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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.
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.
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 |
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
The K-map simplification for the XS-3 bit X0 is shown in the following figure −
On simplifying this K-map, we obtain the following Boolean expression,
$$\mathrm{X_{0} \: = \: \overline{B_{0}}}$$
K-Map for XS-3 Bit X1
The K-map simplification for the XS-3 bit X1 is depicted below −
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
The K-map simplification for the XS-3 bit X2 is shown in the figure below.
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
The K-map simplification for the XS-3 bit X3 is depicted in the figure below −
This K-map gives the following Boolean expression,
$$\mathrm{X_{3} \: = \: B_{3} \: + \: B_{2} \: B_{1} \: + \: B_{2} \: B_{0}}$$
The logic circuit diagram of the BCD to XS-3 converter is shown in the following figure −
This circuit converters a 4-bit BCD code into an equivalent XS-3 code.
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