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.
:- module gray.
 
:- interface.
:- import_module int.
 
:- type gray.
 
% VALUE conversion functions
:- func gray.from_int(int) = gray.
:- func gray.to_int(gray) = int.
 
% REPRESENTATION conversion predicate
:- pred gray.coerce(gray, int).
:- mode gray.coerce(in,   out) is det.
:- mode gray.coerce(out,  in)  is det.
 
:- implementation.
 
:- import_module list.
 
:- type gray
  ---> gray(int).
 
gray.from_int(X) = gray(X `xor` (X >> 1)).
 
gray.to_int(gray(G)) = (G > 0 -> G `xor` gray.to_int(gray(G >> 1))
                        ;        G).
gray.coerce(gray(I), I).
 
:- end_module gray.