Combinational logic functions and Boolean algebra, logical tables, Karnaugh maps, minimization, solid execution logic and combinational logic functions
The time sequence of logic signals

In the previous section the logic circuits were designed as a static, solution was made without the influence of time that is the search for all combinations. In real life, it is necessary to keep in mind that depending on the time will change the values of the independent variables. It follows it may be the value of the dependent variable change with time as shown in the example. Simultaneously, over time, may but not occur all combinations of the independent variables.

### Example 4.4

For the expression find time course of output logic values.

The time course of independent variables is shown in the graph. Examples of this type has two possible solutions.

a) Solution the first way consists in creating truth table for all combinations of independent variables. The table and the appropriate combination of independent variables in the interval search result value logic functions.

A | B | C | Y
0 | 0 | 0 | 0
0 | 0 | 1 | 0
0 | 1 | 0 | 0
0 | 1 | 1 | 1
1 | 0 | 0 | 0
1 | 0 | 1 | 1
1 | 1 | 0 | 1
1 | 1 | 1 | 1

b) In the second method the solution you need to realize that the logical function is the disjunction of three conjunctions. In solving with the proceeds of conjunctions. The first conjunction says that the result takes the value 1 if at the same time both the independent variable equal to 1. In the graph are searched those time intervals in which A and C are equal to 1 at the same time and in these intervals is Y = 1. This method is used for other conjunctions. In conclusion, some of the time intervals remain unfilled, those must be assigned a value of 0.

## Implementation of logic function

In the field of automation technology the machine control or files subject to the gradual fulfillment of specified conditions. Any condition can be expressed as a logical variable, because it can also, as a logical variable, assigning two values – "passed" or "failed". Therefore simple feasibility logic variables and thus logic functions. The logic of this problem is the best approach for example.

### Example 4.5

There is one logical independent variable "X". This variable can take two values 1 and 0. The second logical dependent variable "Y" is the result of a logical function:

All options, which can assume the dependent variable Y are described in the table.

X | Y1 | Y2 | Y3 | Y4
1 | 0 | 0 | 1 | 1
0 | 0 | 1 | 0 | 1

It is clear that there are four options, that means four logical functions; forgery, negation, and equivalence verum. Their practical implementation will be presented in the following simple electrical circuit, composed of the power supply, buttons, bulbs and wires. Independent variable X is the mechanical force applied to the button, the dependent variable is the bulb glow. First logical function Y3. When the button is pressed, light bulb, the value of Y = 1 if and only if X = 1.

Fig. 4.1: Logical function Y3

Logic function Y2. When the button is pressed, the lamp is dark, the value of Y = 1 if and only if X = 0

Fig. 4.2: Logical function Y2

Logical Y4. It does not matter if the button is pressed or not, the bulb lights up every value Y = 1 and is not dependent on X.

Fig. 4.3: Logical function Y4

Logic function Y1. It does not matter if the button is pressed or not, the bulb does not light, the value Y = 0 and does not depend on X.

Fig. 4.4: Logical function Y1