Write a program to extract the \(10^k\)s digit from a number \(n\), given \(k\) and \(n\). Assume \(k\) and \(n\) are both positive integers, and \(n\) has at least \(k+1\) digits. For example, to extract the
100’s digit from 1531 we’d run our program with \(n=1531\) and \(k=2\) (because \(10^2\) is 100). Hint: try using
modulus and integer divison together - for example, notice that the
100’s digit of 3624 can be calculated as 3624 // 100 % 10.
A couple example runs are given below:
>>> %Run P04_extract_digit.py 1531 2
The 100s digit of 1531 is 5
>>> %Run P04_extract_digit.py 13 0
The 1s digit of 13 is 3Write a program that prints the table of powers of two as in the
example below. Use one print call per line and use the
sep keyword argument.
2^0: 1
2^1: 2
2^2: 4
2^3: 8
2^4: 16
2^5: 32
2^6: 64
2^7: 128Suppose a variable p contains a positive integer.
Write a Python expression that evaluates to a string containing
the binary representation of \(2^p -
1\) with no leading zeros. For example: if p = 3, you’d give the
binary for \(2^3 - 1 = 7\), which comes
out to 111. Hint: work out a couple more examples
with different values of \(p\) and see
if you can find a pattern.
Typically, integers are stored on computers by default using 64 bits. What’s the largest integer that can be represented using 64 bits? I recommend using a calculator (or Python!) for this one.
(*) Integers can be negative, but computer memory can’t store “+” and “-” signs, only 0s and 1s. For this reason, the decimal-to-binary integer conversion approach I presented doesn’t have any way to represent negative integers. Can you come up with an approach to represent both negative and positive integers using binary?