> For the complete documentation index, see [llms.txt](https://docs.1l.lol/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.1l.lol/computer-basics/binary-encoding.md).

# 数据编码（原码、反码、补码）

### 三种编码

计算机中整数用**补码**存储。以 8 位为例：

| 编码 | 正数         | 负数          |
| -- | ---------- | ----------- |
| 原码 | 符号位 0 + 数值 | 符号位 1 + 数值  |
| 反码 | 与原码相同      | 符号位不变，数值位取反 |
| 补码 | 与原码相同      | 反码 + 1      |

### 举例：+5 与 -5（8 位）

```
+5 原码/反码/补码：0000 0101
-5 原码：1000 0101
-5 反码：1111 1010
-5 补码：1111 1011
```

### 为什么要用补码

* 把减法变成加法：`a - b = a + (-b) 的补码`
* 0 只有一种表示，避免 +0 和 -0 的歧义
* 表示范围：8 位补码为 `-128 ~ 127`

### 溢出的直观理解

```cpp
#include <iostream>
using namespace std;

int main() {
    int x = 2147483647;   // int 最大值
    cout << x + 1 << endl; // 溢出，变为 -2147483648
    return 0;
}
```

> 注意区分：`unsigned int` 没有符号位，范围是 `0 ~ 4294967295`，溢出后从 0 重新开始。


---

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