Two's complement

最新推荐文章于 2025-03-15 00:53:56 发布

weixin_33858336

最新推荐文章于 2025-03-15 00:53:56 发布

阅读量154

点赞数

CC 4.0 BY-SA版权

原文链接：http://www.cnblogs.com/daizuozhuo/archive/2012/06/07/3052433.html

本文深入解析了计算机组织课程中提到的二进制补码概念，解释了如何通过翻转位元并加一来表示负数，以及为何这种表示方法使得整数运算在计算机中变得高效直接。文章引用了具体实例和算法书籍的解释，以清晰地阐述补码背后的数学逻辑。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

I have learned two's complement in the computer organization course. At that time, I simply knew that to express a negative number, first find it's positive form, then flip every bit of it and finally add one on it. Although the specific steps are clear, I don't know the reason for it, in other words, I don't know why should I do this until I read an algorithm book which happens referred the two's complement.

The reason is this. For a n-bit long word, the all possible combination of numbers is 2ⁿ-1. Since we want to represent sign numbers, the range is (-2^n-1 , 2^n-1-1). Here’s a much simpler way to think about it: any number in this range is stored modulo 2ⁿ . Negative numbers −x therefore end up as 2ⁿ − x. Arithmetic operations like addition and subtraction can be performed directly in this format, ignoring any overﬂow bits that arise.

转载于:https://www.cnblogs.com/daizuozhuo/archive/2012/06/07/3052433.html