1、 Simplification of digital logic

And or not ： Logical multiplication Logical addition Logic is not
Truth table ： In a slightly complicated situation , It's hard to give enough logical expressions , At this time, use the truth table .N Input ,2^N Power table items .
The same logic can have many different forms of logical expression , But the representation of truth table is unique .
There is an equivalent transformation relationship between the two , So truth table plays an important role in logic simplification .
The basic formula of logical operation P35;
Three rules of logical operation P36;
Simplification of digital logic ：
1. Formula simplification method
2. Karnaugh map simplification
（ One ） The standard form of logical function ：
a,SOP and POS ;

b, Minimum and maximum terms ;
Minimum term ： have N Function of variables “” And item “” Include all N A variable , Each variable appears once as a factor in the form of original variable or inverse variable , Only once . So this “ And item ” It is called the minimum term . I think the corresponding is SOP.
The biggest item : The corresponding is POS , Summation term .
C. Standard form ; （ We usually use SOP Standard discussion ）
（ Two ） The standard form of logical function ：
a. x From truth table to standard formula

（ 3、 ... and ） From the standard SOP To the simplest SOP
Use formulas to simplify , But generally, when we encounter complex problems, we may not effectively simplify the results , Therefore, we need to use the logical simplification method of Karnaugh map .
in other words , What we get from the truth table is the standard logical expression SOP.POS, But this is not the simplest , So the problem of simplification if the formula method doesn't work , Then consider the simplification of Karnaugh map .
（ Four ） Karnaugh map simplification
review “ Formula 1 ”：

You can find , standard SOP To Simplest SOP, The idea of simplification is mainly to use the combination of minimum terms , Under what circumstances can the smallest items be merged ： When there is only one variable between the two, the form of the original variable is transformed into the inverse variable , In this way, you can merge , So the purpose of using Karnaugh map is to establish the table of minimum items , In this way, it is easier to find the law of merger .

（ 5、 ... and ） Steps of Karnaugh map simplification
a, Fill in the picture b, Merge

P46 QM Systematic simplification method