Gray code
Karnaugh maps
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):

if b[i-1] = 1
   g[i] = not b[i]
else
   g[i] = b[i]
Or:

g = b xor (b logically right shifted 1 time)
Decoding (MSB is bit 0, b is binary, g is Gray code):

b[0] = g[0]

for other bits:
b[i] = g[i] xor b[i-1]
Reference
 Converting Between Gray and Binary Codes. It includes step-by-step animations.
defmodule Gray_code do
  use Bitwise
  def encode(n), do: bxor(n, bsr(n,1))
 
  def decode(g), do: decode(g,0)
 
  def decode(0,n), do: n
  def decode(g,n), do: decode(bsr(g,1), bxor(g,n))
end
 
Enum.each(0..31, fn(n) ->
  g = Gray_code.encode(n)
  d = Gray_code.decode(g)
  :io.fwrite("~2B : ~5.2.0B : ~5.2.0B : ~5.2.0B : ~2B~n", [n, n, g, d, d])
end)