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Author: Joel Gray Published: 1 July 2020 Read Time: ~3 minutes

Gray Code

In this article, we will delve into the concept of Gray Code, explore its properties, applications, and understand why it is considered a valuable tool in various technological fields.

A Brief Intro to Gray Code

Gray Code is not just this website. This website is actually named after the Gray Code system, created by Frank Gray in the 1940’s to represent binary numbers in a sequence of bits, where the current group of bits differs only by one bit from the last. It is sometimes known as Binary Reflected code.

What is Gray Code?

Gray Code is a binary numbering system where consecutive numbers differ by only one bit. Unlike traditional binary representation, where changing a single bit can cause a significant jump in the represented value, Gray Code ensures incremental changes by altering only one bit at a time. This property simplifies logic operations, reduces errors, and enhances the reliability of encoding.

The Encoding Process

Let’s take a closer look at how Gray Code is generated. To obtain the Gray Code equivalent of a given decimal or binary number, we apply a specific algorithm. The exact algorithm may vary depending on the bit size of the Gray Code sequence, but the general principle remains the same.

Properties of Gray Code:

  1. Consecutive Numbers Differ by Only One Bit: In Gray Code, each successive number in the sequence differs from the previous one by only a single bit flip. This feature ensures a smooth transition between adjacent values, which is particularly advantageous in applications where incremental changes need to be accurately tracked.
  2. Simplified Logic Operations: Due to its incremental nature, Gray Code simplifies logical operations. With only one bit changing at a time, the complexity of evaluating logical conditions or performing arithmetic operations is reduced. This simplification leads to improved efficiency and reduced chances of errors in practical implementations.

Take a look at the table below. ‘State’ indicates the integer value of the ‘Binary’ numbers shown in the 2nd Column, and ‘Gray’ indicates the Gray Code equivalent of the number.
It’s important to note that Gray Code is not weighted as Binary is. Binary numbers are transformed to integers as follows: the least significant bit (LSB) this is the bit furthest to the right is 1 (2^0), the second column (the column to the left of the LSB) is 2 (2^1), the third column would be 4 (2^2) the fourth being 6 (2^3) etc…


In Binary the number for 1 (001) is the same as (0*4) + (0*2) + (1*1) = 1
In the same manner the Binary number for 5 (101) would be (1*4) + (0*2) + (1*1) = 5

State Binary Gray
0 000 000
1 001 001
2 010 011
3 011 010
4 100 110
5 101 111
6 110 101
7 111 100

Applications of Gray Code:

Gray Code is often used in angle encoders and Analog to Digital Converters mainly.

  1. Angle Encoders: Gray Code finds significant usage in angle encoders, which are devices used to measure the rotation angle of a shaft. By encoding the rotational position using Gray Code, precise and reliable tracking of incremental changes becomes possible. This is crucial in various applications such as robotics, automation, and positioning systems.
  2. Analog to Digital Converters (ADCs): Analog to Digital Converters play a vital role in converting continuous analog signals into discrete digital representations. Gray Code is often utilized in ADCs to minimize errors and provide a more accurate representation of the input signal. By reducing the chances of misinterpretation during the conversion process, Gray Code ensures reliable and high-fidelity digitization of analog data.

The reason it has been adopted for use is because it helps to reduce errors and incorrect codes, when being used in encoders.


Gray Code, developed by Frank Gray, offers a reliable and efficient way to represent binary numbers. Its unique property of incremental changes, where only one bit flips at a time, simplifies logic operations and reduces errors. With applications in angle encoders, ADCs, telecommunications, robotics, and digital systems, Gray Code proves to be a valuable tool in various technological domains. By understanding the principles and advantages of Gray Code, engineers and developers can leverage its benefits to enhance the accuracy, reliability, and efficiency of their systems.

Remember, when it comes to encoding binary numbers in a systematic and error-reducing manner, Gray Code stands as a trusted choice.

Written by Joel Gray