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	Decimal
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.

Save or share this article