Program of the Day #7

Write a program that takes a single positive integer, \(n\) as a command line argument, and outputs the number of digits in the binary representation of \(n\). For example, recall that 14 can be written as 1x8 + 1x4 + 1x2 + 0x1, or in binary as 1110. Since this representation has 4 digits, the program should output 4 when given 14 as input. Hint: because each binary digit represents a power of two, the number of binary digits is the number of times you can divide \(n\) by 2 (using integer division) before it becomes zero.

```
>>> %Run P07_binarydigits.py 15
4
>>> 
```

Other Practice Problems

1. Write a program that prompts the user for a positive integer \(p\) and prints the powers of 2 up to \(2^p\).

   Enter a power: 4
   2^0: 1
   2^1: 2
   2^2: 4
   2^3: 8
   2^4: 16

2. Write a program that prompts the user for a positive integer \(n\) and prints the powers of 2 less than \(n\).

   Enter a number: 9
   2^0: 1
   2^1: 2
   2^2: 4
   2^3: 8

3. Write a program that prompts the user until they enter the a secret password correctly. For this problem, the secret password can be whatever you want and should be hard-coded into the program. For example, if I chose "banana" as the secret password, a run of the program might look like this:

   Enter the password: algebra
   Incorrect, try again: bookend
   Incorrect, try again: banana
   You're in!

4. Write a program that repeatedly prompts a user for positive numbers until a negative number is entered, then print the sum of the positive numbers entered (be sure not to include the negative number in the sum).

   Enter a number: 4
   Enter a number: 8
   Enter a number: 3
   Enter a number: -9
   The positive numbers entered sum to 15

5. Write a program that prints a multiplication table for all possible combinations of the numbers 1 through 6. Ideally, print spaces as needed to pad out single-digit numbers so the table’s columns line up neatly.

   1  2  3  4  5  6
   2  4  6  8 10 12
   3  6  9 12 15 18
   4  8 12 16 20 24
   5 10 15 20 25 30
   6 12 18 24 30 36

6. (*) Write a program that prompts the user for a positive integer and prints the binary representation of that integer, with no leading zeros.

   Enter a positive integer: 65
   65 in binary is 1000001