二进制十进制十六进制转换

Prerequisite: Number systems

先决条件： 数字系统

To convert binary number to its respective decimal number we use the place values or what we call the positional weights and multiply it with the corresponding bit and add them all together to obtain the decimal number.

为了将二进制数转换为其相应的十进制数，我们使用位置值或所谓的位置权重，然后将其与相应的位相乘，然后将它们全部相加在一起，以获得十进制数。

• In an integral part of the binary number, the weights follow the pattern as 2⁰, 2¹, 2², 2³, 2⁴, 2⁵ and so on from right to left.

  在二进制数的一个组成部分 ，权重按照图案作为2 ^{0，2 1，2 2，2 3，2 4，2 5}等从右到左。

• In the fractional part of the binary number, the weights follow the pattern as 2^-1, 2^-2, 2^-3, 2^-4, 2^-5 and so on from left to right.

  在二进制数的小数部分 ，权重按照图案作为2 ^{-1，2 -2，2 -3，2 -4，-5} 2等从左到右。

To convert a mixed binary number, we convert its integral and fractional part individually and then combine them to get the desired decimal number.

要转换混合的二进制数 ，我们分别转换其整数和小数部分，然后将它们组合以获得所需的十进制数。

Let's take a few examples to understand the concept better.

让我们举几个例子来更好地理解这个概念。

Example 1: Convert (101.11)₁₀

范例1：转换(101.11) ₁₀

Solution:

解：

Now, after converting both integral part and fractional part separately, we combine them and get the desired decimal number for the binary number i.e., (101.11)₂ = (5.75)₁₀

现在，将整数部分和小数部分分别转换之后，我们将它们组合起来，得到所需的二进制数十进制数，即(101.11) ₂ =(5.75) ₁₀

Example 2: Convert (11011.101)₁₀

示例2：转换(11011.101) ₁₀

Solution:

解：

Now, after converting both integral part and fractional part separately, we combine them and get the desired decimal number for the binary number i.e., (11011.101)₂ = (27.625)₁₀

现在，将整数部分和小数部分分别转换之后，我们将它们组合起来，得到所需的二进制数十进制数，即(11011.101) ₂ =(27.625) ₁₀

翻译自: https://www.includehelp.com/basics/conversion-of-binary-number-system-to-decimal-number-system.aspx

二进制十进制十六进制转换