1)將八進(jìn)制數(shù)制轉(zhuǎn)換為二進(jìn)制數(shù)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(jìn)制數(shù)轉(zhuǎn)換為二進(jìn)制數(shù)，我們可以使用八進(jìn)制數(shù)和二進(jìn)制數(shù)之間的關(guān)系。

Octal NumberBinary Number

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

八進(jìn)制數(shù) 二進(jìn)制數(shù)

0	000
1個(gè)	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(zhuǎn)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(jìn)制數(shù)字替換為其等效的二進(jìn)制數(shù)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(zhuǎn)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(jìn)制數(shù)字替換為其等效的二進(jìn)制數(shù)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(jìn)制數(shù)制轉(zhuǎn)換為十進(jìn)制數(shù)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(quán)重將八進(jìn)制數(shù)轉(zhuǎn)換為十進(jìn)制數(shù)，方法是將位置權(quán)重乘以相應(yīng)的位，然后將它們?nèi)考釉谝黄鹨垣@得十進(jìn)制數(shù)。

• 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(jìn)制數(shù)的一個(gè)組成部分，權(quán)重按照?qǐng)D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(jìn)制數(shù)的小數(shù)部分，權(quán)重按照?qǐng)D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(zhuǎn)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(gè)位乘以相應(yīng)的位置權(quán)重，然后將它們加在一起以獲得結(jié)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(zhuǎn)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(gè)位乘以相應(yīng)的位置權(quán)重，然后將它們加在一起以獲得結(jié)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(zhuǎn)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(shù)字(482.31) ₈不是八進(jìn)制數(shù)字，因?yàn)榘诉M(jìn)制數(shù)字的范圍是從0到7，并且給定數(shù)字包括8。因此，不能將其轉(zhuǎn)換為十進(jìn)制數(shù)字 。

3)將八進(jìn)制數(shù)制轉(zhuǎn)換為十六進(jìn)制數(shù)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(jìn)制數(shù)到十六進(jìn)制的轉(zhuǎn)換只能使用某個(gè)確定的路徑來(lái)完成。 我們首先必須將八進(jìn)制數(shù)轉(zhuǎn)換為二進(jìn)制數(shù)，然后將二進(jìn)制數(shù)轉(zhuǎn)換為十六進(jìn)制數(shù)，即八進(jìn)制數(shù)→二進(jìn)制數(shù)→十六進(jìn)制數(shù)

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

示例1：將(35.7) ₈轉(zhuǎn)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(jìn)制數(shù)轉(zhuǎn)換為二進(jìn)制數(shù)。
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(jìn)制數(shù)轉(zhuǎn)換為十六進(jìn)制數(shù)。
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(jìn)制數(shù)轉(zhuǎn)換為十六進(jìn)制數(shù)，請(qǐng)閱讀： 將二進(jìn)制數(shù)轉(zhuǎn)換為十六進(jìn)制數(shù) 。

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

示例2：將(73.2) ₈轉(zhuǎn)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(jìn)制數(shù)轉(zhuǎn)換為二進(jìn)制數(shù)。
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(jìn)制數(shù)轉(zhuǎn)換為十六進(jìn)制數(shù)。
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

總結(jié)

以上是生活随笔為你收集整理的将八进制数制转换为二进制，十进制和十六进制数制的全部?jī)?nèi)容，希望文章能夠幫你解決所遇到的問(wèn)題。

如果覺(jué)得生活随笔網(wǎng)站內(nèi)容還不錯(cuò)，歡迎將生活随笔推薦給好友。