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Excess-3 to BCD Converter
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.
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.
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 |
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.