位运算
前言
看到有些人对位运算还存在问题，于是决定写这篇文章作个简要说明。
什么是位(bit)？
很简单，位(bit)就是单个的0或1，位是我们在计算机上所作一切的基础。计算机上的所有数据都是用位来存储的。一个字节(BYTE)由八个位组成，一个字(WORD)是二个字节或十六位，一个双字(DWORD)是二个字(WORDS)或三十二位。如下所示：
0 1 0 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0
| | | | | | |
| +- bit 31 | | | bit 0 -+ |
| | | | |
+-- BYTE 3 ---- -+---- BYTE 2 ---+---- BYTE 1 ---+--- BYTE 0 -----+
| | |
+------------ WORD 1 ------------+----------- WORD 0 -------------+
| |
+----------------------------- DWORD -----------------------------+
使用位运算的好处是可以将BYTE, WORD 或 DWORD 作为小数组或结构使用。通过位运算可以检查位的值或赋值，也可以对整组的位进行运算。
16进制数及其与位的关系
用0或1表示的数值就是二进制数，很难理解。因此用到16进制数。
16进制数用4个位表示0 - 15的值，4个位组成一个16进制数。也把4位成为半字节(nibble)。一个BYTE有二个nibble，因此可以用二个16进制数表示一个BYTE。如下所示：
NIBBLE HEX VALUE
====== =========
0000 0
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 8
1001 9
1010 A
1011 B
1100 C
1101 D
1110 E
1111 F
如果用一个字节存放字母"r"(ASCII码114)，结果是：
0111 0010 二进制
7 2 16进制
可以表达为：'0x72'
有6种位运算：
& 与运算
| 或运算
^ 异或运算
~ 非运算(求补)
>> 右移运算
<< 左移运算
与运算(&)
双目运算。二个位都置位(等于1)时，结果等于1，其它的结果都等于0。
1 & 1 == 1
1 & 0 == 0
0 & 1 == 0
0 & 0 == 0
与运算的一个用途是检查指定位是否置位(等于1)。例如一个BYTE里有标识位，要检查第4位是否置位，代码如下：
BYTE b = 50;
if ( b & 0x10 )
cout << "Bit four is set" << endl;
else
cout << "Bit four is clear" << endl;
上述代码可表示为：
00110010 - b
& 00010000 - & 0x10
----------------------------
00010000 - result
可以看到第4位是置位了。
或运算( | )
双目运算。二个位只要有一个位置位，结果就等于1。二个位都为0时，结果为0。
1 | 1 == 1
1 | 0 == 1
0 | 1 == 1
0 | 0 == 0
与运算也可以用来检查置位。例如要检查某个值的第3位是否置位：
BYTE b = 50;
BYTE c = b | 0x04;
cout << "c = " << c << endl;
可表达为：
00110010 - b
| 00000100 - | 0x04
----------
00110110 - result
异或运算(^)
双目运算。二个位不相等时，结果为1，否则为0。
1 ^ 1 == 0
1 ^ 0 == 1
0 ^ 1 == 1
0 ^ 0 == 0
异或运算可用于位值翻转。例如将第3位与第4位的值翻转：
BYTE b = 50;
cout << "b = " << b << endl;
b = b ^ 0x18;
cout << "b = " << b << endl;
b = b ^ 0x18;
cout << "b = " << b << endl;
可表达为：
00110010 - b
^ 00011000 - ^0x18
----------
00101010 - result
00101010 - b
^ 00011000 - ^0x18
----------
00110010 - result
非运算(~)
单目运算。位值取反，置0为1，或置1为0。非运算的用途是将指定位清0，其余位置1。非运算与数值大小无关。例如将第1位和第2位清0，其余位置1：
BYTE b = ~0x03;
cout << "b = " << b << endl;
WORD w = ~0x03;
cout << "w = " << w << endl;
可表达为：
00000011 - 0x03
11111100 - ~0x03 b
0000000000000011 - 0x03
1111111111111100 - ~0x03 w
非运算和与运算结合，可以确保将指定为清0。如将第4位清0：
BYTE b = 50;
cout << "b = " << b << endl;
BYTE c = b & ~0x10;
cout << "c = " << c << endl;
可表达为：
00110010 - b
& 11101111 - ~0x10
----------
00100010 - result
移位运算(>> 与 <<)
将位值向一个方向移动指定的位数。右移 >> 算子从高位向低位移动，左移 << 算子从低位向高位移动。往往用位移来对齐位的排列(如MAKEWPARAM, HIWORD, LOWORD 宏的功能)。
BYTE b = 12;
cout << "b = " << b << endl;
BYTE c = b << 2;
cout << "c = " << c << endl;
c = b >> 2;
cout << "c = " << c << endl;
可表达为：
00001100 - b
00110000 - b << 2
00000011 - b >> 2
译注：以上示例都对，但举例用法未必恰当。请阅文末链接的文章，解释得较为清楚。
位域(Bit Field)
位操作中的一件有意义的事是位域。利用位域可以用BYTE, WORD或DWORD来创建最小化的数据结构。例如要保存日期数据，并尽可能减少内存占用，就可以声明这样的结构：
struct date_struct {
BYTE day : 5, // 1 to 31
month : 4, // 1 to 12
year : 14; // 0 to 9999
}date;
在结构中，日期数据占用最低5位，月份占用4位，年占用14位。这样整个日期数据只需占用23位，即3个字节。忽略第24位。如果用整数来表达各个域，整个结构要占用12个字节。
| 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 |
| | | |
+------------- year --------------+ month+-- day --+
现在分别看看在这个结构声明中发生了什么
首先看一下位域结构使用的数据类型。这里用的是BYTE。1个BYTE有8个位，编译器将分配1个BYTE的内存。如果结构内的数据超过8位，编译器就再分配1个BYTE，直到满足数据要求。如果用WORD或DWORD作结构的数据类型，编译器就分配一个完整的32位内存给结构。
其次看一下域声明。变量(day, month, year)名跟随一个冒号，冒号后是变量占用的位数。位域之间用逗号分隔，用分号结束。
使用了位域结构，就可以方便地象处理普通结构数据那样处理成员数据。尽管我们无法得到位域的地址，却可以使用结构地址。例如：
date.day = 12;
dateptr = &date;
dateptr->year = 1852;
ref:http://www.cnblogs.com/flying_bat/archive/2008/06/17/1224178.html
Sep 19, 2010 07:41:45 AM
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