Python 教學：位元運算 (Bitwise Operation)

Operator	Description	Example
&	Bitwise AND Operator	8 & 29 = 8
|	Bitwise OR Operator	8 | 29 = 29
^	Bitwise XOR Operator	8 ^ 29 = 21
<<	Bitwise Leftshift Operator	8 << 1 = 16
>>	Bitwise Rightshift Operator	8 >> 1 = 4

解說

• 8 (Decimal) = 01000 (Binary)
• 29 (Decimal) = 11101 (Binary)
• 8 & 29 -> 01000 & 11101 = 01000 -> 8
• 8 | 29 -> 01000 | 11101 = 11101 -> 29
• 8 ^ 29 -> 01000 ^ 11101 = 10101 -> 21
• 8 << 1 -> 01000 << 1 = 10000 -> 16
• 8 >> 1 -> 01000 >> 1 = 00100 -> 4

技巧 記巧

• & AND Bitwise Operator: 只要其中一個 bit 是 0，則結果為 0
• | OR Bitwise Operator: 只要其中一個 bit 是 1，則結果為 1
• ^ XOR Bitwise Operator: 兩個 bit 一樣 (0,0) 或(1,1) 則結果為 0，兩個bit不一樣則結果為1

重要性質

令 x 為一串bits，0s 代表與 x 同樣長度但所有bits皆為0，1s 代表皆為 1

AND &	x & 1s = x	x & 0s = 0s	x & x = x
OR |	x | 1s = 1s	x | 0s = x	x | x = x
XOR ^ (非常重要)	x ^ 1s = ~x	x ^ 0s = x	x ^ x = 0s