table of Contents:
definition
nature
relationship
Precautions
1. Definition
Minimum term: the logical multiplication of n variables, that is, and form, each variable appears once in the form of the original variable or the inverse variable. There are 2n smallest items for n variables. Expressed by m, such as ABC, expressed as m0.
Maximum term: the logical sum of n variables, that is, or form, each variable appears once in the form of the original variable or the inverse variable. There are 2n largest items for n variables. Expressed by M, such as A+B+C, expressed as M0.
The following is the representation of the minimum and maximum terms of the three variables:
2. Nature
- For n variables, if the values determined by these variables are given, then only one group of 2n smallest items has a value of 1, and the rest are all 0; only one group of 2n largest items has a value of 0, and the rest are all 1. .
- The sum of all the smallest items is always equal to 1; the product of all the largest items is always equal to 0. (It can be seen from the first nature)
- The product of any two smallest terms is equal to 0; the sum of any two largest terms is equal to 0. (It can be seen from the first nature)
- The sum of several smallest items is equal to the inverse of the other smallest items. It can be simply remembered as being divided into two parts on the Karnaugh map, and the relationship between them is inverse.
3. Relationship
The inverse of the smallest term is the largest term, and the inverse of the largest term is the smallest term.
In this case, we can understand the composition of the Karnaugh map in another way: for n variables, the Karnaugh map is composed of several minimum items and their corresponding maximum items.
Let's take a look at this example:
The result can be calculated as option B. When we calculate the minimum term, the maximum term can be calculated directly from the subscript.
4. Matters needing attention
When describing the minimum and maximum terms, the expression must include all variables, otherwise the expression cannot be regarded as the minimum or maximum term. Examples are as follows:
