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3.0 KiB
title | localeTitle |
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Binary Decimal Hexadecimal Conversion | 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
- 计算器网站 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 。