3CNF Formula

I am working with 3CNF formulae and trying to figure out if there is some logical way to find a formula given a pair of satisfying assignments. For example, if I want to find a formula that can only be satisfied by the two assignments x1=0,x2=x3=1 and x1=x2=1, x3=0, is there some method to make this easy. Perhaps a truth table or Karnaugh map will help, but I am unsure how to apply either to find a solution. I am trying to understand some things about boolean algebra and digital logic and this item seems to escape me.

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