2-布尔代数1

一、布尔代数

1，Boolean Algebra defines a set of laws, operations and theorems on the set of elements {0, 1}.

Algebra will allow us to describe a circuit as a mathematical expression, as a functional specification of its outputs in terms of its inputs. It will allow us to manipulate the functional specification for the purposes of simplification of a circuit reducing the number of logic gates required to implement it. Algebra will help us substitute alternative implementation solutions for circuits or parts of circuits that may require using certain types of logic gates.

二、Boolean Operators

三、Boolean Functions

1，形式

2，函数的对偶【dual of a function】 函数的对偶是通过将AND运算符改为OR AND得到的 反过来1和0的关系也是一样的。变量保持不变。

3，The complement of a function 方法1：先求对偶function，再对每一个单独变量求bar The complement of a function can be found by complementing each variable in the dual of that function.

方法2：De Morgan:

4，运算符优先级别 （）>NOT>AND>OR

5 any Boolean function can in fact be expressed using only OR and NOT operators. any Boolean function can in fact be expressed using only AND and NOT operators. ,Boolean functions can be implemented entirely using only NAND gates or alternatively NOR gates.

6，常用公式

7，化简

四、Truth Tables

A truth table is a method of describing a Boolean function 1，SOP【找1】 和POS【找0】表示 n个变量，2的n次方行

3，Principle of Duality 对偶性原则

4，真值表的n不宜过大

5，常用