Turing reducibility of 2 versions of the satisfiability problem I need help with this problem.


  There are 2 versions of the satisfiability problem:
  
  [1] decision version: determine whether an arbitrary formula f is
  satisfiable or not
  
  [2] search version: if an arbitrary formula f is satisfiable, return
  an assignment of truth values to variables in the formula that makes f
  satisfiable. if f is unsatisfiable, return NIL.
  
  Show that [2] is Turing reducible to [1].


I have to prove that the oracle algorithm of [1] entails that of [2] to say "[2] is Turing reducible to [1]". 

I see that [2] is just the oracle algorithm of [1] since it discriminates the satisfiability of an arbitrary formula f. 

Can this mean the oracle algorithm of [1] entails that of [2]? If can, what would be the reason?
Any algorithm that decides the satisfiability of a formula can also be used to find an assignment for a satisfiable formula: 

While not all variables are assigned: 


Pick a variable and choose value 0. 
If formula is no longer satisfiable, replace value with 1.