Question

Given this Python program:

  num = input("Enter a number: ")
  result = 1024
  for i in range(num):
     result = result / 2
  print result

If the number you enter is 4, why is the output of this program 64?

Answer 1

Trace through the program to see what happens. range(num) here is range(4), which gives the values 0, 1, 2, and 3.

When i = 0, we divide 1024 by 2 to get 512.

When i = 1, we divide 512 by 2 to get 256.

When i = 2, we divide 256 by 2 to get 128.

When i = 3, we divide 128 by 2 to get 64.

And voila! There’s your 64.

More generally, each iteration of the loop will divide result by 2, so after num iterations of the loop, result will be 1024 / 2^num. Since 1024 = 2¹⁰, this means that the result is 2¹⁰ / 2^num = 2^{10 – num}. That said, if num > 10, because result is an integer, Python will round down to zero. In other words:

• If the number entered is negative, range(num) is the empty range and the program prints 1024.
• If the number entered is in the range of 0 to 10, the result is 2^{10 – num}.
• If the number entered is greater than 10, the result is 0.

Hope this helps!