What's the nature of the self in the continuity of consciousness?

Since consciousness operates continuously (we can't be aware of only one thing at a time; it changes, and what we notice doesn't necessarily change our awareness of it, or cause memory loss etc.) does this mean our consciousness is just one interconnected entity, or are we conscious in the moment, as a singular entity, and the past is just memory? <br><br>Does consciousness become memory, or are they two separate things, or memory is conscious? This memory consciousness is also continuous memory, and not conscious memory. <br><br>If we don't remember something, does it mean we are no longer conscious of it?