Old testament trivia

Anyone familiar with Old testament:
When Samuel anoints David, does David realize that this anointing means he is the new King of Israel? Scripture just says he is anointed and the Spirit of the Lord came upon him. David is anointed in front of his father and brothers. That is it. There is no mention of what this anointing mean. Is that because the people knew what it meant without saying it? David is only Israel's second king. The previous king was Saul. Saul was anointed King by Samuel privately and Samuel does tell him that it is a kingship anointing. Is this because he was the first, or not? What I really what to know is does David know he is king when he is hiding away in the caves of the desert hiding from Saul who is trying to kill him?
Please let me ASAP. Thanks.