1)将八进制数制转换为二进制数制 (1) Conversion of Octal Number System to Binary Number System)

To convert octal numbers into binary numbers, we can use the relationship between octal and binary numbers.

要将八进制数转换为二进制数，我们可以使用八进制数和二进制数之间的关系。

Example 1: Convert (73.2)₈ into ( ? )₂

示例1：将(73.2) ₈转换为(？) ₂

Solution:

解：

Using the table provided above, we can replace octal numbers with their equivalent binary digits.

使用上面提供的表，我们可以将八进制数字替换为其等效的二进制数字。

    7 = 111
3 = 011
2 = 010

Therefore, (73.2)₈ = (111 011.010)₂

因此， (73.2) ₈ =(111 011.010) ₂

Example 2: Convert (475.62)₈ into ( ? )₂

示例2：将(475.62) ₈转换为(？) ₂

Solution:

解：

Using the table provided above, we can replace octal numbers with their equivalent binary digits.

使用上面提供的表，我们可以将八进制数字替换为其等效的二进制数字。

    4 = 100
7 = 111
5 = 101
6 = 110
2 = 010

Therefore, (475.62)₈ = (100 111 101.110 010)₂

因此， (475.62) ₈ =(100111 101.110 010) ₂

2)将八进制数制转换为十进制数制 (2) Conversion of Octal Number System to Decimal Number System)

Conversion of octal number into a decimal number can be done using the positional weights by multiplying the positional weights with the corresponding bit and add them all together to obtain the decimal number.

可以使用位置权重将八进制数转换为十进制数，方法是将位置权重乘以相应的位，然后将它们全部加在一起以获得十进制数。

• In an integral part of the octal number, the weights follow the pattern as 8⁰, 8¹, 8², 8³, 8⁴, 8⁵ and so on from right to left.

  在八进制数的一个组成部分，权重按照图案作为8 ^{0，8 1，8 2，8 3，8 4，8 5}等从右到左。

• In the fractional part of the octal number, the weights follow the pattern as 8^-1, 8^-2, 8^-3, 8^-4, 8^-5 and so on from left to right.

  在八进制数的小数部分，权重按照图案作为8 ^{-1，8 -2，-3} 8，8 ^-4，-5 8等从左到右。

Example 1: Convert (75.3)₈ = ( ? )₁₀

示例1：转换(75.3) ₈ =(？) ₁₀

Solution:

解：

We multiply each bit with the corresponding positional weight and then add them together to get the result.

我们将每个位乘以相应的位置权重，然后将它们加在一起以获得结果。

Therefore, (75.3)₈ = (61.375)₁₀

因此， (75.3) ₈ =(61.375) ₁₀

Example 2: Convert (624.712)₈ = ( ? )₁₀

示例2：转换(624.712) ₈ =(？) ₁₀

Solution:

解：

We multiply each bit with the corresponding positional weight and then add them together to get the result.

我们将每个位乘以相应的位置权重，然后将它们加在一起以获得结果。

Therefore, (624.712)₈ = (404.894)₁₀

因此， (624.712) ₈ =(404.894) ₁₀

Example 3: Convert (482.31)₈ = ( ? )₁₀

示例3：转换(482.31) ₈ =(？) ₁₀

Solution:

解：

Given number (482.31)₈ is not an octal number as a range of octal number is from 0 to 7 and the given number includes 8. So, it cannot be converted to a decimal number.

给定数字(482.31) ₈不是八进制数字，因为八进制数字的范围是从0到7，并且给定数字包括8。因此，不能将其转换为十进制数字 。

3)将八进制数制转换为十六进制数制 (3) Conversion of Octal Number System into Hexadecimal Number System)

Conversion of the octal number to hexadecimal can only be done using a certain definite path. We first have to convert octal number to binary number and then convert the binary number into hexadecimal number i.e., Octal Number → Binary Number → Hexadecimal Number

八进制数到十六进制的转换只能使用某个确定的路径来完成。 我们首先必须将八进制数转换为二进制数，然后将二进制数转换为十六进制数，即八进制数→二进制数→十六进制数

Example 1: Convert (35.7)₈ into ( ? )₁₆

示例1：将(35.7) ₈转换为(？) ₁₆

Solution:

解：

Step 1: Convert octal number to binary number.
Therefore, (35.7)₈ = (011101.111)₂

步骤1：将八进制数转换为二进制数。
因此， (35.7) ₈ =(011101.111) ₂

Step 2: Convert binary number to a hexadecimal number.
Therefore, (011101.111)₂ = (1D.E)₁₆

步骤2：将二进制数转换为十六进制数。
因此， (011101.111) ₂ =(1D.E) ₁₆

Therefore, (35.7)₈ = (1D.E)₁₆

因此， (35.7) ₈ =(1D.E) ₁₆

Note: To know how to convert the binary number into a hexadecimal number?, Read: Conversion of binary number into a hexadecimal number.

注意：要知道如何将二进制数转换为十六进制数，请阅读： 将二进制数转换为十六进制数 。

Example 2: Convert (73.2)₈ into ( ? )₁₆

示例2：将(73.2) ₈转换为(？) ₁₆

Solution:

解：

Step 1: Convert octal number to binary number.
Therefore, (73.2)₈ = (111011.010)₂

步骤1：将八进制数转换为二进制数。
因此， (73.2) ₈ =(111011.010) ₂

Step 2: Convert binary number to a hexadecimal number.
Therefore, (111011.010)₂ = (3B.4)₁₆

步骤2：将二进制数转换为十六进制数。
因此， (111011.010) ₂ =(3B.4) ₁₆

Therefore, (73.2)₈ = (3B.4)₁₆

因此， (73.2) ₈ =(3B.4) ₁₆

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