Logical conjunction – AND
In the following examples, it is possible to study the technical implementation of the conjunction of two independent variables. The dependent variable takes value true only if at the same time both the independent variables are true. The control circuit is the solution to serial connection buttons. Implementation of transistors is solved using serial connection of transistors.
Logical disjunction – OR
In the following examples, it is possible to study the technical implementation of the disjunction of two independent variables. The dependent variable takes a value of true if at least one independent variable is true. The control circuit is connected in parallel solution keys. Implementation using transistors is also dealt with parallel connection of transistors.
Logical negation – NOT
In the following examples, it is possible to study the technical implementation of the negation of one independent variable. The dependent variable takes a value of true if the independent variable is false. The control circuit is the solution involved opening contacts button. Implementation is solved using a shorting transistor voltage transistor.
Schematic symbols for logic circuits
Given that the logical operations can be implemented using different technologies are generated logic diagrams. In logic circuit diagrams schematic symbols are used. Figure 3.2 Circuit symbol to represent logical sum, which has two inputs (left) and one output. Figure 3.3 is the schematic symbol for the logical product, which has two inputs and one output. Wheel in Figure 3.4 indicates negation. The diagrams are not drawn separately, but always in input or output tag for the product or sum.
Note: In some, particularly older schemes may be signs of another shape, not a square or a rectangle. Mark for negation is the same.
Draw the logic diagram of the circuit, which is expressed by the relation:
Editing logical expressions
It is clear that each logic operation is represented by a single block in the logical schema that represents the relevant technology. The more logical blocks, the more components and the greater the probability of the failure of the control system. Reducing the number of used logic blocks is achieved by modifying and simplifying the logic functions. The simplification is performed on the basis of Boolean algebra rules, as stated in paragraph. Found source of reference. For clarity, the following example:
Example 1.1.5:
The function f (A, B, C), three logical variables is given by the following relation:
For its implementation need 14 logic blocks and the logic diagram is depicted in the following figure:
After making changes mathematical logic function is the following result:
This means that the result does not depend on the values of the logical variables B and C. The result is only negation of A. Implementation in the logical diagram in the following figure:
Comparing the two schemes, it is clear that there is a significant saving of logic blocks and thus reduces the probability of failure control system.