# A logic system will be called a combinator if the output or output depends

only from the current state of the inputs. So far we have studied the solution

electronic of uncomplicated problems following the steps of

following:

1. Problem analysis (determining the amount of inputs and outputs)

2. Build the truth table

3. Determination of the logical function in the canonical form SOP or POS

4. Simplify the logical function using Bool postulates

5. Construction of the combinatorial logic circuit diagram

## Simplifying the logical function using Bool postulates is one

easy solution to use when dealing with low complexity of

problem. At the moment that the logic circuit for one must be implemented

more complex problem, which results in a more algebraic function

expression, the use of Bool postulates is very difficult to do

simplification and requires a lot of time and concentration.

In addition to the algebraic way of simplifying logical expressions there are

also some other simpler methods which we will see in the following. The Karno map, otherwise known as the Venn diagram or the K map, is

a two-dimensional form of the truth table, drawn in order

such that the simplification of the final logical function can be seen immediately by

### location of units on the map. The map is a diagram consisting of

small squares, where each square represents a combination from the table of

authenticity. Since any logical function can be expressed as many products (many minterms), then the function can be expressed

graphically on the map marked with 1 in the squares representing the minterms

on the map.

To construct the logic circuit of a combinatorial system by means of the method

that map Karno, follow the steps below:

#### 1. Problem analysis (determining the amount of inputs and outputs)

2. Build the truth table

3. Build the appropriate carno map and if we want to use a lot

products, placed 1 in each box that represents the minterm where the output

is 1, or set to 0 if we want to use the product of sums

4. Group the 1-shat on the map using the following rules:

a. Groups can contain one, two units, four units,

eight units (generally the number of units in a group is e

equal to a double power)

#### b. The group contains one-sha that are neighboring boxes (two boxes will be called

neighbors only if the minterms they represent differ from alone

a bit)

c. Groups are built in such a way as to form as few groups as possible

with as many units as possible

5. Simplified logical function is extracted

6. Construct the logic circuit diagram. For the Karno map with three input variables:

#### • The one-unit group gives a logical expression with three variables

• The two-unit group gives a logical expression with two variables

• The group of four units gives a logical expression with a variable

For the Karno map with four input variables:

• The one-unit group gives a logical expression with four variables

• The two-unit group gives a logical expression with three variables

• The group of four units gives a logical expression with two variables

• The group of eight units gives a logical expression with a variable

d. Karno map with five variables

#### A carno table with 5 variables will have 25 = 32 combinations. It is not a table

below is given the truth table with 5 variables and the values of

possible minterms and maxterms. For problems that contain a large number of input variables the Karno method is difficult to

its use. Table Minimization Method, also known as Quine Method

McCluskey, is widely used when we have a large number of input variables, for example 6

This constantly requires that

complex logical expressions are reduced to simpler expressions which

produce the same results in all possible conditions. The expression with e

#### simply then it can be applied with a smaller and simpler circuit, which

on the other hand it saves the price of unnecessary gates, reduces the number of gates

necessary and reduces the power and amount of space required by those gates.

Simple circuits are cheaper to produce, consume less energy and

work faster than complex circuits.

#### input variable. The advantage of this method lies in the fact that it does not try to detect

optimal groupings of minterms, but acts directly on them by identifying the implicants of

first.

The basic idea of this method is to compare the minterms with each other, as well as the logical products that

flow from them by checking if the property of the bullet is applied:

ab + ab̅ = a

We apply this comparison of minterms and the application of the above property cyclically until

to no longer have simplifications to realize. At the end of this process, everyone is identified

the first implicates of the function.