Operators, Precedence and Expression Evaluation

Operators are special symbols which represents computation. They are applied on operand(s), which can be values(constants) or variables. Same operator can behave differently on different data types. Operators when applied on operands form an expression Operators are categorized as

Arithmetic Operators
Comparison (Relational) Operators
Assignment Operators
Logical Operators
Bitwise Operators
Membership Operators
Identity Operators

Arithmetic Operators( Mathematical)

Symbol	Description	Example 1	Example 2
+	Addition	>>>55+45 100	>>> “Good” + “Morning” GoodMorning
-	Subtraction	>>>55-45 10	>>>30-80 -50
*	Multiplication	>>>55*45 2475	>>> “Good” * 3 GoodGoodGood
/	Division	>>>17/5 3 >>>17/5.0 3.4	>>> 17.0/5 3.4 >>>28/3 9
%	Remainder/ Modulo	>>>17%5 2	>>> 23%2 1
**	Exponentiation	>>>2**3 8 >>>16**0.5 4.0	>>>2**8 256
//	Integer Division	>>>7.0//2 3.0	>>>3/ / 2 1

Comparison (Relational) Operators

These operators compare the values on either side of them and decide the relation among them.

They are also called Relational operators.

Symbol	Description	Example 1	Example 2
<	Less than	>>>7<10 True	>>>'Goodbye' < 'Hello' True
>	Greater than	>>>7>5 True	>>>'Goodbye' > 'Hello' False
<=	less than equal to	>>> 2<=5 True	>>>"Hello" <= “Goodbye” False
>=	greater than equal to	>>>10>=10 True	>>>"Hello" >= “Goodbye” True
! =	not equal to	>>>10!=11 True	>>>‟Hello”!= “HELLO" True
==	equal to	>>>10==10 True	>>>"Hello" == “Hello” True

Note: two values that are of different data type will never be equal to each other.

Assignment Operators
Assignment Operator combines the effect of arithmetic and assignment operator

Symbol	Description	Example	Explanation
=	Assigned values from right side operands to left variable	>>>x=12 >>>y="greetings"	x=12 ( we will assume x=12 for all examples)
+=	added and assign back the result to left operand	>>>x+=2	x=x+2 x=14
-=	subtracted and assign back the result to left operand	x-=2	x will become 10
*=	multiplied and assign back the result to left operand	x*=2	x will become 24
/=	divided and assign back the result to left operand	x/=2	x will become 6
%=	taken modulus using two operands and assign the result to left operand	x%=2	x will become 0
**=	performed exponential (power) calculation on operators and assign value to the left operand	x**=2	x will become 144
//=	performed floor division on operators and assign value to the left operand	x / /= 2	x will become

Logical Operators 

The following logical operators are supported by Python language. Assume variable A holds True and variable B holds False.

Symbol	Description	Example
or	If any one of the operand is true, then the condition becomes true.	A or B is True
and	If both the operands are true, then the condition becomes true.	A and B is False
not	Reverses the state of operand/condition.	not A is False

 

Python Bitwise Operators

Bitwise operator works on bits and performs bit-by-bit operation. Assume if a = 60; and b = 13; Now in binary format they will be as follows −

a = 0011 1100

b = 0000 1101

-----------------

a&b = 0000 1100

a|b = 0011 1101

a^b = 0011 0001

~a = 1100 0011

Python's built-in function bin() can be used to obtain binary representation of an integer number.

The following Bitwise operators are supported by Python language 

Operator	Description	Example
& Binary AND	Operator copies a bit, to the result, if it exists in both operands	(a & b) (means 0000 1100)
| Binary OR	It copies a bit, if it exists in either operand.	(a | b) = 61 (means 0011 1101)
^ Binary XOR	It copies the bit, if it is set in one operand but not both.	(a ^ b) = 49 (means 0011 0001)
~ Binary Ones Complement	It is unary and has the effect of 'flipping' bits.	(~a ) = -61 (means 1100 0011 in 2's complement form due to a signed binary number.
<< Binary Left Shift	The left operand's value is moved left by the number of bits specified by the right operand.	a << 2 = 240 (means 1111 0000)
>> Binary Right Shift	The left operand's value is moved right by the number of bits specified by the right operand.	a >> 2 = 15 (means 0000 1111)

Membership Operators

Python’s membership operators test for membership in a sequence, such as strings, lists, or tuples. There are two membership operators as explained below

Let  S=”Python”  c=’o’

Operator	Description	Example
in	Evaluates to true if it finds a variable in the specified sequence and false otherwise.	c  in S will result True
not in	Evaluates to true if it does not finds a variable in the specified sequence and false otherwise.	c not in S will result False

Identity Operators

Identity operators compare the memory locations of two objects. There are two Identity operators as explained below

Let x=10 and y=x

id(x) and id(y) are same in this case

Operator	Description	Example
is	Evaluates to true if the variables on either side of the operator point to the same object and false otherwise.	x is y will return True
is not	Evaluates to false if the variables on either side of the operator point to the same object and true otherwise.	x is not y will return False

 Operators Precedence

The following table lists all operators from highest precedence to the lowest.

Sr.No.	Operator & Description
1	** Exponentiation (raise to the power)
2	~ + - Complement, unary plus and minus
3	* / % // Multiply, divide, modulo and floor division
4	+ - Addition and subtraction
5	>>    << Right and left bitwise shift
6	& Bitwise 'AND'
7	^ | Bitwise exclusive `OR' and regular `OR'
8	<=   <   >    >= Comparison operators

Arithmetic Expressions and Evaluation

When we have an expression consisting of several operators how does Python decide the order of operations? It is done based on precedence of operator. Higher precedence operator is worked on before lower precedence operator.

Operator associativity determines the order of evaluation when they are of same precedence and are not grouped by parenthesis. Parenthesis has high precedence.

An operator may be Left-associative or Right –associative. In left associative, the operator falling on left side will be evaluated first, while in right assosiative operator falling on right will be evaluated first.

Note: In python “=” and “**” are Right Associative.Other operators are left associative means they are evaluated from left to right.

Examples:

>>>2+3**2 
11
here 3**2 will be evaluated first because it is having high precedence. So 2+9=11 will be the result.

>>>2**3**2
512
Here 3**2 will be evaluated first because the associativity is from right to left. So 2**9=512 will be the result.>>>-4**2 # here unary operator applied later
-16
>>4%0
This will produce division by zero exception
>>>2+3/2*4**2
18

Here the sub expression 4**2 will be evaluated first because ** having high precedence. So the expression becomes 2+3/2*16. Now we have two operators / and * having same precedence. The associativity is from left to right so division will be done first. The expression become 2 + 1 * 16 after integer division. Now we have two operators + and * .But * is having high precedence so multiplication will be done first followed by the addition and the final result become 18.

>>2*3//2+3/2

4.5

Try your own examples....