(1) union method uses the formula AB+AB'=A to combine two and terms into one and eliminate one of the variables.
(2) The absorption method uses the formula A+AB=A to absorb the redundant sum term.
(3) Factor elimination method uses the formula A+A'B=A+B to eliminate the redundant factors of the sum term.
④ The elimination method uses the formula AB+A'C=AB+A'C+BC to match entries, so as to eliminate more and entries.
⑤ The collocation method simplifies the expression by using formulas A+A=A, A+A'= 1.
Second, the Karnaugh map simplification method
Karnaugh map representation of logical functions
All the smallest terms of n variables are represented by a small square, and the logically adjacent smallest terms are arranged adjacent to each other in geometric position. The obtained graph is called Karnaugh map of the minimum term of n variables.
Logical adjacency: the two smallest items with only one variable different and the other variables the same are called logical adjacency.
1. represents the Karnaugh map of the smallest term.
The logical variables are divided into two groups, and all the value combinations of each group of variables are arranged in the form of cyclic codes in two directions, forming a graph of 2n squares, and each square corresponds to a value combination of a variable. The smallest items with logical adjacency are also arranged adjacently in position.
Using Karnaugh map to represent logical function;
Method 1: 1. Formulating a known logical function into the sum of the smallest terms.
2. Fill 1 in the box corresponding to the Karnaugh map of the smallest term contained in the function formula, and fill 0 in other boxes.
Method 2: Fill in the Karnaugh map directly according to the function formula.
Simplifying logic function with Karnaugh map;
The basis of simplification: the smallest items of logical adjacency can be merged and the factors can be eliminated.
Simplified rule: The minimum number of items that can be merged together is 2n.
How to be the simplest: the fewer laps, the simpler; The more smallest items in the circle, the simpler it is.
Note: 1 in Karnaugh Map must be circled completely, and 1 that cannot be merged must be circled separately.
This shows that the simplification result of a logical function may not be unique.
The principle of merging the smallest items:
1) Any two adjacent minimum terms can be merged into one term, and a variable can be eliminated.
2) Any four adjacent minimum terms can be merged into one term to eliminate two variables.
3) Any eight adjacent minimum terms can be merged into one term, and three variables can be eliminated.
Steps to simplify Karnaugh map:
Draw the Karnaugh map of the function;
Draw a circle (isolate 1 grid first; The smallest term in a circle with only one direction (1 lattice combination);
Principle of drawing a circle: the number of combinations is 2n; The circle should be as large as possible (the product item contains the least number of factors); The fewer cycles, the better (the least number of products); At least one minimum item in each circle is circled only once to avoid redundant items.