余3码 到 BCD 转换器

余3码 到 BCD 转换器是数字电子中的一种代码转换器，用于将 XS-3 代码转换为等效的二进制编码十进制。

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等效的 BCD 格式的数字代码。

XS-3 到 BCD 代码转换器的真值表如下所示 −

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

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

This K-map gives the following Boolean expression,

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

K-Map for BCD Bit B₁

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

This K-map gives the following Boolean expression,

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

K-Map for BCD Bit B₂

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

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

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

K-Map for BCD Bit B₃

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

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

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

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

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 −

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