Binary to Gray Code Converter

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A binary-to-gray code converter is a type of code converter that can translate a binary code into its equivalent gray code.

The binary-to-gray code converter accepts a binary number as input and produces a corresponding gray code as output.

Here is the truth table explaining the operation of a 4-bit binary-to-gray code converter.

Let us derive the Boolean expressions for the gray code output bits. For this, we will simplify the truth table using the K-map technique.

K-Map for Gray Code Bit G₀

The K-Map simplification to obtain the Boolean expression for the gray code bit G₀ is shown in the following figure.

Hence, the Boolean expression for the gray code bit G₀ is,

$$\mathrm{G_{0} \: = \: \overline{B_{1}} \: B_{0} \: + \ B_{1} \: \overline{B_{0}} \: = \: B_{0} \: \oplus \: B_{1}}$$

K-Map for Gray Code Bit G₁

The K-Map simplification for the gray code bit G₁ is shown below −

Thus, the Boolean expression for the gray code bit G₁ is,

$$\mathrm{G_{1} \: = \: \overline{B_{2}} \: B_{1} \: + \ B_{2} \: \overline{B_{1}} \: = \: B_{1} \: \oplus \: B_{2}}$$

K-Map for Gray Code Bit G₂

The K-Map simplification for the gray code bit G₂ is depicted in the following figure −

The Boolean expression for the gray code bit G₂ will be,

$$\mathrm{G_{2} \: = \: \overline{B_{3}} \: B_{2} \: + \ B_{3} \: \overline{B_{2}} \: = \: B_{2} \: \oplus \: B_{3}}$$

K-Map for Gray Code Bit G₃

The K-Map simplification for the gray code bit G₃ is shown in the following figure −

Hence, the Boolean expression for the gray code bit G₃ is,

$$\mathrm{G_{3} \: = \: B_{3}}$$

Let us now utilize these Boolean expressions to implement the logic circuit of the binary-to-gray code converter.

The following figure shows the logic circuit diagram of a 4-bit binary code to gray code converter −

This circuit can convert a 4-bit binary number into an equivalent gray code.

We can follow the same procedure to design a binary-to-gray code converter for any number of bits.