Digital-electronics 简明教程

What is Excess-3 Code?

Excess-3 code 为非加权 BCD（二进制编码十进制数）编码。由于它是通过向 8421 BCD 编码添加 0011 (3) 获得的，因此称为 XS-3 编码。XS-3 编码也称为附加 3 编码，是一种将每个十进制数位表示为 4 位二进制编码的 BCD 编码。

Excess-3 code is a non-weighted BCD (Binary Coded Decimal) code. It is called excess-3 code because it is obtained by adding 0011 (3) to the 8421 BCD code. Also called XS-3, the excess 3 code is a BCD code that represents each decimal digit as a 4-bit binary code.

附加 3 二进制编码是一种顺序编码，因此我们可以使用它执行算术运算。它还是一种自补码，所以与 8421 BCD 编码相比，使用补码方法的减法运算更为简单。

The excess-3 binary code is a sequential code, so we can use it to perform arithmetic operations. Also, it is a self-complementing code, therefore the subtraction operation by the complement method is simpler than that in the 8421 BCD code.

然而，在附加 3 编码中，有六个无效编码，即 0000、0001、0010、1110 和 1111。

However, in the excess-3 code, there are six invalid codes, they are 0000, 0001, 0010, 1110, and 1111.

How to Obtain Excess-3 Code?

我们可以通过向自然 8421 BCD 编码添加 0011 (3) 来获得附加 3 编码。这里加以解释：

We can obtain the excess-3 code by adding 0011 (3) to the natural 8421 BCD code. It is explained here −

Decimal digit = 0
8421 BCD code = 0000
Excess-3 code = 0000 + 0011 = 0011

Decimal digit = 1
8421 BCD code = 0001
Excess-3 code = 0001 + 0011 = 0100

同样，我们可以获得适用于所有十进制数字的附加 3 编码。

Similarly, we can obtain the excess-3 code for all the decimal digits.

下列表格显示了每个十进制数字的附加 3 编码：

The following table shows the excess-3 code for each decimal digit −

Decimal Digit	Excess-3 Code
0	0011
1	0100
2	0101
3	0110
4	0111
5	1000
6	1001
7	1010
8	1011
9	1100

Note − 当今，附加 3 编码并不普遍使用。它主要用于早期的数字系统中。现在，许多其他先进高效的二进制编码正被用来取代附加 3 编码。

Note − The Excess-3 code is not so widely used today. It was mainly used in early digital systems. Nowadays, many other advanced and efficient binary codes are being used in place of the excess-3 code.

Importance of Excess-3 Code in Digital Electronics

附加 3 编码是早期数字系统中广泛使用的二进制编码之一。以下是附加 3 编码在数字电子领域使用的几个关键原因：

Excess-3 code is one of the widely used binary codes in early digital systems. Here are some of the key reasons why excess-3 code was used in the field of digital electronics −

It provides a simplified way of converting a decimal number into binary code.
It has self-complementing property that makes it suitable for error detection and correction applications.
It is sequential code, hence it can be used to perform arithmetic operations in digital systems.
Excess-3 code is highly compatible with decimal IO devices. Thus, it provides a convenient interface between digital systems and other devices.

Advantages of Excess-3 Code

然而，在现代数字系统中，超3编码不太常见。但它具有以下关于其他二进制编码方案的主要优点——

Although, the excess-3 code is less common in modern digital systems. But it has the following key benefits over other binary coding schemes −

Excess-3 code provides an easy method of representing decimal numbers in binary form.
Excess-3 code provides an easier way of performing addition and subtraction operations without using any complex conversion methods.
Excess-3 code is quite easy to convert to and from decimal numbers.
Excess-3 code being a binary-coded decimal is highly compatible with a wide range of decimal devices.

Disadvantages of Excess-3 Code

超3编码有几个优点，但也有某些缺点，这就是它在现代数字系统中不太常用的原因。以下是一些超3编码的主要缺点——

Excess-3 code has several advantages, but it also has certain disadvantages as well that’s why it is less commonly used in modern digital systems. The following are some key disadvantages of excess-3 code −

Excess-3 code is an inefficient binary representation of decimal numbers as compared to pure binary. This is because it requires more bits to represent a decimal digit.
Excess-3 code requires additional arithmetic circuit to add 3 to the standard binary code.
Excess-3 code has limited compatibility with pure binary systems.

Applications of Excess-3 Code

超3编码广泛用于早期数字系统和数字计算机。超3编码应用程序的关键领域如下所示——

Excess-3 code was widely used in early digital systems and digital computers. The key areas of excess-3 code applications are listed below −

Excess-3 code was used in early digital computers.
Excess-3 code is also used in decimal data processing through digital systems.
Excess-3 code is also used in digital devices likes printers, card readers, etc. where decimal data is employed.
The self-complementing property of excess-3 code makes it suitable to use in error detection and correction applications.
Excess-3 code is also communication and data transmission applications.

Excess-3 Addition

在超3加法中，从LSD（最低有效位）开始，我们在每一列中添加4位组。

In excess-3 addition, starting from LSD (least significant digit), we add the 4-bit group in each column.

如果在对 4 位组进行加法时未生成进位，我们必须将 0011 从和中减去才能得到结果。这是因为，没有进位意味着结果为 XS-6 格式。因此，我们可以通过将 0011 加到和中得到正确的和。

If no end-around carry is generated from the addition of 4-bit group, we have to subtract 0011 from the sum term to obtain the result. This is because, no carry means the result is in XS-6 format. Thus, we obtain the correct sum by adding 0011 to the sum term.

如果在加法中生成了环绕进位，我们必须将 0011 加到和中才能得到准确的结果。这是因为，进位表明和为无效的 3 进制超额码，可以通过将 0011 计入和中进行修正。

If an end-around carry is produced from the addition, we have to add 0011 to the sum term to obtain the corrected result. This is because the carry out represents that the sum term is an invalid excess-3 code, which is corrected by adding 0011 to the sum term.

让我们通过一个示例，了解一下 XS-3 加法。

Let us understand the XS-3 addition with the help of examples.

Example

在 XS-3 代码中加 35 和 28。

Add 35 and 28 in XS-3 code.

Solution

给定的十进制数和它们的 XS-3 代码为：

The given decimal numbers and their XS-3 code are

35 = 0110 1000

28 = 0101 1011

在加 XS-3 代码后，

Adding the XS-3 codes,

因此，35 和 28 在 XS-3 中的正确和为 1001 0110，在十进制中为 63。

Hence, the correct sum of 35 and 28 is 1001 0110 in XS-3 and 63 in decimal.

Excess-3 Subtraction

在 XS-3 减法中，从最低有效位开始，我们通过从被减数的 4 位组中减去减数的每个 4 位组来找到两个数字的差值。

In the XS-3 subtraction, starting from the least significant digit, we find the difference of two numbers by subtracting each group of 4-bits of subtrahend from he corresponding 4-bit group of the minuend.

在 XS-3 减法中，如果高 4 位组没有借位，则我们向差分项中添加 0011 来得到纠正的结果。这是因为，如果没有借位，则结果为法线二进制，必须通过添加 0011 来将其转换为 XS-3。

In the XS-3 subtraction, if there is no borrow from the higher 4-bit group, then we add 0011 to the difference term to obtain the corrected result. This is because if there is no borrow, then the result is in the normal binary that has to be converted into XS-3 by adding 0011 to it.

如果从下一个 4 位组中借了一位，则差分项将是无效的 XS-3 代码，可以通过从中减去 0011 来对其进行更正。

If a borrow is taken from the next 4-bit group, then the difference term will be an invalid XS-3 code which is corrected by subtracting 0011 from it.

让我们通过一个已解决的示例来了解 XS-3 减法。

Let us understand the XS-3 subtraction through a solved example.

Example

在 XS-3 代码中从 56 中减去 28。

Subtract 28 from 56 in XS-3 code.

Solution

给定，

Given,

被减数 = (56)10 = (1000 1001)XS-3

Minuend = (56)10 = (1000 1001)XS-3

减数 = (28)10 = (0101 1011)XS-3

Subtrahend = (28)10 = (0101 1011)XS-3

在 XS-3 代码中减去，我们得到：

Subtracting in the XS-3 code, we get,

因此，数字 56 和 28 的更正后的差为 0101 1011，XS-3 代码中的差为 28。

Hence, the corrected difference of the numbers 56 and 28 is 0101 1011 in XS-3 code and 28 in decimal.

Conclusion

总之，3 进制超码 (XS-3) 是在旧数字系统中广泛使用的二进制编码方案。它基本上是 BCD 方案，用于以二进制格式表示十进制数字。

In conclusion, the Excess-3 (XS-3) code is a binary coding scheme widely used in old digital systems. It is basically a BCD scheme used to represent decimal digits in binary format.

在现代数字系统中，过度 3 码被更有效的二进制码所取代，例如 8421 BCD 码、ASCII 码等。

In modern digital systems, the excess-3 code is replaced by more efficient binary codes like 8421 BCD code, ASCII code, etc.