Bitwise Gray

Converts a standard binary number into its reflected Gray code.

What is Gray code? It is a way of numbering things so that going from one value to the next always changes exactly one bit. Ordinary binary does not have this property: counting from 3 (011) to 4 (100) flips all three bits at once. Gray code re-orders the bit patterns so every step is a single-bit change.

Compare the two encodings side by side:

In the binary column several bits jump at the boundaries (3→4 changes all three). In the Gray column only ever one bit changes from each row to the next.

Why does that matter? When a physical sensor reads several bits at the same instant, the bits never switch perfectly together. With plain binary, during the 3→4 transition the reader can momentarily see a bogus value like 111 (7) or 000 (0) while the bits are settling — a glitch. Because Gray code changes only one bit per step, there is no in-between value to misread, so the reading is always either the old value or the new one. This is exactly why many rotary encoders, linear position sensors and absolute shaft encoders output Gray code.

Settings

in

Input value.

out

Output value.

Example — encoding

Feed a normal binary count in and read the Gray-coded equivalent out — note that only one bit changes between consecutive rows:

Example — driving a rotary encoder display

Suppose you have a 4-bit absolute rotary encoder wired to Usine as four on/off inputs. As the shaft turns it emits Gray code, so the raw reading is not a usable position number yet. To turn it into a clean 0–15 angle:

4 encoder bits  ->  [Bitwise Bit Array to Bitwise]  ->  [Bitwise un-Gray]  ->  [Bitwise to Integer]  ->  position 0..15

Use Bitwise un-Gray for decoding the encoder (this is the common direction). This Bitwise Gray module does the opposite — it encodes a plain number into Gray code, which is useful when you need to drive a Gray-coded device or simulate an encoder signal:

position 0..15  ->  [Bitwise Gray]  ->  [Bitwise to Bit Array]  ->  4 output bits (Gray-coded)

See also

• Bitwise
• Bitwise XNOR
• Bitwise to String
• Bitwise Constant
• Bitwise un-Gray
• Bitwise MULT
• Bitwise SHR
• Bitwise MOD
• Bitwise ROL
• Bitwise SUB
• Bitwise NAND
• Bitwise ADD
• Bitwise to Bit Array
• Bitwise Set Bit
• Bitwise String to Bitwise
• Bitwise to Integer
• Bitwise NOR
• Bitwise Reverse
• Bitwise LSB
• Bitwise AND
• Bitwise Gray
• Bitwise Field
• Bitwise DIV
• Bitwise Mask
• Bitwise OR
• Bitwise Integer to Bitwise
• Bitwise Get Bit
• Bitwise CRC32
• Bitwise Bit Array to Bitwise
• Bitwise SHL
• Bitwise Counter
• Bitwise NOT
• Bitwise XOR
• Bitwise MSB
• Bitwise Swap Bytes
• Bitwise ROR
• Bitwise Pop Count