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Exercise 1: Compound Boolean expressions

Evaluate the following expressions.

x = 4
y = 2

(a)  x > 0 and y < 5

(b)  x == 4 and False

(c)  (not x == 3) and (not y <= 2)

(d)  x == 0 or (x > 1 and y != 14)

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Exercise 2: Truth tables

Write truth tables for the following expressions.

(a)  a and (not b)

(b)  (a and b) or (not a and not b)

(c)  not (a and b)

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Exercise 3: Truth tables, revisited

Part a: more truth tables

Write truth tables for the following expressions.

(a)  a and (not b or a)

(b)  (a or b) and (not a or b)

(c)  not (a or (b and a))

Part b: simplification via truth table

Use your truth tables from Part a to verify the following simplified expressions are equivalent to the original expressions.

(a) a

(b) b

(c) not a

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Exercise 4: A simple while loop

Write a function that uses a while loop to build a list of negative numbers the user enters, until they type 0.

def keepNegatives():
    """
    Asks the user to enter integers, and keeps track of negative numbers entered.
    Stops once the user inputs `0`.

    returns: the negative numbers entered (a list of ints)
    """
    return [] # replace with your code

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Exercise 5: Dividing by 2

Write a function that takes a value n and returns the number of times that n can be divided by 2 (using integer division) before reaching 1. Your function should use a while loop.

def numberTimesDivisible(n):
    """
    Returns the number of times n can be divided by 2
    (integer division) before reaching 1.
    Assumes n is at least 1.

    ex: n=1 -> 0
        n=2 -> 1
        n=3 -> 1
        n=4 -> 2
    """
    return -1 # replace with your code

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Exercise 6: More practice with while

The greatest common divisor (GCD) of two values can be computed using Euclid’s algorithm. Starting with the values m and n, we repeatedly apply the formula: n, m = m, n % m, until m is 0. Then, n is the GCD of the original values of m and n.

Write a function that finds the GCD of two numbers using this algorithm.

Hint: You should use the formula from above as a line of code in the loop; if you don’t use “simultaneous assignment” of two variables at once, you’ll need a temp variable to avoid losing the value of n after updating it via n = m.

def gcd(m, n):
    """
    Calculates the GCD of m and n using Euclid's algorithm.

    Process:
      * n = m
      * m = n % m (note this must be simultaneous)
      * continue until m is 0, then the result is in n
    """
    return -1 # replace with your code

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