Equality of Cardinality of a Power Set to a Set of Functions

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Let A be a set. Define D to be the collection of all functions f : A → {0, 1}. Prove that |P(A)| = |D| by constructing a bijection F : P(A) → D

I know the power set of A contains 2^(|A|) elements. To show that |P(A)|=|D|, I think I need to use CSB theorem. From what I'm understanding, the set D would have values like {(a, 0),(a, 1)}.

How do I go about solving this problem? I would be very grateful if someone explained this to me or gave an answer.