PYTHON TWO. Problem We are going to use recursion to do some conversions, from integer to binary and then from binary back to integer. (Please put a lot of comments)

Your Task

You prompt for an integer, convert the integer to a binary number string (there is no type for actual binary numbers so we just represent it as a string). We then take the string and turn it back into a regular integer. Things to remember

1. If the integer is 0, this is the base case since conversion back and forth of 0 is still 0. The program simply prints a note saying it is 0 and quits.

2. If the integer is negative, then we probably dont know how to do it, so the program prints a message saying it is negative and quits.

3. Otherwise, we do the conversion of the integer to a binary string (a string of 1s and 0s) and then convert that same string back to an integer to make sure we did it right.

Hints

How do we get a binary string from an integer? The easiest method uses integer division by 2 on successive quotients and then collects the remainders. It is best illustrated by an example. Consider the decimal number 156.

156 divided by 2 gives the quotient 78 and remainder 0.

78 divided by 2 gives the quotient 39 and remainder 0.

39 divided by 2 gives the quotient 19 and remainder 1.

19 divided by 2 gives the quotient 9 and remainder 1.

9 divided by 2 gives the quotient 4 and remainder 1.

4 divided by 2 gives the quotient 2 and remainder 0.

2 divided by 2 gives the quotient 1 and remainder 0.

1 divided by 2 gives the quotient 0 and remainder 1.

Stop at reaching a quotient of 0. The binary equivalent is given by concatenating the remainders, in reverse (so the last remainder is the most significant bit and the first is the least). In this example: `10011100 How do we get an integer from a binary string? First, we know it is a string, so the elements are 1 and 0. For every 1 in this string, we add a power of two to the overall decimal value. The power of 2 that we add depends on the position of the 1 in the binary string. A 1 in the far right (last) position of the string adds 2**0, in the next to last position adds 2**1, in the next to the next to the last position adds 2**2, and so on. If the bit is a 1, then we add that power of 2 to the overall sum; if it is 0 we do nothing. For example, starting the last (right most) position of 10011100 last bit is 0, so it contributes nothing to the sum. next bit is 0, so it contributes nothing to the sum. next bit is 1, so it contributes 2**2 to the sum. next bit is 1, so it contributes 2**3 to the sum. next bit 1, so it contributes 2**4 to the sum. next bit is 0, so it contributes nothing to the sum. next bit is 0, so it contributes nothing to the sum. next bit is 1, so it contributes 2**7 to the sum. The decimal equivalent is therefore 2**2 + 2**3 + 2**4 + 2**7, which equals 156. If you want to try something more challenging Can you take an integer and turn it into hexadecimal (base 16, see http://en.wikipedia.org/wiki/Hexadecimal ). Can you turn a hexadecimal string back into integer? Can you have the user enter the base as well as the integer and convert it to that base?