Search for a tool
Gray Code

Tool to convert Gray code. Gray code, or reflected binary code, is a binary system which changes only one bit for each incrementation of one unity.

Results

Gray Code -

Tag(s) : Character Encoding, Electronics

Share
dCode and you

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!

Team dCode likes feedback and relevant comments; to get an answer give an email (not published). It is thanks to you that dCode has the best Gray Code tool. Thank you.

# Gray Code

## Code Gray Encoder

Tool to convert Gray code. Gray code, or reflected binary code, is a binary system which changes only one bit for each incrementation of one unity.

### What is the gray code? (Definition)

The Gray code, also called reflected binary, is a binary code having the property of modifying only one bit when a number is increased (or decreased) by one unit.

Example:

NumberBinaryGray
000000000
100010001
200100011
300110010
401000110
501010111
601100101
701110100
810001100

This property can have several interesting practical applications, and the gray code appears in Baudot code, in Hanoi towers resolution, or position encoders.

### How to convert binary to Gray code?

The conversion uses the xor function to transform binary into reflected binary (Gray code).

The algorithm consists of calculating the exclusive OR between the binary value and itself but shifted one row to the right (the last bit is deleted).

Example: \begin{align} 1 0 1 1 & \\ \oplus \rightarrow 1 0 1 & (1) \\ = 1 1 0 1 & \end{align} The binary code 1011 has for value 1101 in its reflected version in Gray code.

The algorithm implemenation uses binary operators xor and shift: gray = n ^ (n >> 1)

### How to convert Gray code to binary?

Gray code conversion can be done bit by bit. Given a number $G = {g_0,g_1,\dots,g_n}$ with $g_i$ each of its bits, then $B = {b_0,b_1,\dots,b_n}$ is calculated as: $$b_0 = g_0 \\ b_1 = g_0 \oplus g_1 \\ b_2 = g_0 \oplus g_1 \oplus g_2 \\ b_n = g_0 \oplus g_1 \oplus \dots \oplus g_n$$

In gray code, the most significant bit ($g_0$, often on the left) is always the same as the binary one ($b_0$).

The implementation of the conversion calculation also uses the xor and shift binary operators:n2 = n1; while (n1 >>= 1) n2 ^= n1; return n2;

### What are the first values in Gray Code?

Gray Code allow to count in binary but, to increment of one, only one bit changes. Here are the 16 first characters.

0000, 0001, 0011, 0010, 0110, 0111, 0101, 0100, 1100, 1101, 1111, 1110, 1010, 1011, 1001, 1000

### What are the advantages of Gray Code?

Gray code is modified only one bit at once when incrementing, with simplifies calculations and speed them up in some cases.

### When Gray Code have been invented?

The Gray code is protected by a patent from 1953

## Source code

dCode retains ownership of the source code of the script Gray Code online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Gray Code script for offline use on PC, iPhone or Android, ask for price quote on contact page !