number-of-bits - a non-negative integer.

 (integer-length 0)  0
 (integer-length 1)  1
 (integer-length 3)  2
 (integer-length 4)  3
 (integer-length 7)  3
 (integer-length -1)  0
 (integer-length -4)  2
 (integer-length -7)  3
 (integer-length -8)  3
 (integer-length (expt 2 9))  10
 (integer-length (1- (expt 2 9)))  9
 (integer-length (- (expt 2 9)))  9
 (integer-length (- (1+ (expt 2 9))))  10

(defun integer-length (integer)
  (ceiling (log (if (minusp integer)
                    (- integer)
                    (1+ integer))
                2)))

If integer is non-negative, then its value can be represented in unsigned binary form in a field whose width in bits is no smaller than (integer-length integer). Regardless of the sign of integer, its value can be represented in signed binary two's-complement form in a field whose width in bits is no smaller than (+ (integer-length integer) 1).