(defparameter *test1* #b111111111111111111111111/100000000000000000000000
  "A rational exactly equal to 1.99999988079071044921875 and representable
  within IEEE 754's single-precision floating-point representation. Its IEEE 754
  encoding is #*00111111111111111111111111111111.")

(defun integer-to-bit-vector (int len)
  (let ((vec (make-array len :element-type 'bit)))
    (loop :for i :from 0 :below len :do
      (setf (aref vec (- len 1 i)) (ldb (byte 1 i) int)))
    vec))

(integer-to-bit-vector (ieee-floats:encode-float32 (float *test1*)) 32)
;; => #*00111111111111111111111111111111

(format nil "~,50f" (float *test1*))
;; => "1.99999990000000000000000000000000000000000000000000"