Gray Code in Digital Electronics – Binary to Gray and Gray to Binary Conversion

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Introduction

In Digital Electronics, codes are used to represent numbers and data efficiently. One such code is the Gray Code, also known as the Reflected Binary Code. Unlike normal binary numbers, Gray Code ensures that only one bit changes at a time between successive numbers. This makes it highly useful in error detection, position encoders, and digital systems.

In this blog, we’ll learn:

  • What is Gray Code?

  • Properties of Gray Code

  • Conversion: Binary to Gray Code

  • Conversion: Gray Code to Binary

  • Applications of Gray Code


What is Gray Code?

  • Gray Code is a non-weighted code.

  • It differs from BCD and Excess-3 codes, which are weighted.

  • In Gray Code, only one bit changes when moving from one value to the next.

  • Also called Unit Distance Code because only one bit differs between consecutive codes.

Example (4-bit Gray Code sequence):
0000, 0001, 0011, 0010, 0110, 0111, 0101, 0100, 1100, …

Notice how only one bit changes each time.


Conversion Methods

Binary to Gray Code Conversion

Rule:

  • The MSB (Most Significant Bit) of Gray = MSB of Binary.

  • Each next Gray bit = XOR of previous Binary bit and current Binary bit.

Example: Convert Binary 1011 to Gray

  • MSB → same → 1

  • Next: 1 XOR 0 = 1

  • Next: 0 XOR 1 = 1

  • Next: 1 XOR 1 = 0

So, Binary 1011 → Gray 1110


Gray Code to Binary Conversion

Rule:

  • The MSB of Binary = MSB of Gray.

  • Each next Binary bit = XOR of previous Binary bit and current Gray bit.

Example: Convert Gray 1110 to Binary

  • MSB → same → 1

  • Next: 1 XOR 1 = 0

  • Next: 0 XOR 1 = 1

  • Next: 1 XOR 0 = 1

So, Gray 1110 → Binary 1011


Applications of Gray Code

✔ Used in rotary encoders to avoid errors during mechanical movement.
✔ Minimizes data errors in digital communication.
✔ Important in Karnaugh Maps (K-Maps) for simplification of Boolean expressions.
✔ Applied in error detection and correction.


 Advantages of Gray Code

  • Only one bit changes at a time → reduces transmission errors.

  • Useful in digital systems where accuracy is critical.

  • Makes logic design easier in some applications.

Gray Code is one of the most important non-weighted codes in Digital Electronics.
It provides a reliable way to represent binary numbers where error minimization is crucial.
By mastering Binary ↔ Gray conversions, students can strengthen their knowledge of number systems and logic design.


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