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.
: >gray ( n -- n' ) dup 2/ xor ;   \ n' = n xor (n logically right shifted 1 time)   
                                               \ 2/ is Forth divide by 2, ie: shift right 1                                                
: gray> ( n -- n )
  0  1 31 lshift  ( -- g b mask )             
  begin
    >r                                        \ save a copy of mask on return stack
     2dup 2/ xor
     r@ and or                               
     r> 1 rshift
     dup 0=
  until
  drop nip ;                                  \ clean the parameter stack leaving result only
 
: test
  2 base !                                    \ set system number base to 2. ie: Binary
  32 0 do
    cr I  dup 5 .r ."  ==> "                  \ print numbers (binary) right justified 5 places
    >gray dup 5 .r ."  ==> "  
    gray>     5 .r
  loop
  decimal ;                                   \ revert to BASE 10
 