Binary to Decimal Converter
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A type of code converter used to convert data from binary format to decimal format is called a binary-to-decimal converter.
The input to the binary-to-decimal converter is a number represented in a format of 0s and 1s. Then, the converter uses an algorithm to convert the input binary number into an equivalent decimal number. Finally, it generates a decimal code as output.
Let us now understand the logic circuit implementation of a binary-to-decimal converter.
The truth table of a two-bit binary-to-decimal converter is given below.
| Binary Input | Decimal Output | |
|---|---|---|
| B1 | B0 | |
| 0 | 0 | Q0 |
| 0 | 1 | Q1 |
| 1 | 0 | Q2 |
| 1 | 1 | Q3 |
Let us now derive the logical expression for each of the decimal outputs.
$$\mathrm{Q_{0} \: = \: \overline{B_{1}}\: cdot \:\overline{B_{0}}}$$
$$\mathrm{Q_{1} \: = \: \overline{B_{1}}\: cdot \: B_{0}}$$
$$\mathrm{Q_{2} \: = \: B_{1} \: cdot \:\overline{B_{0}}}$$
$$\mathrm{Q_{3} \: = \: B_{1} \: cdot \: B_{0}}$$
The logic circuit diagram of the binary-to-decimal converter is shown in the following figure.
This circuit converts a 2-bit binary number into an equivalent decimal number. However, we can implement the binary-to-decimal converter for any number of bits in the same way.
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