Convert a given decimal non negative integer `n` into its binary representation

[kedarmhaswade]

As you know, we use the decimal place-value system to represent numbers. We write the number three hundred and forty-eight as 348 in decimal representation: write the most significant digit (MSD, 3 in this case) first and then write the subsequent digits from left to right.

But 348 is just a representation of an abstract number using the integer powers of the number 10.

It is clear that 348 = 3 10² + 4 10¹ + 8 * 10⁰.

To represent a given number, we can use increasing powers (0, 1, 2, ...) of any number other than 1 (called the base). Perhaps you are familiar with James Tanton's exploding dots (using the n-to-1 machine).

Implement a function that when applied to a decimal integer, n, returns its representation in base 2 (the so-called binary representation). As you might have correctly guessed, the binary representation of a number only consists of the digits 0 and 1.

Note that the function returns a binary representation. What value will the function return?

Take for example a number (decimal) 9. You know that its binary representation is 1001. In what form will the function return this representation?

How will you automatically test your function?

[kedarmhaswade]

As discussed today, you should write two functions that test each other out:

• decimal_to_binary(n): applies to an integer, n, and returns a list that contains its binary representation.
• binary_to_decimal(ds): applies to a list of digits (each digit being either a0or a1) and returns its decimal representation (the number like348` directly, not a list of "decimal digits" although that is quite possible).

When returning the binary representation as a list of 0s and 1s, you must specify the place value system of choice.

You have at least two choices:

• Place the most significant bit first and the least significant bit last in the list. This system represents the decimal 6 as [1, 1, 0] in binary. We call this the BE system.
• Place the least significant bit first and the most significant bit last in the list. This system represents the decimal 6 as [0, 1, 1] in binary. We call this the LE system.

Pay attention to the specifications.

Testing your code will become easier when you have these two complementary functions.