Computer Logical Organization 简明教程
Boolean Algebra
布尔代数用于分析和简化数字（逻辑）电路。它只使用二进制数，即 0 和 1。它也被称为 Binary Algebra 或 logical Algebra 。布尔代数是由 George Boole 于 1854 年发明的。
Boolean Algebra is used to analyze and simplify the digital (logic) circuits. It uses only the binary numbers i.e. 0 and 1. It is also called as Binary Algebra or logical Algebra. Boolean algebra was invented by George Boole in 1854.
Rule in Boolean Algebra
以下是布尔代数中使用的重要规则。
Following are the important rules used in Boolean algebra.
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Variable used can have only two values. Binary 1 for HIGH and Binary 0 for LOW.
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Complement of a variable is represented by an overbar (-). Thus, complement of variable B is represented as . Thus if B = 0 then = 1 and B = 1 then = 0.
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ORing of the variables is represented by a plus (+) sign between them. For example ORing of A, B, C is represented as A + B + C.
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Logical ANDing of the two or more variable is represented by writing a dot between them such as A.B.C. Sometime the dot may be omitted like ABC.
Boolean Laws
有六种类型的布尔定律。
There are six types of Boolean Laws.
Commutative law
满足以下表达式的任何二进制运算都称为交换运算。
Any binary operation which satisfies the following expression is referred to as commutative operation.
交换定律指出，更改变量的顺序对逻辑电路的输出没有任何影响。
Commutative law states that changing the sequence of the variables does not have any effect on the output of a logic circuit.
Associative law
此定律指出，执行逻辑运算的顺序无关紧要，因为它们的效果相同。
This law states that the order in which the logic operations are performed is irrelevant as their effect is the same.
AND law
这些律使用 AND 运算。因此它们被称为 AND 律。
These laws use the AND operation. Therefore they are called as AND laws.
