data Bit = B0 | B1 deriving (Show)

bitToInt :: Bit -> Int
bitToInt B0 = 0
bitToInt B1 = 1

bitsToInt :: [Bit] -> Int
bitsToInt bits = sum (zipWith (*) digits digitValues)
    where
        digits = map bitToInt bits
        digitValues = map (2^) [0..]

boolToBit :: Bool -> Bit
boolToBit True  = B1
boolToBit False = B0

intToBits :: Int -> [Bit]
intToBits 0 = [B0]
intToBits 1 = [B1]
intToBits n = let (rem, quotient) = (n `mod` 2, n `div` 2)
              in (boolToBit (rem /= 0)) : intToBits quotient

xor :: [Bit] -> [Bit] -> [Bit]
xor []  y = y
xor x  [] = x
xor (x:xs) (y:ys) = (x `xorBit` y) : (xor xs ys)

xorBit :: Bit -> Bit -> Bit
xorBit B0 B1 = B1
xorBit B1 B0 = B1
xorBit B0 B0 = B0
xorBit B1 B1 = B0

main = do
    let one = intToBits 1
    let six = intToBits 6
    let ten = intToBits 10

    print ("Should be 11", bitsToInt $ one `xor` ten)
    print ("Should be 12", bitsToInt $ six `xor` ten)