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.
 
#lang racket
 
(define (gray-encode n) (bitwise-xor n (arithmetic-shift n -1)))
 
(define (gray-decode n)
  (letrec ([loop (lambda(g bits)
                   (if (> bits 0)
                       (loop (bitwise-xor g bits) (arithmetic-shift bits -1))
                       g))])
	 (loop 0 n)))
 
(define (to-bin n) (format "~b" n))
(define (show-table)
  (for ([i (in-range 1 32)]) 
    (printf "~a | ~a | ~a ~n"
            (~r i #:min-width 2 #:pad-string "0")
            (~a (to-bin(gray-encode i)) #:width 5 #:align 'right #:pad-string "0")
            (~a (to-bin (gray-decode(gray-encode i))) #:width 5 #:align 'right #:pad-string "0"))))
 