--- title: Binary Decimal Hexadecimal Conversion localeTitle: 二进制十进制十六进制转换 --- # 转换: 您可以使用基于n的数字的定义轻松地将数字从一个基数转换为另一个基数,这需要您了解我们的位置系统如何工作: 让我们从两位数字开始,例如`12` 。为了获得它的10的基数值,我们需要将其单个数字乘以`10^n` ,其中n是从右边开始的数字位置并从0开始计数。然后我们简单地对所有值求和。 例如,将以这种方式获得`12`的base-10值: \`\`\` 1 _(10 ^ 1)+ 2_ (10 ^ 0)= 10 + 2 = 12 ``` This was obvious but what if you had a base-2 number and wanted to know its base-10 value? First of all mind that a base n number only has `n` total symbols to represent its values. In the binary base we have then just 2 (base-2) symbols: `1` and `0`. Applying the procedure you have seen before you will be able to obtain a decimal number starting from a binary one like `101`: ``` 101 = 1 _(2 ^ 2)+ 0_ (2 ^ 1)+ 1 \*(2 ^ 0)= 4 + 0 + 1 = 5 ``` In the same way a hexadecimal (base-16) number has 16 symbols to represent its values: `0, 1, 2, 3, 4, 5, 6 ,7, 8, 9, A, B, C, D, E, F`. Converting a base-16 number like `7AF` to a decimal will be easy then: ``` 7AF = 7 _(16 ^ 2)+ A_ (16 ^ 1)+ F _(16 ^ 0)= 7_ 256 + 10 _16 + 15_ 1 = 1967 ``` What if you wished to convert a decimal number into a n-based number? A common way to accomplish this is dividing the decimal number by the n base repeatedly. Take note of all remainders, and when your quotient reaches 0 stop. Now simply write all your remainders setting the last one as the most significant digit (your newly converted n-based number should have as last digit your first remainder). EG: Let's convert the base-10 `12` to its base-2 value ``` 12/2 = 6,余数为0 6/2 = 3,余数为0 3/2 = 1,余数为1 1/2 = 0,余数为1 base-10 12 = base-2 1100 \`\`\` 现在使用上面写的第一个方法,您可以检查一切是否正常: `1100 = 1*(2^3) + 1*(2^2) + 0*(2^1) + 0*(2^0) = 8+4+0+0 = 12` ## 二进制十进制十六进制转换器 二进制,十进制和十六进制转换器它是一个工具,允许您转换在不同数字系统中表示的相应数字中的一个数字。允许的数字系统是`base-2` (二进制), `base-10` (十进制),这是我们通常使用的数字和`base-16` (十六进制)。 网上有很多这样的工具: * [二进制十六进制转换器](www.binaryhexconverter.com/) * [计算器网站](http://www.calculator.net/) 通常科学计算器也包括基本转换工具,在MacOSX默认计算器中,您可以使用程序员视图按`Cmd+3`或在菜单`View->Programmer`下使用此功能。 ### 你自己的转换器: 练习编程和完全理解数字转换的好主意是编写自己的在线转换工具。 如果您想了解有关此主题的更多信息,请查看[此维基百科条目](https://en.wikipedia.org/wiki/Positional_notation) 。