Combinational logic functions and Boolean algebra, logical tables, Karnaugh maps, minimization, solid execution logic and combinational logic functions
Boolean algebra

Technical elements used in the regulation and control of machines as buttons or switches. This is a two-valued element. For a mathematical description of these components was created two valued algebra, which, after its creator, British mathematician Boole, called Boolean algebra. These are the calculations with binary variables. For computations in Boolean algebra defined laws and rules as in other algebras. These are the laws and rules.

- Commutative law
- The associative law
- Distributive Law
- The rule of neutrality and aggressiveness 0 and 1
- Rule of Independence (Independence) elements
- The rule of the excluded middle
- The rule of double negation
- De Morgan's rules
- Rule of the uptake and absorption of negation

## Legislation

Basic laws of commutative, associative and distributive, which are defined for any algebra, thus Boolean (Table 2), are expressed in two forms, disjunction and conjunction. In classical algebra is about addition and subtraction. In Boolean algebra is a logical sum and logical product.

Table 2: Main rules
Property | Disjunction | Conjunction
Commutative property | A ˅ B = B ˅ A | A ˄ B = B ˄ A
Associative property | (A ˅ B) ˅ C = A ˅ (B ˅ C) | (A ˄ B) C = A ˄ (B ˄ C)
Distributive property | (A ˅ B) ˄ C = A ˄ C ˅ B ˄ C | (A ˄ B) ˅ C = (A ˅ C) (B ˄ C)

In practice, the logical functors disjunction, conjunction and negation may use other methods of marking. Sample labeling the various ways in Table 3.

Table 3: Different type designation for logical operations
A ˅ B | A + B |  | A or B
A ˄ B |  |  |
| ¬ A |  | not A

## Rules

Boolean algebra is complemented by a set of rules that are used to simplify logic functions. List of all the rules in Table 4.

Table 4: Boolean algebra rules
Rules | Addition | Multiplication
Rule of neutrality 0 and 1 | A + 0 = A |
Rule of aggressiveness 0 and 1 | A + 1 = 1 |
Rule of independence elements | A + A = A |
Rule of excluded middle |  |
De Morgan’s rule |  |
Rule of absorption |  |
Rule of absorption negation |
Rule of double negation |

### Example 4.2

Simplify the function of three variables:

First, it is done before pointing out brackets and braces is a third application of the rule of absorption of negation.

Furthermore, the rule is applied Independence elements is performed multiplication brackets and application rules exclude the third. The result is 0

This means that the function value is always zero, regardless of the combination of values of input variables, a function is called forgery.