> 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/number-systems.md).

# 进制转换

### 常见进制

* 二进制：逢二进一，数字 0、1，前缀 `0b`
* 八进制：逢八进一，数字 0\~7，前缀 `0`
* 十进制：逢十进一，数字 0\~9
* 十六进制：逢十六进一，数字 0~~9、A~~F，前缀 `0x`

### 二进制转十进制

按权展开求和。例如 `1101₂ = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 13`。

### 十进制转其他进制

**除基取余，逆序排列**。例如 13 转二进制：

```
13 ÷ 2 = 6 余 1
 6 ÷ 2 = 3 余 0
 3 ÷ 2 = 1 余 1
 1 ÷ 2 = 0 余 1
从下往上：1101
```

### 二进制与八/十六进制的快速互转

* **八进制**：每 3 位二进制对应 1 位八进制
* **十六进制**：每 4 位二进制对应 1 位十六进制

例如 `1101 0110₂ = D6₁₆`。

### C++ 中的进制输出

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

int main() {
    int n = 13;
    cout << n << endl;         // 13（十进制）
    cout << hex << n << endl;   // d（十六进制）
    cout << oct << n << endl;   // 15（八进制）
    cout << bitset<8>(n) << endl; // 00001101（二进制，需 <bitset>）
    return 0;
}
```


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