There are three basic logical operations:
1) logical AND
-
Represented by AB: when both A and B are 1, their values are 1, otherwise they are zero;
2) Logical OR
-
use
A+B
Indication: when both A and B are 0, the value is 0, otherwise it is1;
3) Logical negation
-
use
"Is it up?" It means that when A=0, the negation of a is 1, and when A= 1, the negation of a is 0.
Logic algebra is an algebra that performs logic operations according to certain logic rules, and it is a mathematical tool for analyzing digital circuits. Corresponding to the three basic logical relations of logical AND, logical OR and logical NOT, logical algebra has three basic logical operations: logical multiplication, logical addition and logical NOT.
1. What are the characteristics of logical variables?
Variables in logical algebra, including independent variables (antecedents) and dependent variables (consequences), have only two values: "1" and "0". In logical algebra, "1" and "0" do not represent specific quantities, but only represent logical states. For example, the level of potential, the presence or absence of signals, the on-off of circuits, the on-off of switches, the off-off of transistors and so on.
Second, logical multiplication.
The logical operation that reflects the logic sum relation is called logical multiplication, which indicates its logical function.
The type is:
Y=AB (abbreviated as: y = ab)
Where a and b are input variables and y is output variable. ...
Represents a logical multiplication operation.
1. The significance of logical multiplication
The meaning of logical multiplication is: when both A and B are "1", Y is "1"; A
As long as one of B and B is "0", Y must be "0".
For example, the two switches mentioned in the previous section are connected in series to control the electric lamp circuit (see Figure 2-2). If the switch is closed to "1", the electric lamp is turned on to "1" and not turned on to "0", obviously only when A(S 1),
=
1 and B(S2)
=
When 1, there is Y(EL).
=
1; As long as one of a and b is 0, Y(EL)
=
0。 Therefore, the operation rules of logical multiplication are as follows:
0 0
=
0 1
=
1 0
=
1 1
=
1
The basic formulas and rules of logical algebra can be used to transform logical functions, thus obtaining the simplest expression form. The simplest form here refers to the simplest and or or the simplest or and, and there are two criteria for judging them: the least number of items; In the case of the least number of items, the text in the item is the least.
Karnaugh map is formed according to certain laws. It is precisely because of these laws that many characteristics of logical algebra are vividly and intuitively reflected in graphics, thus becoming a powerful tool for formula proof and function simplification.