit requires 3 logic gates for the
function.**

F and 4 logic gates for the G function, see figure 3. (a). But if we look closely at these two

**functions have a
common term. The term, A * B, is also included in function F and function G.**

**So we can build a
single system with three inputs and two outputs, which requires a total of 6
logic gates,**

**see figure 3. (b)
.The tabular method of minimization for multi-output systems is similar to the
tabular method we have**

**explained earlier,
with the only difference that the minterms / terms will be grouped together
when**

**differ by one bit and
have the same output function. We illustrate the steps of this method through**

**the following
example.First we construct the table of minterms divided by the number of ‘1’
they contain. In this table,**

a new column is added, which will show which miner the output function belongs to. As we have

**illustrated and
previously, for indifferent conditions it is assumed that the output function
has the value 1. So far we have addressed problems of logical conception of
combinatorial systems, for which the values of**

**the output depended
only on the inputs at the same time. In practice, there are systems where the
output is**

**at the same time a
function of the current and past input states.**

**During the study of
combinatorial systems, time was not introduced and was not considered**

**as a “variable” that
affects the behavior of a system. In fact a combinatorial network is defined as**

**a network whose
behavior depends only on the instantaneous values of the inputs and does not
depend on the previous string**

**of events. Quite
different happens in the other category of numerical systems. System behavior**

**sequential at a given
moment depends on both the input value at the same time and the string of**

**events that have
happened before. In this way, time appears as a “variable” of systems**

**sequentially.**

**Sequential systems
consist of a basic combinatorial system equipped with a memory unit for it**

**maintain the previous
entry states (figure 1). The output Z, is a function of the input states x and**

**previous states
(internal or secondary) y. In Table 1, a comparison of**

**combinatorial systems
with sequential systems. A sequential system is categorized into two different
types of systems:**

**Sink Synchronous
sequential systems**

**As Asynchronous
sequential systems**

**MAIN OPERATORS AND
PLATES**

**When it comes to
logic circuits (like computers), we don’t just have to**

**deal with logical
functions; but we also need some symbols of**

**special to define
these functions in a logical scheme. There are three**

**basic logical
operations, from which all functions of**

**others, however
complex. These functions are named AND, OR, and NOT. each**

**of them there is a
special symbol and a clearly defined behavior.**

**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**

**secondary vary in
fixed time intervals. The time interval is commanded by the frequency of one
hour**

outside the system. Examples of these systems are bistables. Asynchronous systems are known differently and as

**systems without
clocks, this as the change in state of the system depends only on the internal
delays of**

**system and can occur at any time**.