Description of logical functions and logical problems

After discussing the three basic logic operations of AND, OR, and NOT, we will start from engineering practice, propose logic propositions, and then describe them with truth tables. From the truth tables, we can write logic functions. Generally speaking, a more complex logic circuit is often controlled by multiple factors, that is, there are multiple logic variables, and the relationship between the output and input variables is usually described by logic functions. Let's take a look at a simple example.

Figure 1.6.1 is a circuit for controlling stair lighting. Single-pole double-throw switch A is installed downstairs
and switch B is installed upstairs. This way, after turning on the light downstairs, you can turn off the light upstairs. Similarly, you can turn on the light upstairs and turn it off downstairs. Because the light will only be on when both switches are turned up or down; when one is turned up and the other is turned down, the light will not be on.
The logical relationship of the above circuit can be described by a logical function. Let L represent the state of the light, that is, L=1 means the light is on, and L=0 means the light is off. Use A and B to represent the position status of switch A and switch B, with 1 indicating that the switch is turned up and 0 indicating that the switch is turned down. Then
the relationship between L and A and B can be expressed by truth table 1.6.1

From the truth table, we can see that among the four different combinations of A and B states, only the first (
A=B=0) and the fourth (A=B=0) combinations can make the light turn on (L=1
). A and B have an AND relationship, while the two state combinations have an OR relationship. Regardless of the variables A, B or output L, the value of 1 is represented by the original variable, and the value of 0 is represented by the inverse variable. Therefore, the logic function of the light can be written.
It describes that the light will only turn on when switches A and B are both turned up or down. This is the process of building a logic function from a logic problem.