title: Fibonacci Bit Representation Haskell
body: <p>I already have the following functions</p>
  
  <pre><code>toBin, auxBin :: Integer -&gt; [Integer]
  toBin 0 = [0]
  toBin n = reverse (auxBin n)
  
  auxBin 0 = []
  auxBin n = n `mod` 2 : auxBin (n `div` 2)
  
  fib :: Int -&gt; Integer
  fib n = fibs !! n
    where
      fibs = 0 : 1 : zipWith (+) fibs (tail fibs)
  
  fibonacci = [fib n | n &lt;- [0..]]
  </code></pre>
  
  <p>But when I map the Fibonacci list with the <code>toBin</code> function, I obtained an incorrect list:</p>
  
  <p>Becuase, I obtained this:</p>
  
  <pre><code>[[0],[1],[1],[1,0],[1,1],[1,0,1],[1,0,0,0],[1,1,0,1],[1,0,1,0,1],[1,0,0,0,1,0]]
  </code></pre>
  
  <p>But, I want this:</p>
  
  <pre><code>[0,1,10,101,1010,10101,101010,1010101,10101010,101010101]
  </code></pre>
  
  <p>Could you help me?</p>