1, basic concept
Logical Constants and Variables: There are only two logical constants, namely 0 and 1, which are used to represent two opposing logical states. Like ordinary algebra, logical variables can also be represented by letters, symbols, numbers and their combinations, but there are essential differences between them, because logical variables have only two values, namely 0 and 1, and there is no intermediate value.
Logical operations: In logical algebra, there are three basic logical operations: AND, or NAND. There are many expressions of logical operations, such as statement description, logical algebra, truth table, Karnaugh map and so on. Logical function: A logical function is an algebraic expression in which logical variables and constants are connected by operators. Similarly, logical functions can also be expressed in the form of tables and graphs.
Logic Algebra: Logic Algebra is a mathematical system that studies the operation and simplification of logic functions. The operation and simplification of logic function is the foundation of digital circuit course, and it is also the key of digital circuit analysis and design.
2. Three basic logical operations
combine
Figure 1(a) shows a simple logic circuit. Voltage V supplies power to the light bulb L through switches A and B. Only when A and B are turned on at the same time, the light bulb L will light up. As long as one or both of A and B are not connected, the light bulb L will not light, and its truth table is shown in Figure 1(b). So from this circuit, we can sum up the logical relationship with operation.
Statement description: Only when several conditions (switches A and B are on) of one thing (light L is on) are met, this thing will happen. This relationship is called AND operation.
Logical expression:
l=a b
The point ""in the formula represents the AND operation of A and B, which is also called logical multiplication. On the premise of not causing confusion, the multiplication sign ""is omitted. In some documents, symbols ∧ and ∩ are also used to represent and operate.
Truth table: if the switch is blocked and the light is off, it is all represented by 0, while the switch is on and the light is on, it is all represented by 1, and the truth table description as shown in figure 1(c) is obtained. The left side of the truth table lists all combinations of values of all variables, and the right side lists the output of each combination of values corresponding to variables A and B. Because there are two input variables, there are 22 = 4 combinations of values, and n variables should have 2n combinations of values.
Logical symbol: The logical symbol of AND operation is shown in figure 1(d), where A and B are inputs and L is output.