haskell need help with binarys

[nyuszi]

im making a program which uses binarys so convert decimal numbers, characters, strings to binary numbers and work with them. but i got stucked because i want to divide Bin with Bin. something like this: 11010110110000 / 10011

= 01001110110000 so the new number will the 1001110110000 / 10011... until the weri last result

here is my code:

import Data.Char (ord)
import Data.List

toBinary :: Int -> [Int]
toBinary 0 = []
toBinary x = reverse (kisegf x)

kisegf 0 = []
kisegf x | x `mod` 2 == 1 = 1 : kisegf (x `div` 2)
         | x `mod` 2 == 0 = 0 : kisegf (x `div` 2)

chrToBinary :: Char -> [Int]    
chrToBinary x 
                |length (toBinary (ord x)) == 8 = (toBinary (ord x)) 
                |otherwise = take (8-(length (toBinary (ord x))))[0,0..] ++ (toBinary (ord x))

strToBinary :: String -> [Int]
strToBinary [] = []
strToBinary (x:xs) = [l | l <- chrToBinary x] ++ strToBinary xs

bxor :: [Int] -> [Int] -> [Int]
bxor [] [] = []
bxor (x:xs) (y:ys)
            |length (x:xs) == length (y:ys) && (x /= y) = 1 : bxor xs ys
            |length (x:xs) == length (y:ys) && (x == y) = 0 : bxor xs ys
            |length (x:xs) < length (y:ys) && (x /= y) = 1 : bxor (take (length (y:ys)-(length (x:xs)))[0,0..] ++ xs) ys
            |length (x:xs) < length (y:ys) && (x == y) = 0 : bxor (take (length (y:ys)-(length (x:xs)))[0,0..] ++ xs) ys
            |length (x:xs) > length (y:ys) && (x /= y) = 1 : bxor xs (take (length (x:xs)-(length (y:ys)))[0,0..] ++ ys)
            |length (x:xs) > length (y:ys) && (x == y) = 0 : bxor xs (take (length (x:xs)-(length (y:ys)))[0,0..] ++ ys)
{-this will compare 2 bin if a bigger than true else false-}
(%>=%) :: [Int] -> [Int] -> Bool
(%>=%)[] [] = True
(%>=%)[] _ = False
(%>=%)_ [] = True
(%>=%) (x:xs) (y:ys) = x==1 && y==1 && elemIndex 1 (x:xs) == elemIndex 1 (y:ys)

bmod :: [Int]{-number-} -> [Int]{-div-} -> [Int]{-result-}
bmod (x:xs) (y:ys)
            |length(x:xs) >= length(y:ys) && (take (length (y:ys)) (x:xs)) %>=% (y:ys) = ???
            |length(x:xs) >= length(y:ys) = ???
            |otherwise = (x:xs)

what should i write in the place of "???"

another and bigger for example:

bmod 11010110110000 10011.

       _______________
10011 ) 11010110110000
        10011,,.,,....
        -----,,.,,....
         10011,.,,....
         10011,.,,....
         -----,.,,....
          00001.,,....
          00000.,,....
          -----.,,....
           00010,,....
           00000,,....
           -----,,....
            00101,....
            00000,....
            -----,....
             01011....
             00000....
             -----....
              10110...
              10011...
              -----...
               01010..
               00000..
               -----..
                10100.
                10011.
                -----.
                 01110  
                 10011  <- bigger so cant div again
                 -----
                  1110 = what i want