The "literal" way to do this would be something like
(defvar *array* (make-array 4 :element-type 'bit :initial-element 0))
(setf (bit *array* 2) (mod (1+ (bit *array* 2)) 2))
(print *array*) ;; ==> #*0010
(setf (bit *array* 2) (mod (1+ (bit *array* 2)) 2))
(print *array*) ;; ==> #*0000