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.