c - 按位运算——算术运算

Question

您能用一些很好的例子来解释下面几行吗？

A left arithmetic shift by n is equivalent to multiplying by 2ⁿ (provided the value does not overflow).

还有:

A right arithmetic shift by n of a two's complement value is equivalent to dividing by 2ⁿ and rounding toward negative infinity. If the binary number is treated as ones' complement, then the same right-shift operation results in division by 2ⁿ and rounding toward zero.

Answer 1

我将解释一下我们更熟悉的基地中发生的情况:10。

以 10 为基数，假设您有一个数字 N=123。现在，您将这个数字向左“移动”k=3 个位置，用 0 填充空的数字。因此您得到 X=123000。

请注意，X = N * 10^k。

基数为 2 的情况类似。

 Example 1 (base 10)   |  Example 2 (base 2)
                       |
 N        =    123     |  N       =   110101 (53 in base 10)
 k        =      3     |  k       =        2 (in base 10)
 N << k   = 123000     |  N << k  = 11010100 (212 in base 10)
                       |
 10^k     =   1000     |  2^k     =      100 (in base 2; 4 in base 10)
 N * 10^k = 123000     |  N * 2^k = 11010100 (53 * 4 = 212 in base 10)
                       |

右移的情况只是该过程的镜像，并且在基数 10 中也类似。例如，如果我在基数 10 中有 123456，并且我“右移”3 个位置，则得到 123。这是123456/1000(整数除法)，其中 1000 = 10³。