Need help with an assignment, in python programming language.

Problem 1 Powers of two without going over Write and test a function called pow2() that takes one (positive) number as input and returns the largest power of 2 thats less than or equal to that number. Some examples include: pow2(2) 2 pow2(12) 8 pow2(20) 16 pow2(284) 256

Problem 2 Decimal to Binary Write and test a function called decToBin() that takes in a decimal number as an argument and returns a string representing that number in binary. Your solution should not use the built-in bin() function (though it may be helpful when testing your function to verify your answers).

The design for this algorithm should work as follows:

Let x be the input value, Let p be the largest power of 2 less than or equal to x, and Let output be "". Repeat until p is 0: If p < x, Then subtract p from x, and add a "1" to the output. Otherwise add a "0" to the output Divide p by 2 Return output

Some examples: decToBin(2) "10" decToBin(10) "1010" decToBin(16) "10000"

Problem 3 User inputs Write a function called userBin() that takes an integer as an argument. This function should display the integer to the user and prompt them to enter the corresponding binary value. Have your function simply return the user's input (it will be used in the next problem). Problem 4 Making a game Finally, create a main() function for your program. The purpose of this function is to control the game-logic for a Binary Quiz game. The steps of this game are as follows: Generate a random integer in the range [0,256] Ask the user to enter the corresponding binary number. Check if their answer is correct or not o If so, add 1 to their score The above steps should repeat until the user types "stop". Some tips: Your program should not use the built-in bin() function, use the decToBin function you created. The user's input, and the result of decToBin are both strings, so don't convert the binary numbers to integers. The user's score should be displayed each round.