Digital-electronics 简明教程

Excess-3 to BCD Converter

XS-3 到 BCD 转换器是一种数字电子设备中的代码转换器类型，用于将 XS-3 代码转换为等效的二进制编码十进制数。

An excess-3 to BCD converter is a type of code converter in digital electronics used to translate an XS-3 code into an equivalent binary-coded decimal.

因此，XS-3 到 BCD 代码转换器接受 XS-3 格式的数字代码，并生成 BCD 格式的等效数字代码。

Therefore, an XS-3 to BCD code converter accepts a digital code in XS-3 format and produces an equivalent digital code in BCD format.

XS-3 到 BCD 码转换器的真值表如下所示 -

The truth table of the XS-3 to BCD code converter is given below −

Excess-3 Code	BCD Code
X3	X2
X1	X0
B3	B2
B1	B0
0	0
0	0
X	X
X	X
0	0
0	1
X	X
X	X
0	0
1	0
X	X
X	X
0	0
1	1
0	0
0	0
0	1
0	0
0	0
0	1
0	1
0	1
0	0
1	0
0	1
1	0
0	0
1	1
0	1
1	1
0	1
0	0
1	0
0	0
0	1
0	1
1	0
0	1
0	1
1	0
1	0
1	0
0	1
1	1
1	0
1	1
1	0
0	0
1	1
0	0
1	0
0	1
1	1
0	1
X	X
X	X
1	1
1	0
X	X
X	X
1	1
1	1
X	X
X	X

现在，我们将使用 K-map 方法化简此真值表，以获得输出位的布尔表达式。

Now, we will simplify this truth table using K-map method to obtain the Boolean expression for the output bits.

K-Map for BCD Bit B0

下图显示了 BCD 位 B0 的 K-map 简化。

The following figure shows the K-map simplification for the BCD bit B0.

这个卡诺图得到以下布尔表达式：

This K-map gives the following Boolean expression,

\(\mathrm{B_{0} \: = \: \overline{X_{0}}} \)

\mathrm{B_{0} \: = \: \overline{X_{0}}}

K-Map for BCD Bit B1

下图显示了 BCD 位 B1 的 K-map 简化。

The following figure shows the K-map simplification for the BCD bit B1.

这个卡诺图得到以下布尔表达式：

This K-map gives the following Boolean expression,

\(\mathrm{B_{1} \: = \: \overline{X_{1}} \: X_{0} \: + \: X_{1} \: X_{0}}\)

\mathrm{B_{1} \: = \: \overline{X_{1}} \: X_{0} \: + \: X_{1} \: X_{0}}

K-Map for BCD Bit B2

BCD 位 B2 的 K-map 简化如下所示 -

The K-map simplification for the BCD bit B2 is shown below −

此 K-map 的简化给出了以下布尔表达式，

The simplification of this K-map gives the following Boolean expression,

\(\mathrm{B_{2} \: = \: \overline{X_{2}} \: \overline{X_{1}} \: + \: \overline{X_{2}} \: \overline{X_{0}} \: + \: X_{2} \: X_{1} \: X_{0}}\)

\mathrm{B_{2} \: = \: \overline{X_{2}} \: \overline{X_{1}} \: + \: \overline{X_{2}} \: \overline{X_{0}} \: + \: X_{2} \: X_{1} \: X_{0}}

K-Map for BCD Bit B3

BCD 位 B3 的 K-map 简化如下图所示 -

The K-map simplification for the BCD bit B3 is shown in the following figure −

通过简化此 K-map，我们得到以下布尔表达式，

By simplifying this K-map, we obtain the following Boolean expression,

\(\mathrm{B_{3} \: = \: X_{3} \: X_{2} \: + \: X_{3} \: X_{1} \: X_{0}}\)

\mathrm{B_{3} \: = \: X_{3} \: X_{2} \: + \: X_{3} \: X_{1} \: X_{0}}

我们可以使用这些布尔表达式来实现数字逻辑电路，以执行 XS-3 到 BCD 的转换。

We can use these Boolean expressions to implement the digital logic circuit to perform the XS-3 to BCD conversion.

将 XS-3 码转换为等效 BCD 码的逻辑电路图（即过度 3 到 BCD 转换器）如下图所示 -

The logic circuit diagram to convert an XS-3 code into equivalent BCD code i.e., Excess-3 to BCD converter is shown in the following figure −

这是有关各种数字电子应用中常用的一些数字码转换器的全部内容。

This is all about some commonly used digital code converters used in various digital electronic applications.