Carno Table

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


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


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


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


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.

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Thu Apr 9 , 2020
We explained above that the output of sequential logic systems depends on the input of the system and the state of his previous. So, these systems need to use a memory element for it maintaining the previous state of the system, bistables are used for this purpose. A bistable can […]

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