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 Data.Bits
import Data.Char
import Numeric
import Control.Monad
import Text.Printf
 
grayToBin :: (Integral t, Bits t) => t -> t
grayToBin 0 = 0
grayToBin g = g `xor` (grayToBin $ g `shiftR` 1)
 
binToGray :: (Integral t, Bits t) => t -> t
binToGray b = b `xor` (b `shiftR` 1)
 
showBinary :: (Integral t, Show t) => t -> String
showBinary n = showIntAtBase 2 intToDigit n ""
 
showGrayCode :: (Integral t, Bits t, PrintfArg t, Show t) => t -> IO ()
showGrayCode num = do
    let bin  = showBinary num
    let gray = showBinary (binToGray num)
    printf "int: %2d -> bin: %5s -> gray: %5s\n" num bin gray
 
main = forM_ [0..31::Int] showGrayCode