Question: Binary and ternary representations (a) Find the binary representation of 2457. Show your work. (b) If b = b t . . . b 1

Binary and ternary representations

(a) Find the binary representation of 2457. Show your work.

(b) If b = b_t . . . b₁b₀ is the binary representation of a number n, then what is the binary representation of 4n + 2? Explain your answer.

(c) Give a recursive algorithm to compute the ternary (base 3) representation of any non-negative integer n. Adapt the algorithm for binary representation.

(d) Use strong induction to show that your algorithm gives the correct ternary representation for all n 0.

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