Digital-electronics 简明教程
BCD to Excess-3 Converter
数字电子学中用于将二进制编码十进制数转换为等效的超 3 代码的一种代码转换器称为 BCD to excess-3 converter 。
A type of code converter in digital electronics that is used to convert a binary-coded decimal number into an equivalent excess-3 code is called a BCD to excess-3 converter.
因此，在 BCD 到超 3 代码转换器的情况下，输入为 8421 BCD 代码，输出为 XS-3 代码。
Hence, in the case of a BCD to excess-3 code converter, the input is an 8421 BCD code and the output is an XS-3 code.
以下是 BCD 到超 3 代码转换器的真值表 -
The following is the truth table of a BCD to excess-3 code converter −
BCD Code |
Excess-3 Code |
B3 |
B2 |
B1 |
B0 |
X3 |
X2 |
X1 |
X0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
1 |
1 |
0 |
1 |
1 |
0 |
0 |
1 |
0 |
0 |
0 |
1 |
1 |
1 |
0 |
1 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
0 |
1 |
0 |
1 |
1 |
1 |
1 |
0 |
1 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
1 |
1 |
1 |
0 |
0 |
1 |
1 |
1 |
0 |
0 |
1 |
0 |
1 |
0 |
X |
X |
X |
X |
1 |
0 |
1 |
1 |
X |
X |
X |
X |
1 |
1 |
0 |
0 |
X |
X |
X |
X |
1 |
1 |
0 |
1 |
X |
X |
X |
X |
1 |
1 |
1 |
0 |
X |
X |
X |
X |
1 |
1 |
1 |
1 |
X |
X |
X |
X |
让我们使用卡诺图求解真值表，以便导出 XS-3 输出位 X0、X1、X2 和 X3 的布尔表达式。
Let us solve the truth table using the K-map to derive the Boolean expressions for the XS-3 output bits X0, X1, X2, and X3.
K-Map for XS-3 Bit X0
XS-3 位 X0 的卡诺图化简如下所示 -
The K-map simplification for the XS-3 bit X0 is shown in the following figure −
化简这个卡诺图，我们得到以下布尔表达式：
On simplifying this K-map, we obtain the following Boolean expression,
\mathrm{X_{0} \: = \: \overline{B_{0}}}
K-Map for XS-3 Bit X1
XS-3 位 X1 的卡诺图化简如下所示 -
The K-map simplification for the XS-3 bit X1 is depicted below −
这个卡诺图化简给出以下布尔表达式：
This K-map simplification gives the following Boolean expression,
\mathrm{X_{1} \: = \: \overline{B_{1}} \: \overline{B_{0}} \: + \: B_{1} \: B_{0}}
K-Map for XS-3 Bit X2
XS-3 位 X2 的卡诺图化简如下图所示。
The K-map simplification for the XS-3 bit X2 is shown in the figure below.
化简这个卡诺图，我们得到以下布尔表达式：
On simplifying this K-map, we obtain the following Boolean expression,
\mathrm{X_{2} \: = \: B_{2} \: B_{1} \: + \: \overline{B_{2}} \: B_{0} \: + \: B_{2} \: \overline{B_{1}} \: \overline{B_{0}}}
K-Map for XS-3 Bit X3
XS-3 位 X3 的卡诺图化简如下图所示 −
The K-map simplification for the XS-3 bit X3 is depicted in the figure below −
这个卡诺图得到以下布尔表达式：
This K-map gives the following Boolean expression,
\mathrm{X_{3} \: = \: B_{3} \: + \: B_{2} \: B_{1} \: + \: B_{2} \: B_{0}}
BCD 转 XS-3 转换器的逻辑电路图如下图所示 −
The logic circuit diagram of the BCD to XS-3 converter is shown in the following figure −
此电路将 4 位 BCD 代码转换为等效的 XS-3 代码。
This circuit converters a 4-bit BCD code into an equivalent XS-3 code.