An adopted child is treated in law as if he or she is the natural child of their adoptive parents and not the child of any other person.
This means, in terms of inheritance, that any reference to a 'child' in your adopted parents Will or Wills, shall include yourself as their adopted child. If they do not leave a Will or Wills at all, you will have the identical legal right to benefit from their estates as any natural child would have.
It is not possible however for you to make a successful claim to your birth parent's estates upon their deaths, even if you know one or both of them and have a relationship of any kind with them. The only way that you could benefit from the estates of your birth parents is if they specifically named you as a beneficiary of their Will or Wills but they are not obliged to make any such provision for you at all.
If your adoptive parents have natural children as well, then for inheritance purposes, you will be treated as the proper sibling of these children.