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BCD to Decimal Converter
A digital circuit that can convert a binary-coded decimal (BCD) number into an equivalent decimal number is referred to as a BCD-to-decimal converter.
The input to a BCD to decimal converter is an 8421 BCD code and the output generated by the converter is a decimal number.
The following is the truth table of the BCD to decimal converter describing its operation.
| BCD Code | Decimal | |||
|---|---|---|---|---|
| B3 | B2 | B1 | B0 | |
| 0 | 0 | 0 | 0 | D0 |
| 0 | 0 | 0 | 1 | D1 |
| 0 | 0 | 1 | 0 | D2 |
| 0 | 0 | 1 | 1 | D3 |
| 0 | 1 | 0 | 0 | D4 |
| 0 | 1 | 0 | 1 | D5 |
| 0 | 1 | 1 | 0 | D6 |
| 0 | 1 | 1 | 1 | D7 |
| 1 | 0 | 0 | 0 | D8 |
| 1 | 0 | 0 | 1 | D9 |
We can derive the Boolean expressions for each of the decimal outputs in terms of 8421 BCD code. These Boolean expressions are given below −
$$\mathrm{D_{0} \: = \: \overline{B_{3}} \: \overline{B_{2}} \: \overline{B_{1}} \: \overline{B_{0}}}$$
$$\mathrm{D_{1} \: = \: \overline{B_{3}} \: \overline{B_{2}} \: \overline{B_{1}} \: B_{0}}$$
$$\mathrm{D_{2} \: = \: \overline{B_{3}} \: \overline{B_{2}} \: B_{1} \: \overline{B_{0}}}$$
$$\mathrm{D_{3} \: = \: \overline{B_{3}} \: \overline{B_{2}} \: B_{1} \: B_{0}}$$
$$\mathrm{D_{4} \: = \: \overline{B_{3}} \: B_{2} \: \overline{B_{1}} \: \overline{B_{0}}}$$
$$\mathrm{D_{5} \: = \: \overline{B_{3}} \: B_{2} \: \overline{B_{1}} \: B_{0}}$$
$$\mathrm{D_{6} \: = \: \overline{B_{3}} \: B_{2} \: B_{1} \: \overline{B_{0}}}$$
$$\mathrm{D_{7} \: = \: \overline{B_{3}} \: B_{2} \: B_{1} \: B_{0}}$$
$$\mathrm{D_{8} \: = \: B_{3} \: \overline{B_{2}} \: \overline{B_{1}} \: \overline{B_{0}}}$$
$$\mathrm{D_{9} \: = \: B_{3} \: \overline{B_{2}} \: \overline{B_{1}} \: B_{0}}$$
The logic circuit implementation of the BCD to decimal converter is shown in the following figure.
