CS105: Introduction to Python

Execute these two instructions in the Repl.it command line window:

8**(1/3)
8**1/3

You should recognize the first instruction from the previous section. Observe that these instructions yield two totally different answers. The reason is that there is an order in which operators are evaluated. The "order of operations" and "operator precedence" define how arithmetic calculations are to be evaluated. As expected from basic arithmetic, exponentiation takes place before multiplication and division which take place before addition and subtraction. In addition, operations are generally read from left to right.

As an example, consider the expression 8**1/3 as shown above. In this case, exponentiation taking precedence over division means that 8**1 is computed first to obtain a value of 8 and then that result is divided by 3. Hence, the final computed result is 8/3 = 2.6666...67. Notice that, when parentheses are added around the exponent to form 8**(1/3), the exponent evaluates to 1/3 and the cube root of 8 is computed. The term inside the parentheses has higher precedence and takes place before exponentiating. This should be a refresher about the order arithmetic expressions are evaluated in.

Now, we will consider order precedence when operations are phrased within the Python programming language. Before running this set of instructions in the run window, try to predict the value each variable will contain.

a=3
b=4
c=1
d=5
e=3
f=a+b-c*d+e/d
g=a+b-c*(d+e)/d
h=a+(b-c)*d+e/d
i=(a+b-c)*d+e/d

You may use the print statement to verify your answer.

It is important to note that // and % are considered division operations and, because of that, have precedence equal to * and /. Try to predict the value of each variable in these commands:

v=2
w=3
x=4
y=19
z=23
a=v**v//x%x+y%w*z//x
b=v**(v//x)%x+y%(w*z)//x

Again, you should use insert some print commands to verify your answer.

A useful guiding principle when writing code is: if the order precedence is not clear to you by looking at the expression, use parentheses to make things obvious, since parentheses always take the highest precedence.

The bool data type is necessary for the evaluation of logical data (which is inherently different from the numerical or string data types introduced so far). "bool" stands for Boolean data which can only take on one of two possible values: True or False. You should recall from the previous unit that True and False are reserved words within the Python language. Try executing these commands in the Repl.it run window:

a=True
print(a)
print(type(a))
b=False
print(b)
print(type(b))

You should see that True and False appear in your program as blue text indicating that they are reserved Python words. Furthermore, the data type should be identified as bool. Let's investigate how this data type can be used.

Relational operators are those that compare values in order to determine their relationship. Here is a shortlist of very useful relational operators:

Copy and paste these commands into the Repl.it run window:

a=2
b=3
print(a==b)
print(a!=b)
print(a>=b)
print(a>=a)
print(a<=a)
print(a>b)
print(a < b) 

It should be clear why these are called relational operators. Also, note that the only possible answers when using these operators are either True or False.

Be EXTREMELY careful to NEVER confuse the assignment operator (=) with the relational equals (==) operator. They serve two totally different purposes. Copy and paste and run this set of commands:

a=2
b=5
a=b
print(a)
a=2
b=5
print(a==b)

The assignment operator assigns the numerical value contained in the variable b to the variable a. The relational operator compares the variables a and b for equality which evaluates to the bool data type False.

Finally, there are logical operators that allow us to form combinations of logical expressions. Watch the video for a description of relational and logical operators. Afterwards, you should understand these definitions for logical operators given two boolean variables x and y:

These operators will be incredibly important in the next unit. For now, we just need to practice using them in order to get used to the syntax.

In this video, course designer Eric Sakk walks through the major topics we covered in Unit 2. As you watch, work through the exercises to try them out yourself.