A Brief Introduction to Boolean Algebra（布尔代数简介）

I. Notations

∧  -  AND
∨  -  OR
¬  -   NOT
⊕  -   XOR ()
|    -   NAND

In electronics:
x  -  AND  (xy <= x∧y )
+  -  OR    (x+y <= x∨y)
-   -  NOT  (-x <= &#172;x)

A

Function	Description	Expression
1.	NULL	0
2.	IDENTITY	1
3.	Input A	A
4.	Input B	B
5.	NOT A	A
6.	NOT B	B
7.	A AND B (AND)	A . B
8.	A AND NOT B	A . B
9.	NOT A AND B	A . B
10.	NOT A AND NOT B (NAND)	A . B
11.	A OR B (OR)	A + B
12.	A OR NOT B	A + B
13.	NOT A OR B	A + B
14.	NOT OR (NOR)	A + B
15.	Exclusive-OR	A.B + A.B
16.	Exclusive-NOR	A.B + A.B

II. Laws 

 

Online Boolean Calculator:
http://www.selmer.uib.no/odbf/check.html

Refer to: http://en.wikipedia.org/wiki/Boolean_algebra_(logic)