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.
fun gray_encode b =
  Word.xorb (b, Word.>> (b, 0w1))
 
fun gray_decode n =
  let
    fun aux (p, n) =
      if n = 0w0 then p
      else aux (Word.xorb (p, n), Word.>> (n, 0w1))
  in
    aux (n, Word.>> (n, 0w1))
  end;
 
val s = Word.fmt StringCvt.BIN;
fun aux i =
  if i = 0w32 then
    ()
  else
    let
      val g = gray_encode i
      val b = gray_decode g
    in
      print (Word.toString i ^ " :\t" ^ s i ^ " => " ^ s g ^ " => " ^ s b ^ "\t: " ^ Word.toString b ^ "\n");
      aux (i + 0w1)
    end;
aux 0w0