Digital-electronics 简明教程

Digital Electronics - Code Conversion

在数字电子中，我们会根据数字系统的规格使用不同类型的二进制代码。为了不同数字系统之间适当的数据交换，会执行一个称为 code conversion 的基本过程。

In digital electronics, we use different types of binary codes depending on the specifications of the digital systems. For proper data exchange among different digital systems, an essential process is carried out called code conversion.

代码转换是将一种格式的数字代码转换为另一种格式的过程。代码转换被认为是计算机、微控制器、通信系统等各种数字系统中一个基本的过程。

Code conversion is the process of converting a digital code from one format to another. Code conversion is considered an essential process in various digital systems like computers, microcontrollers, communication systems, etc.

在本章中，我们将学习以下主要代码转换 -

In this chapter, we will study the following major code conversions −

Binary to BCD Code Conversion
BCD to Binary Code Conversion
Binary to Gray Code Conversion
Gray to Binary Code Conversion
BCD to Excess-3 Code Conversion
Excess-3 to BCD Code Conversion
Exces-3 to Gray Code Conversion
Gray to Excess-3 Code Conversion

让我们在示例的帮助下详细了解每种类型的代码转换。

Let us understand each type of code conversion in detail with the help of examples.

Binary to BCD Code Conversion

BCD 代表二进制编码十进制数。因此，BCD 是以二进制格式表示的十进制数。纯二进制到 BCD 的转换按照以下步骤进行 -

BCD stands for Binary Coded Decimal. Hence, BCD is a decimal number represented in binary format. The conversion of pure binary into BCD is done as per the following steps −

Step 1 − 将给定的纯二进制数转换为其等效的十进制数。

Step 1 − Convert the given pure binary number into its equivalent decimal number.

Step 2 − 将获得的十进制数转换为 BCD 代码。

Step 2 − Convert the obtained decimal number into BCD code.

让我们通过一个示例来理解二进制到 BCD 代码转换。

Let us understand the binary to BCD code conversion through an example.

Example

将 (100111)2 转换为 BCD 代码。

Convert (100111)2 into BCD code.

Solution

给定的二进制数是，

The given binary is,

二进制数 = 100111

Binary = 100111

给定二进制数的十进制等价数是

The decimal equivalent of given binary is

1 × 25 + 0 × 24 + 0 × 23 + 1 × 22 + 1 × 21 + 1 × 20

1 × 32 + 0 × 16 + 0 × 8 + 1 × 4 + 1 × 2 + 1 × 1

32 + 0 + 0 + 4 + 2 + 1 = (39)10

现在，将 (39)10 转换为 BCD 码，得到：

Now, converting (39)10 into BCD code, we get,

(3)10 = (0011)BCD

(9)10 = (1001)BCD

因此，给定的二进制数字的 BCD 等价为：

Thus, the BCD equivalent of the given binary number is,

(100111)2 = (0011 1001)BCD

BCD to Binary Code Conversion

如前所述，BCD 转换为二进制码的转换是二进制转换为 BCD 码转换的逆过程。

BCD to binary code conversion is the reverse process of binary to BCD code conversion as discussed previously.

BCD 转换为二进制码的转换按照以下步骤执行：

The BCD to binary code conversion is performed as per the following steps −

Step 1 - 将给定的 BCD 码转换为等效的十进制格式。

Step 1 − Convert the given BCD code into its equivalent decimal format.

Step 2 - 将获得的十进制转换为等效的二进制格式。

Step 2 − Convert the obtained decimal to the equivalent binary format.

以下示例演示了 BCD 转换为二进制码的转换。

The following example demonstrates the BCD to binary code conversion.

Example

将 (1001 0111 0010)BCD 转换为二进制码。

Convert (1001 0111 0010)BCD into binary code.

Solution

将给定的 BCD 码转换为十进制等价：

Converting the given BCD code into decimal equivalent −

(1001)BCD = (9)10

(0111)BCD = (7)10

(0010)BCD = (2)10

因此，给定 BCD 的十进制等价为：

Thus, the decimal equivalent of the given BCD is

(1001 0111 0010)BCD = (972)10

现在，将获得的十进制转换为等效的二进制：

Now, converting the obtained decimal to equivalent binary,

因此，(1001 0111 0010)BCD 的二进制等价为 (1111001100)2。

Thus, the binary equivalent of (1001 0111 0010)BCD is (1111001100)2.

Binary to Gray Code Conversion

将二进制数转换成其等效格雷码的过程称为二进制到格雷码转换。我们知道格雷码是一种二进制编码方案，其中两个连续代码只相差 1 比特。

The process of converting a binary number into its equivalent gray code is termed as binary to gray code conversion. We know that the gray code is a binary coding scheme where two successive codes are differed in one bit only.

将二进制码转换成格雷码的分步程序如下所述 -

The step-by-step procedure to convert a binary code into gray code is explained below −

考虑给定的二进制码为 Bn Bn-1 Bn-2 … B2 B1，等效的格雷码为 Gn Gn-1 Gn-2 … G2 G1。那么，

Consider the given binary code is Bn Bn-1 Bn-2 … B2 B1 and the equivalent gray code is Gn Gn-1 Gn-2 … G2 G1. Then,

Step 1 - 将二进制码的最重要比特 (MSB) 或最左边的比特 (Bn) 写为格雷码的最左边的比特 (Gn)，即

Step 1 − Write the most significant bit (MSB) or left most bit (Bn) of the binary code as the left most bit of the gray code (Gn), i.e.,

Gn = Bn

Step 2 - 异或二进制码的 MSB (Bn) 和下一个比特 (Bn-1)。将结果记录为格雷码的下一个比特 (Gn-1)，即

Step 2 − XOR the MSB (Bn) and the next bit(Bn-1) of the binary code. Record the result as the next bit of the gray code (Gn-1) i.e.,

\mathrm{G_{n-1} \: = \: B_{n} \oplus B_{n-1}}

Step 3 - 异或下一个比特 Bn-1 和 Bn-2，将结果记录为格雷码的下一个比特 (Gn-2)，即

Step 3 − XOR the next bits Bn-1 and Bn-2, record the result as the next bit of the gray code (Gn-2), i.e.,

\mathrm{G_{n-2} \: = \: B_{n-1} \oplus B_{n-2}}

Step 4 - 重复此过程，直到给定二进制码的所有比特都用尽。获得的代码将是等效的格雷码。

Step 4 − Repeat this process until all the bits of the given binary code are exhausted. The obtained code will be the equivalent gray code.

让我们借助一个示例来理解二进制到格雷码的转换。

Let us understand the conversion of binary to gray code with the help of an example.

Example

将 (110110)2 转换成其等效的格雷码。

Convert (110110)2 into its equivalent gray code.

Solution

给定的二进制码是，

The given binary code is,

二进制 = 110110

Binary = 110110

将给定的二进制转换成其等效的格雷码，

Converting the given binary into its equivalent gray code,

因此，等效的格雷码 (101101)gray

Hence, the equivalent gray code (101101)gray

Gray to Binary Code Conversion

将格雷码转换成其等效二进制码的过程称为格雷到二进制码转换。根据以下步骤将给定的格雷码转换为等效的二进制码 -

The process of translating a gray code into its equivalent binary code is called gray to binary code conversion. The conversion of a given gray code into the equivalent binary code is done as per the following steps −

考虑给定的格雷码是 Gn Gn-1 Gn-2 … G2 G1，二进制码是 Bn Bn-1 Bn-2 … B2 B1。那么，

Consider the given gray code is Gn Gn-1 Gn-2 … G2 G1 and the binary code is Bn Bn-1 Bn-2 … B2 B1. Then,

Step 1 - 等效二进制码的最左边的比特或 MSB 与格雷码的 MSB 相同，因此，复制它，即

Step 1 − The left most bit or MSB of the equivalent binary code is same as the MSB of the gray code, thus, copy it, i.e.,

Bn = Gn

Step 2 - 按位异或二进制数 Bn 的最高有效位和格雷码的下一个有效位 (Gn-1)。将其记录为二进制数的下一个有效位，即

Step 2 − XOR the MSB of the binary number Bn and the next significant bit of the gray code (Gn-1). Record it as the next significant bit of the binary number, i.e.,

\mathrm{B_{n-1} \: = \: B_{n} \oplus G_{n-1}}

Step 3 - 按位异或位 Bn-1 和格雷码的下一个有效位 (Gn-2)。将结果记录为二进制数的下一个有效位，即

Step 3 − XOR the bit Bn-1 and the next significant bit of the gray code (Gn-2). Record the result as the next significant bit of the binary number, i.e.,

\mathrm{B_{n-2} \: = \: B_{n-1} \oplus G_{n-2}}

Step 4 - 继续此过程，直到所有格雷码位用尽。所获得的位序列将是给定格雷码的纯二进制代码等效项。

Step 4 − Continue this process until all the gray code bits are exhausted. The obtained sequence of bits will be the pure binary code equivalent of the given gray code.

让我们举个例子来了解格雷码到等效二进制码的转换。

Let us take an example to understand the conversion of gray code to equivalent binary code.

Example

将格雷码 (110010)gray 转换成其等效的二进制码。

Convert the gray code (110010)gray into its equivalent binary code.

Solution

格雷码到二进制的转换如下所示 -

The conversion of gray code into binary is done as given below −

因此，(110010)gray 的二进制等效项为 (100011)2。

Hence, the binary equivalent of (110010)gray is (100011)2.

BCD to Excess-3 Code Conversion

将给定的 BCD（二进制编码十进制数）转换成其等效的补码 3 的过程称为 BCD 到补码 3 的转换。

The process of translating a given BCD (binary coded decimal) into its equivalent excess-3 code is referred to as BCD to excess-3 code conversion.

要将 BCD 代码转换成其等效的补码 3 代码，我们按照以下步骤进行 -

To convert a BCD code into its equivalent excess-3 code, we follow the steps given below −

Step 1 - 向给定 BCD 代码中的每个 4 位组中添加 0011 (3)。

Step 1 − Add 0011 (3) to each 4-bit group of given BCD code.

Step 2 - 结果代码将是等效的 XS-3 代码。

Step 2 − The resulting code will be the equivalent XS-3 code.

请务必注意，在 XS-3 代码中，有六个无效位组合。它们是 0000、0001、0010、1101、1110 和 1111。

It is important to note that in XS-3 code, there are six invalid bit combinations. They are 0000, 0001, 0010, 1101, 1110, and 1111.

让我们举一个例子来了解 BCD 到补码 3 的转换。

Let us take an example to understand the BCD to excess-3 code conversion.

Example

将 (0011 1001 1000)BCD 转换成其等效的 XS-3 代码。

Convert (0011 1001 1000)BCD into its equivalent XS-3 code.

Solution

将给定的 BCD 代码转换成其等效的 XS-3 代码如下所示 -

The conversion of given BCD code into its equivalent XS-3 code is shown below −

BCD Code	0011	1001	1000
*Adding	0011	0011	0011
0011	0011	0011	0011
0011	0011	0011	0011
0011	0011	XS-3 Code	0110

因此，(0011 1001 1000)BCD 的等效的 XS-3 代码是 (0110 1100 1011)XS-3。

Thus, the equivalent XS-3 code of (0011 1001 1000)BCD is (0110 1100 1011)XS-3.

Excess-3 to BCD Code Conversion

将给定的 XS-3 代码转换成其等效 BCD（二进制编码十进制）代码的过程称为 XS-3 到 BCD 代码转换。

The process of converting a given XS-3 code into its equivalent BCD (binary coded decimal) code is known as excess-3 to BCD code conversion.

XS-3 代码到 BCD 代码的转换按照如下步骤进行 −

The conversion of excess-3 code into BCD code is done as per the following steps −

Step 1 − 从 XS-3 代码的每个 4 位组中减去 0011 (3)。

Step 1 − Subtract 0011 (3) from the each 4-bit group of XS-3 code.

Step 2 − 结果代码将是给定 XS-3 代码的 BCD 代码等效项。

Step 2 − The resulting code will be the BCD code equivalent of the given XS-3 code.

让我们借助一个示例了解 XS-3 到 BCD 代码转换。

Let us understand the excess-3 to BCD code conversion with the help of an example.

Example

将 (1100 1001 0110)XS-3 转换成其等效 BCD 代码。

Convert (1100 1001 0110)XS-3 into its equivalent BCD code.

Solution

XS-3 代码到 BCD 代码的转换如下−

The conversion of XS-3 code to BCD code is given below −

XS-3 Code	1100	1001	0110
*Subtracting	0011	0011	0011
0011	0011	0011	0011
0011	0011	0011	0011
0011	0011	BCD Code	1001

因此，(1100 1001 0110)XS-3 的等效 BCD 代码为 (1001 0110 0011)BCD。

Hence, the equivalent BCD code of (1100 1001 0110)XS-3 is (1001 0110 0011)BCD.

Conclusion

总之，代码转换是将二进制代码从一种格式转换为另一种格式的过程。例如，我们可以将 BCD 代码转换成其等效的纯二进制代码，或将 XS-3 代码转换成其等效的 BCD 代码等。在本章中，我们解释了不同类型的代码转换。

In conclusion, code conversion is the process of converting a binary code from one format to another. For example, we can convert a BCD code into its equivalent pure binary code, or an XS-3 code into its equivalent BCD code, etc. In this chapter, we explained different types of code conversion.