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.
 
#proto GrayEncode(_X_)
#synon _GrayEncode    *getGrayEncode
#proto GrayDecode(_X_)
#synon _GrayDecode    *getGrayDecode
 
#include <hbasic.h>
 
Begin
   Gray=0
   SizeBin(4)   // size 5 bits: 0->4
   Take (" #    BINARY   GRAY     DECODE\n")
   Take ("------------------------------\n"), and Print It
   For Up( i := 0, 31, 1)
      Print( LPad$(" ",2,Str$(i))," => ", Bin$(i)," => ")
      get Gray Encode(i) and Copy to (Gray), get Binary; then Take(" => ")
      now get Gray Decode( Gray ), get Binary, and Print It with a Newl
   Next
End
 
Subrutines
 
Gray Encode(n)
Return (XorBit( RShift(1,n), n ))
 
Gray Decode(n)
    p = n
    While ( n )
        n >>= 1
        p != n
    Wend
Return (p) 
 