# What is Gray code

Gray code is essentially a binary numbering system characterized by a unique property: each consecutive binary number in the sequence differs from the previous one by only one bit. It can be applied to any number of bits, denoted by K. For example, in a 3-bit Gray code sequence, the progression would be 000, 001, 011, 010, 110, 111, 101, 100, with each subsequent number differing by exactly one bit from its predecessor.

A Gray code is not weighted, in contrast to binary numbers, meaning that its bits are not assigned any weight based on where they are located.

In the binary system, for example, the least important bit weights of 2^0=1, and so on. The second chunk from the right weights 2^1=1. The gray code consists of positional bits that are not weighted, unlike the binary code. The gray code is a numerical representation of a cyclic encoding scheme that repeats itself after a certain amount of time.

### How would you build an N-Bit Gray Code?

**Use the prefix and reflect method**

The n-bit gray code is generated through a recursive process.

The following are the steps to create a gray code:

- In the simplest scenario, we produce the codes as 0 and 1 for n = 1.
- Add the reversed list of the same codes to the preceding list of codes, i.e., add sequence 1, 0 in 0, 1, and the final code is 0, 1, 1, 0.
- We now append prefix 0 to the first half of the original list, or 00,01,11,10, and prefix 1 to the second half of the reversed list, or 111,10.

### What kinds of Gray Codes are there?

Gray codes mostly have three varieties.

**1) N-ary Gray code:** The description of N-ary Gray code as a type of Gray code used for non-boolean data is accurate. However, it's important to note that N-ary Gray codes can represent any base, not just quaternary (base-4) numbers. N-ary Gray codes can be used to encode data in bases other than binary, such as ternary (base-3), quinary (base-5), or higher. So, while quaternary Gray codes are a specific example of N-ary Gray codes, they are not the only possibility.

**2)Two-dimensional gray codes (n,k): **The description of two-dimensional Gray codes for location-finding systems and communication is accurate. However, it might be helpful to explain the parameters 'n' and 'k' in more detail. In two-dimensional Gray code encoding, 'n' typically represents the number of bits used to encode each dimension, while 'k' represents the total number of dimensions. Additionally, it's worth mentioning that two-dimensional Gray codes are also used in applications such as error correction and pattern recognition, not just for location-finding systems.

### How do you apply gray codes?

**1) Error detection**: Gray codes are employed in digital communication channels like cable TV to identify mistakes since they have the feature that just one bit separates two consecutive values.

**2) Genetics:** Genetic algorithm theory makes use of gray codes.

**3) Tower of Hanoi puzzle:** The problem can be solved using gray code.

**4) Position encoders**: In general, gray codes are preferred to weighted binary encoding in position encoders.

**5) Boolean circuit Minimization:** Labeling the axes of Karnaugh maps with gray codes minimizes the boolean circuits.

### Examples of Gray codes

A 4-bit gray code and the corresponding binary code are shown below:

Conclusion- After all, two successive binary values differing by exactly one bit are considered gray codes.
- Unlike gray codes, which do not have weights assigned to each bit, binary integers do.
- Generating gray codes using the Reflect and Prefix method, one of several methods available, is quite simple.
- Based on its digits, application, and usage, gray codes can be classified into several categories.
- Numerous fields have utilized gray codes, such as position encoders, genetics, error detection, and Boolean circuit minimization.