let bool_bin = function
    |true -> 1
    |false -> 0
let rec binList xs ys = match xs with
    |[] -> ys
    |x::xs -> binList xs ((bool_bin x)::ys)
let rec pow a = function
  | 0 -> 1
  | 1 -> a
  | n ->
    let b = pow a (n / 2) in
    b * b * (if n mod 2 = 0 then 1 else a)
let rec bin_dec xs ys position= match xs with
    |[] -> ys
    |x::xs when position = 0 -> bin_dec xs (x+ys) (position+1)
|x::xs when position <> 0 -> bin_dec xs (x* (pow 2 position) 0)+ys) (position+1)