Question

Use the binary definition of Nat (natural number) and Racket lists in this question. Write functions nat-to-slist (convertting built-in natural numbers to binary Nats) and slist-to-nat (converting binary Nats to built-in natural numbers). For example, (slist-to-nat '(o i i)) should be 6. Next, write add, which consumes two lists and produces an slist. Writing short helper functions will improve the readability. Write the function multiply, which consumes two slists and produces an slist representing their product. This requires pure structural recursion on only one parameter, not two as for add. It will use add as a helper function. All implementations should use structural recursion on lists. Make sure you try a few tests on representations of very large numbers to confirm that your code is efficient.

Answer 1

The question involves creating Racket functions for binary number conversion and arithmetic operations using lists.

Step-by-step explanation:

The question asks to create functions in the Racket programming language for converting natural numbers to and from their binary representation using lists, as well as functions for adding and multiplying these binary numbers. To convert a natural number to a binary list (nat-to-slist).

You would recurse over the number, dividing by 2 and collecting the remainders. The (slist-to-nat) function converts a binary list back into a natural number by summing the powers of two based on the position of each 'i' in the list. For addition (add function), you would recurse over both lists using a carry.

Finally, the multiply function uses recursion on just one parameter and repeated addition for its implementation. Helper functions are suggested to improve readability and maintain a clean functional structure, ensuring efficient execution even for large numbers.