perhaps there's a OM-solution... in this case it's to hard to find... (search-engine?)

otherwise...

 

(defun integer-to-binary-lengths* (alist)
  (loop for i in alist
    when (> (abs i) 1)
    append (append (list 1) (loop repeat (- (abs i) 1)
                      collect 0))
    else collect 1))
  

(integer-to-binary-lengths* '(2 2 2 1 1 4 4 4 4))
(integer-to-binary-lengths* '(6 4 8 5 2 1 10 2))

 

(binary-to-decimal '(1 1 0))
=> 6
(decimal-to-binary '(9 3 6 1 10 11))
=> ((1 0 0 1) (1 1) (1 1 0) (1) (1 0 1 0) (1 0 1 1))

 

it's not decimal-to-binary!!! another idea...

 

for example...

6 => 1 0 0 0 0 0 = a "1" and 5 times a "0")

I've made this long time ago, bit different but may be also of interest, this function use a specs of number of "1" and "0" in input:

 

;;; GEN-BINARY_INTEGER
(defun gen-binary-integer (one-list zero-list &key (flatten t))
  (do-verbose
      ("gen-binary-integer")
  (if flatten
    (flatten
     (loop
       for i in one-list
       for o in (gen-trim (length one-list) zero-list) 
       collect 
       (append
        (gen-repeat i '(1))
        (gen-repeat o '(0))
     )))
    (loop
       for i in one-list
       for o in (gen-trim (length one-list) zero-list) 
       collect 
       (append
        (gen-repeat i '(1))
        (gen-repeat o '(0))
     )))))

#| USAGE
(gen-binary-integer '(3 4 3 2 4 2 5) '(1 1 3))
=> (1 1 1 0 1 1 1 1 0 1 1 1 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0 0 1 1 1 1 1 0)

(gen-binary-integer '(3 4 3 2 4 2 5) '(1 1 3) :flatten nil)
=> ((1 1 1 0) (1 1 1 1 0) (1 1 1 0 0 0) (1 1 0) (1 1 1 1 0) (1 1 0 0 0) (1 1 1 1 1 0))

(setf intg '(3 2 4 5 3))
(setf zero-k '(1 2 1 3))

(gen-binary-integer intg zero-k)

=> '(1 1 1 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 0 0 1 1 1 0)

|#

S.