十六进制数制到二进制，八进制和十进制数制的转换

小灰灰 2023-03-05 05:29 2阅读 0赞

**Prerequisite:** [Number systems][]

**先决条件：** [数字系统][Number systems]

### 1)将十六进制数制转换为二进制数制 **(**1) Conversion of Hexadecimal Number System to Binary Number System**)** ###

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

要将十六进制数转换为二进制数，我们可以使用十六进制和二进制数之间的关系。

<table> 
 <tbody> 
  <tr> 
   <th>Decimal</th> 
   <th>Hexadecimal</th> 
   <th>Binary</th> 
  </tr> 
  <tr> 
   <td> 0</td> 
   <td>0</td> 
   <td>0000</td> 
  </tr> 
  <tr> 
   <td> 1</td> 
   <td>1</td> 
   <td>0001</td> 
  </tr> 
  <tr> 
   <td> 2</td> 
   <td>2</td> 
   <td>0010</td> 
  </tr> 
  <tr> 
   <td> 3</td> 
   <td>3</td> 
   <td>0011</td> 
  </tr> 
  <tr> 
   <td> 4</td> 
   <td>4</td> 
   <td>0100</td> 
  </tr> 
  <tr> 
   <td> 5</td> 
   <td>5</td> 
   <td>0101</td> 
  </tr> 
  <tr> 
   <td> 6</td> 
   <td>6</td> 
   <td>0110</td> 
  </tr> 
  <tr> 
   <td> 7</td> 
   <td>7</td> 
   <td>0111</td> 
  </tr> 
  <tr> 
   <td> 8</td> 
   <td>8</td> 
   <td>1000</td> 
  </tr> 
  <tr> 
   <td> 9</td> 
   <td>9</td> 
   <td>1001</td> 
  </tr> 
  <tr> 
   <td>10</td> 
   <td>A</td> 
   <td>1010</td> 
  </tr> 
  <tr> 
   <td>11</td> 
   <td>B</td> 
   <td>1011</td> 
  </tr> 
  <tr> 
   <td>12</td> 
   <td>C</td> 
   <td>1100</td> 
  </tr> 
  <tr> 
   <td>13</td> 
   <td>D</td> 
   <td>1101</td> 
  </tr> 
  <tr> 
   <td>14</td> 
   <td>E</td> 
   <td>1110</td> 
  </tr> 
  <tr> 
   <td>15</td> 
   <td>F</td> 
   <td>1111</td> 
  </tr> 
 </tbody> 
</table>

**Example 1: Convert (7A.2C)16 into ( ? )2**

**示例1：将(7A.2C) 16转换为(？) 2**

**Solution:**

**解：**

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

使用上面提供的表，我们可以将十六进制数字替换为它们的等效二进制数字。

Therefore, **(7A.2C)16 = (0111 1010.0010 1100)2**

因此， **(7A.2C) 16 =(0111 1010.0010 1100) 2**

**Example 2: Convert (D2A.2B7)16 into ( ? )2**

**示例2：将(D2A.2B7) 16转换为(？) 2**

**Solution:**

**解：**

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

使用上面提供的表，我们可以将十六进制数字替换为它们的等效二进制数字。

Therefore, **(D2A.2B7)16 = (1101 0010 1010.0010 1011 0111)2**

因此， **(D2A.2B7) 16 =(1101 0010 1010.0010 1011 0111) 2**

**Example 3: Convert (FF18.5E5)16 into ( ? )2**

**示例3：将(FF18.5E5) 16转换为(？) 2**

**Solution:**

**解：**

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

使用上面提供的表，我们可以将十六进制数字替换为它们的等效二进制数字。

Therefore, **(FF18.5E5)16 = (1111 1111 0001 1000. 0101 1110 0101)2**

因此， **(FF18.5E5) 16 =(1111 1111 0001 1000. 0101 1110 0101) 2**

### 2)将十六进制数制转换为八进制数制 **(**2) Conversion of Hexadecimal Number System into Octal Number System**)** ###

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

可以使用某个确定的路径将十六进制数转换为八进制数。 我们首先必须将十六进制数转换为二进制数，然后将二进制数转换为八进制数，即**十六进制数→二进制数→八进制数**

**Example 1: Convert (1D.E)16 into ( ? )8**

**示例1：将(1D.E) 16转换为(？) 8**

**Solution:**

**解：**

**Step 1:** Converting the first hexadecimal number into a binary number. Thus, **(1D.E)16 = (0001 1101.1110)2**

**步骤1：**将第一个十六进制数转换为二进制数。 因此， **(1D.E) 16 =(0001 1101.1110) 2**

**Step 2:** Now, converting the binary number into an octal number which gives **(00011101.1110)2 = (35.7)8**

**步骤2：**现在，将二进制数转换为八进制数，得出**(00011101.1110) 2 =(35.7) 8**

Therefore, **(1D. E)16 = (35.7)8**

因此**(1D.E) 16 =(35.7) 8**

**Note:** To know how to convert binary number into octal number? Read: [conversion of Binary number system to octal number system][].

**注意：**要知道如何将二进制数转换为八进制数？ 阅读： [将二进制数制转换为八进制数制][conversion of Binary number system to octal number system] 。

**Example 2: Convert (3B.4)16 into ( ? )8**

**示例2：将(3B.4) 16转换为(？) 8**

**Solution:**

**解：**

**Step 1:** Converting the first hexadecimal number into a binary number. Thus, **(3B.4)16 = (0011 1011.0100)2**

**步骤1：**将第一个十六进制数转换为二进制数。 因此， **(3B.4) 16 =(0011 1011.0100) 2**

**Step 2:** Now, converting the binary number into an octal number which gives **(0011 1011.0100)2 = (73.20)8**

**步骤2：**现在，将二进制数转换为八进制数，得出**(0011 1011.0100) 2 =(73.20) 8**

Therefore, **(3B.4)16 = (73.20)8**

因此， **(3B.4) 16 =(73.20) 8**

### 3)将十六进制数系统转换为十进制数系统 **(**3) Conversion of Hexadecimal Number System to Decimal Number System**)** ###

Conversion of hexadecimal 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十六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 hexadecimal number, the weights follow the pattern as **160**, **161**, **162**, **163**, **164**, **165** and so on from right to left.
    
    在十六进制数的一个组成部分，权重按照图案**16 0，16** **1，16 2，16** **3，16 4，16** **5**等从右到左。
    
    In the fractional part of the hexadecimal number, the weights follow the pattern as **16\-1**, **16\-2**, **16\-3**, **16\-4**, **16\-5** and so on from left to right.
    
    在十六进制数的小数部分，权重按照图案**16 \-1，16** **-2，16 \-3，16** **-4，16 \-5**等从左到右。
    
    Only thing to be kept in mind is **A = 10**, **B = 11**, **C = 12**, **D = 13**, **E = 14**, **F = 15**.
    
    唯一要记住的是**A = 10** ， **B = 11** ， **C = 12** ， **D = 13** ， **E = 14** ， **F = 15** 。

**Example 1: Convert (75.3)16 into ( ? )10**

**示例1：将(75.3) 16转换为(？) 10**

**Solution:**

**解：**

(75.3)16    = 7 * 161 + 5 * 160 + 3 * 16-1
                    = 112 + 5 + 0.1875 = (117.1875)10

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)16 = (117.1875)10**

因此， **(75.3) 16 =(117.1875) 10**

**Example 2: Convert (CD3.B70A)16 into ( ? )10**

**示例2：将(CD3.B70A) 16转换为(？) 10**

**Solution:**

**解：**

(CD3.B70A)16    = C*162 + D*161 + 3*160 + B*16-1 + 7*16-2 + 0*16-3 + A*16-4
                        = 12*256 + 13*16 + 3*1 + 11/16 + 7/256 + 0 + 10/65536
                        = 3072+ 208 + 3 + 0.6875 + 0.0273 + 0.0001
                        = (3283.7149)10

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, **(CD3.B70A)16 = (3283.7149)10**

因此， **(CD3.B70A) 16 =(3283.7149) 10**

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

[Number systems]: https://www.includehelp.com/computer-number-systems.aspx
[conversion of Binary number system to octal number system]: https://www.includehelp.com/basics/conversion-of-binary-number-system-into-octal-number-system.aspx
[https_www.includehelp.com_basics_conversion-of-hexadecimal-number-system-to-binary-octal-and-decimal-number-systems.aspx]: https://www.includehelp.com/basics/conversion-of-hexadecimal-number-system-to-binary-octal-and-decimal-number-systems.aspx