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

## Gray Code

### What is Gray Code

- Gray Code, also known as reflected binary code or unit distance code, is a binary numeral system where two successive values differ by only one bit.

- Unlike traditional binary representations, where adjacent numbers can have multiple bits different, Gray Code ensures that only one bit changes as you move from one value to the next.

- This property makes it particularly useful in various applications where minimizing errors during transitions is essential.

### Importance of Gray Code

- Gray Code’s primary importance lies in its property of minimizing errors during binary transitions. In standard binary encoding, multiple bits can change between consecutive values, potentially leading to errors due to bit propagation delays or signal glitches.

- Gray Code minimizes these errors by ensuring that only one bit changes at a time, reducing the chances of misinterpretation during transitions. This feature is crucial in applications where accuracy and reliability are paramount.

### Applications of Gray Code

Gray Code finds application in various fields due to its error-reducing characteristics:

#### 1. Rotary Encoders

- Rotary encoders are devices used to measure the rotation of an object. Gray Code is commonly employed in rotary encoders because it guarantees that only one bit changes at each step of rotation, preventing ambiguity or misreading of the angle.

#### 2. Digital Communications

- Gray Code can be advantageous in digital communication systems, especially in scenarios where signal transitions need to be precise. Its ability to minimize bit transitions helps in reducing the likelihood of transmission errors.

#### 3. Binary Code Decimal (BCD) Encoding

- BCD is a class of binary encodings representing decimal numbers. Gray Code can simplify the conversion between BCD and other binary encodings due to its single-bit transition property.

#### 4. Karnaugh Maps in Digital Logic Design

- Karnaugh maps are used in digital logic design for simplifying Boolean expressions. Gray Code is often used to label the cells of a Karnaugh map, making it easier to identify adjacent cells that differ by only one variable, thus aiding in simplification.

#### 5. Error Detection and Correction

- In error detection and correction codes, Gray Code can assist in reducing errors during the encoding and decoding processes. By minimizing transitions between bits, the likelihood of misinterpretation or misalignment is decreased.

Also Read:Classification of Logic Families |Characteristics of Logic Families

## Binary to Gray Code Converter

In Gray code only one bit changes at a time as we have seen in the definition of the Gray code.

Now we are going to realize the binary to gray code converter.

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

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

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

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

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

### Binary to Gray Code Converter Truth Table

The following table shows the relation between the binary inputs and gray code outputs.

Also Read:Comparison of Logic Families

### Binary to Gray Code Converter K-map

### Binary to Gray Code Converter Circuit

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

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

Also Read:Gray to Binary Code Converter

## FAQs

**What is meant by gray code?**

A Gray code is an encoding of numbers so that adjacent numbers have a single digit differing by 1.

**What are gray code and binary code?**

The Gray code is a binary code in which adjacent numbers differ by only one bit.

Application of Gray Code

The Gray code is used in applications where we need to minimize the errors due to mechanical imperfections, such as rotary encoders.

**What is the gray code of 3 bits?**

Gray codes for 3-bit numbers are: 000, 001, 011, 010, 110, 111, 101, 100