Memory and Remembering:
If we consider the memory is an Order then remembering is purely disorder. The act of remembering depends upon the mental state influenced by similarities in events and the methods of acts and the results those acts produce. If the circumstantial similarities aren't noticed then the remembering would not happen and it is equal to forgetting. So the survival of any memory depends upon the repetition of similar events, acts and results. There are possibilities for even a single event and act upon the event for not occurring in the same fashion. So the possibility of remembering the “same” memory even in an identical situation is also minimal. This is the time we feel the memory is lost or confusing. Any existence is purely depends upon the motion of being. This motion creates various docks for the memory to occupy. So the nature of memory will also not be the same. Remembering which selects (not independently of the outcome of the event) the parts of memory to be applied for a particular situation. Remembering balances the increasable gain of happiness and reducible loss of pain of mind as the happiness and pain are the only points our mind is generally keep on bouncing. In this way by remembering and comparing the bygone with the present we give a sense of continuity to memory. Otherwise the memory is as equal as dead. Every "new" experience will not be necessarily creating memory until otherwise there would be a recurrence of the same or relatively same experience.
Memory and Knowledge :
The act of remembering will make us experienced in handling, analyzing any situation and feeling continuity of the application of knowledge and it also gives multiple choices to act upon. If we suspend applying the memory in handling or analyzing the situation it will lead to discontinuity even in knowledge. Knowledge is remembering and applying the memory to the particular situation. Lack in remembering is equal to lack of knowledge. Memory is the supplier of sources to the knowledge. Without memory knowledge will be consider as either perception or can be simply ignored as a misconception. We have given knowledge a status of supreme thing even in religious, theological, metaphysical and worldly senses. And for the knowledge memory is the supreme tool it possesses in order to continue as the supreme.
We can simply put like this;
Experience -> memory -> knowledge (-> = input)