I am having difficulties with Exercise 1.5.5, could you explain it in detail? Thank you!

Exercise 1.5.4: Let b > 2 be an integer. Define a representation of a real number in [0, 1] in terms of base b rather than base 10 and prove Proposition 1.5.1 for base b. Exercise 1.5.5: Using the previous exercise with b = 2 (binary), show that cardinality of R is the same as the cardinality of P(N), obtaining yet another (though related) proof that R is uncountable. Hint: Construct two injections, one from [0, 1] to of (N) and one from of(N) to [0, 1]. Hint 2: Given a set A C N, let the nth binary digit of x be 1 if n E A