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.
#import std
#import nat
 
xor = ~&Y&& not ~&B                  # either and not both
 
btog = xor*+ zipp0@iitBX             # map xor over the argument zipped with its shift
 
gtob = ~&y+ =><0> ^C/xor@lrhPX ~&r   # fold xor over the next input with previous output
 
#show+
 
test = mat` * 2-$'01'***K7xSS pad0*K7 <.~&,btog,gtob+ btog>* iota32