1)將八進制數制轉換為二進制數制 (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.

要將八進制數轉換為二進制數，我們可以使用八進制數和二進制數之間的關系。

Octal NumberBinary Number

0	000
1	001
2	010
3	011
4	100
5	101
6	110
7	111

八進制數 二進制數

0	000
1個	001
2	010
3	011
4	100
5	101
6	110
7	111

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

示例1：將(73.2) ₈轉換為(？) 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，我們可以將八進制數字替換為其等效的二進制數字。

7 = 1113 = 0112 = 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：將(475.62) ₈轉換為(？) 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，我們可以將八進制數字替換為其等效的二進制數字。

4 = 1007 = 1115 = 1016 = 1102 = 010

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

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

2)將八進制數制轉換為十進制數制 (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.

可以使用位置權重將八進制數轉換為十進制數，方法是將位置權重乘以相應的位，然后將它們全部加在一起以獲得十進制數。

• 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.

  在八進制數的一個組成部分，權重按照圖案作為8 ^{0，8 1，8 2，8 3，8 4，8 5}等從右到左。

• 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.

  在八進制數的小數部分，權重按照圖案作為8 ^{-1，8 -2，-3} 8，8 ^-4，-5 8等從左到右。

Example 1: Convert (75.3)₈ = ( ? )₁₀

示例1：轉換(75.3) ₈ =(？) ₁₀

Solution:

解：

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

我們將每個位乘以相應的位置權重，然后將它們加在一起以獲得結果。

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：轉換(624.712) ₈ =(？) ₁₀

Solution:

解：

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

我們將每個位乘以相應的位置權重，然后將它們加在一起以獲得結果。

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：轉換(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.

給定數字(482.31) ₈不是八進制數字，因為八進制數字的范圍是從0到7，并且給定數字包括8。因此，不能將其轉換為十進制數字 。

3)將八進制數制轉換為十六進制數制 (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

八進制數到十六進制的轉換只能使用某個確定的路徑來完成。 我們首先必須將八進制數轉換為二進制數，然后將二進制數轉換為十六進制數，即八進制數→二進制數→十六進制數

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

示例1：將(35.7) ₈轉換為(？) ₁₆

Solution:

解：

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

步驟1：將八進制數轉換為二進制數。
因此， (35.7) ₈ =(011101.111) ₂

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

步驟2：將二進制數轉換為十六進制數。
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：要知道如何將二進制數轉換為十六進制數，請閱讀： 將二進制數轉換為十六進制數 。

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

示例2：將(73.2) ₈轉換為(？) ₁₆

Solution:

解：

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

步驟1：將八進制數轉換為二進制數。
因此， (73.2) ₈ =(111011.010) ₂

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

步驟2：將二進制數轉換為十六進制數。
因此， (111011.010) ₂ =(3B.4) ₁₆

Therefore, (73.2)₈ = (3B.4)₁₆

因此， (73.2) ₈ =(3B.4) ₁₆

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

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