[[wp:Gray code|Gray code]] is a form of binary encoding where transitions between consecutive numbers differ by only one bit. This is a useful encoding for reducing hardware data hazards with values that change rapidly and/or connect to slower hardware as inputs. It is also useful for generating inputs for [[wp:Karnaugh map|Karnaugh maps]] in order from left to right or top to bottom.

Create functions to encode a number to and decode a number from Gray code.

Display the normal binary representations, Gray code representations, and decoded Gray code values for all 5-bit binary numbers (0-31 inclusive, leading 0's not necessary).

There are many possible Gray codes. The following encodes what is called "binary reflected Gray code."

Encoding (MSB is bit 0, b is binary, g is Gray code):

<pre>if b[i-1] = 1
   g[i] = not b[i]
else
   g[i] = b[i]</pre>

Or:

<pre>g = b xor (b logically right shifted 1 time)</pre>

Decoding (MSB is bit 0, b is binary, g is Gray code):

<pre>b[0] = g[0]

for other bits:
b[i] = g[i] xor b[i-1]</pre>

;Reference
* [http://www.wisc-online.com/Objects/ViewObject.aspx?ID=IAU8307 Converting Between Gray and Binary Codes]. It includes step-by-step animations.