In this lecture, we are going to learn about the Gray to binary Code Converter. We will see the truth table, K-map, and logic diagram of the Gray to binary Code Converter in detail. before the realization of binary to Gray Code Converter let’s discuss the Gray code.

We have already discussed what is gray code, so if you want to know about gray code then click on the below link.

Also Read:What is Gray Code

Now let’s discuss the Gray to Binary Code Converter in detail.

**Gray to Binary Code Converter**

**Steps to convert the Binary to gray code:**

Step 1: | Write the truth table showing the relation between the Gray code as input and the Binary code as output. |

Step 2: | For each Binary code output write a K-map. |

Step 3: | From the K-map obtain a simplified expression for each Binary code output in terms of gray code inputs. |

Step 4: | Realize the code converter using the basic gates. |

**Gray to Binary Truth Table**

The following table shows the relation between the Gray inputs and Binary code outputs.

**Gray to Binary Code Converter K-map**

**Simplified Expression for B1:**

`B_1= \bar G_3 \bar G_2 G_1 + \bar G_3 G_2 \bar G_1+G_3G_2G_1+G_3 \bar G_2 \bar G_1`

`B_1= \bar G_1 (\bar G_3 G_2 + G_3 \bar G_2) + G_1(\bar G_3 \bar G_2 + G_3 G_2)`

`B_1= \bar G_1 (G_3 \oplus G_2) + G_1(\overline{G_3 \oplus G_2})`

`\therefore B_1= \bar G_1 X + G_1 \bar X \, where \,X = G_3 \oplus G_2`

`\therefore B_1= G_1 \oplus X = G_1 \oplus G_2 \oplus G_3`

**Simplified Expression for B0:**

**Gray to Binary Code Converter Circuit**

- Gray to Binary Code Converter Circuit is shown in the figure below:

**You can also learn the Binary to Gray code converter by clicking the below link**

Also Read:Binary to Gray Code Converter