Binary to Decimal Converter

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.

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.