(Groups on expressions after )
The precedence of operators in C dictates the order in which the operators will be evolved in an expression. Associativity, on the other hand, defines the order in which the operators of the same precedence will be evaluated in an expression. Also, associativity can occur from either right to left or left to right.
In this article, we will take a closer look at Operator Precedence and Associativity in C according to the GATE Syllabus for CSE (Computer Science Engineering) . Read ahead to know more.
Table of Contents
Operator associativity.
Precedence and Associativity are two of the characters that are used for operators in an expression for determining the order of sub-expressions when they do not have brackets.
Operator precedence helps us determine which of the operators in an expression must be evaluated first in case the expression consists of more than a single operator.
50 – 2 * 15 is going to yield 20. It is because it gets evaluated as 50 – (2 * 15), and not as (50 – 2) * 15. The reason here is that subtraction (-) has lower precedence as compared to multiplication (*).
We use associativity when two or more than two operators with the same precedence are present in the same expression.
The precedence of Division and Multiplication arithmetic operators is the same. So, let’s say we have an expression with us which is 6 * 3 / 20. The evaluation of this expression would be (6 * 3) / 20 because the associativity will be left to right for both the operators – multiplication and division. In a similar case, the calculation of 40 / 4 * 5 would be (40 / 4) * 5 because the associativity would be from right to left here as well.
Here is how the operator precedence and associativity work in the C language:
. | Direct member selection | Left to right |
-> | Indirect member selection | Left to right |
[] | Array element reference | Left to right |
() | Functional call | Left to right |
~ | Bitwise(1’s) complement | Right to left |
! | Logical negation | Right to left |
– | Unary minus | Right to left |
+ | Unary plus | Right to left |
— | Decrement | Right to left |
++ | Increment | Right to left |
* | Pointer reference | Right to left |
& | Dereference (Address) | Right to left |
(type) | Typecast (conversion) | Right to left |
sizeof | Returns the size of an object | Right to left |
% | Remainder | Left to right |
/ | Divide | Left to right |
* | Multiply | Left to right |
– | Binary minus (subtraction) | Left to right |
+ | Binary plus (Addition) | Left to right |
>> | Right shift | Left to right |
<< | Left shift | Left to right |
> | Greater than | Left to right |
< | Less than | Left to right |
>= | Greater than or equal | Left to right |
<= | Less than or equal | Left to right |
== | Equal to | Left to right |
!= | Not equal to | Left to right |
^ | Bitwise exclusive OR | Left to right |
& | Bitwise AND | Left to right |
|| | Logical OR | Left to right |
| | Bitwise OR | Left to right |
?: | Conditional Operator | Right to left |
&& | Logical AND | Left to right |
, | Separator of expressions | Left to right |
= | Simple assignment | Right to left |
/= | Assign quotient | Right to left |
*= | Assign product | Right to left |
%= | Assign remainder | Right to left |
-= | Assign difference | Right to left |
+= | Assign sum | Right to left |
|= | Assign bitwise OR | Right to left |
^= | Assign bitwise XOR | Right to left |
&= | Assign bitwise AND | Right to left |
>>= | Assign right shift | Right to left |
<<= | Assign left shift | Right to left |
1. We only use associativity when we have two or more operators that have the same precedence in an expression.
The point to note here is that associativity is not applicable when we are defining the order of evaluation of operands with different levels of precedence.
2. All the operators that have a similar level of precedence have the same associativity. It is very important, or else the compiler won’t be able to decide what order of evaluation must an expression follow when it has two operators with the same precedence but different associativity. For example, – and + have the very same associativity.
3. The associativity and precedence of prefix ++ and postfix ++ are very different from each other. Here, the precedence of prefix ++ is less as compared to the postfix ++. Thus, their associativity also turns out to be different. Here, the associativity of prefix ++ is from right to left, while the associativity of postfix ++ is from left to right.
4. We must use a comma (,) very carefully, as it has the least level of precedence among all the other operators present in an expression.
5. We don’t have chaining of comparison in the C programming language. The Python language treats the expressions such as x > y > z as x > y and y > z. No similar type of chaining occurs in the C program.
1. What would be the output/result obtained from this program?
int x = 5, y = 10;
z = x * 2 + y;
printf(“\n output = %d”, z);
Answer – C. 20
We can calculate the output of this code using the precedence table. According to this table, the precedence of the assignment operator ( – ) and the addition operator ( + ) is lower than that of the multiplication operator ( * ). Thus, multiplication will get evaluated first here.
Thus, z = x * 2 + y
z = 5 * 2 + 10
z = 10 + 10
2. What would be the output/result obtained from this program?
int x = 50, y = 5;
z = x / 2 + y;
Answer – B. 30
We can calculate the output of this code using the precedence table. According to this table, the precedence of the assignment operator ( – ) and the addition operator ( + ) is lower than that of the division operator ( / ). Thus, multiplication will get evaluated first here.
Thus, z = x / 2 + y
z = 50 / 2 + 5
3. What would be the output/result obtained from this program?
int x = 30, y = 12;
z = x * 2 / y;
Answer – A. 5
The evaluation of this expression would be (30 * 2) / 12 because the associativity will be left to right for both the operators – multiplication and division.
Thus, z = x * 2 / y
z = (30 * 2) / 12
z = 60 / 12
4. What would be the output/result obtained from this program?
int x = 80, y = 3;
z = x / 2 * y;
Answer – D. 120
The evaluation of this expression would be (80 / 2) * 3 because the associativity will be left to right for both the operators – multiplication and division.
Thus, z = x / 2 * y
z = (80 / 2) * 3
The precedence of Addition and Subtraction arithmetic operators is the same. So, let’s say we have an expression with us which is 20 + 5 – 10. The evaluation of this expression would be (20 + 5) – 10 because the associativity will be left to right for both the operators – multiplication and division. In a similar case, the calculation of 25 – 10 would be 15 because the associativity would be from right to left here as well.
The precedence of Division and Multiplication arithmetic operators is the same. So, let’s say we have an expression with us which is 6 * 3 / 20. The evaluation of this expression would be (6 * 3) / 20 because the associativity will be left to right for both the operators – multiplication and division. In a similar case, the calculation of 40 / 4 * 5 would be (40 / 4) * 5 because the associativity would be from right to left here as well.
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Prec/Ass | Operator | Description | Pattern |
---|---|---|---|
1 L->R | :: :: | Global scope (unary) Namespace scope (binary) | ::name class_name::member_name |
2 L->R | () () type() type{} [] . -> ++ –– typeid const_cast dynamic_cast reinterpret_cast static_cast sizeof… noexcept alignof | Parentheses Function call Functional cast List init temporary object (C++11) Array subscript Member access from object Member access from object ptr Post-increment Post-decrement Run-time type information Cast away const Run-time type-checked cast Cast one type to another Compile-time type-checked cast Get parameter pack size Compile-time exception check Get type alignment | (expression) function_name(arguments) type(expression) type{expression} pointer[expression] object.member_name object_pointer->member_name lvalue++ lvalue–– typeid(type) or typeid(expression) const_cast<type>(expression) dynamic_cast<type>(expression) reinterpret_cast<type>(expression) static_cast<type>(expression) sizeof…(expression) noexcept(expression) alignof(type) |
3 R->L | + - ++ –– ! not ~ (type) sizeof co_await & * new new[] delete delete[] | Unary plus Unary minus Pre-increment Pre-decrement Logical NOT Logical NOT Bitwise NOT C-style cast Size in bytes Await asynchronous call Address of Dereference Dynamic memory allocation Dynamic array allocation Dynamic memory deletion Dynamic array deletion | +expression -expression ++lvalue ––lvalue !expression not expression ~expression (new_type)expression sizeof(type) or sizeof(expression) co_await expression (C++20) &lvalue *expression new type new type[expression] delete pointer delete[] pointer |
4 L->R | ->* .* | Member pointer selector Member object selector | object_pointer->*pointer_to_member object.*pointer_to_member |
5 L->R | * / % | Multiplication Division Remainder | expression * expression expression / expression expression % expression |
6 L->R | + - | Addition Subtraction | expression + expression expression - expression |
7 L->R | << >> | Bitwise shift left / Insertion Bitwise shift right / Extraction | expression << expression expression >> expression |
8 L->R | <=> | Three-way comparison (C++20) | expression <=> expression |
9 L->R | < <= > >= | Comparison less than Comparison less than or equals Comparison greater than Comparison greater than or equals | expression < expression expression <= expression expression > expression expression >= expression |
10 L->R | == != | Equality Inequality | expression == expression expression != expression |
11 L->R | & | Bitwise AND | expression & expression |
12 L->R | ^ | Bitwise XOR | expression ^ expression |
13 L->R | | | Bitwise OR | expression | expression |
14 L->R | && and | Logical AND Logical AND | expression && expression expression and expression |
15 L->R | || or | Logical OR Logical OR | expression || expression expression or expression |
16 R->L | throw co_yield ?: = *= /= %= += -= <<= >>= &= |= ^= | Throw expression Yield expression (C++20) Conditional Assignment Multiplication assignment Division assignment Remainder assignment Addition assignment Subtraction assignment Bitwise shift left assignment Bitwise shift right assignment Bitwise AND assignment Bitwise OR assignment Bitwise XOR assignment | throw expression co_yield expression expression ? expression : expression lvalue = expression lvalue *= expression lvalue /= expression lvalue %= expression lvalue += expression lvalue -= expression lvalue <<= expression lvalue >>= expression lvalue &= expression lvalue |= expression lvalue ^= expression |
17 L->R | , | Comma operator | expression, expression |
Best practice
Value computation (of operations)
Consider the following expression:
Sample problem: x = 2 + 3 % 4 Binary operator has higher precedence than operator or operator , so it gets evaluated first: x = 2 + (3 % 4) Binary operator has a higher precedence than operator , so it gets evaluated next: Final answer: x = (2 + (3 % 4)) We now no longer need the table above to understand how this expression will evaluate. |
. |
Operator precedence defines the order in which operators are evaluated in expressions with multiple operators.
Operators with higher precedence will be bound tighter (as if by parentheses) to its argument than the operators with lower precedence. For example, the expression a + b * c is equivalent to a + ( b * c ) . That is, we firstly evaluate the multiplication operator and only then sum the result of the multiplication and the value of a . This is because the multiplication operator has higher precedence.
If there are multiple operators of the same precedence in the expression, the order of evaluation is defined by their associativity: either right-to-left or left-to-right. For example, a + b - c is equivalent to ( a + b ) - c as associativity of these particular operators is left to right.
The following table lists the precedence and associativity of C++ operators.
Operators are listed top to bottom, in descending precedence. in an
Precedence | Operator | Description | Associativity |
---|---|---|---|
1 | Scope resolution | Left-to-right | |
2 | Suffix/postfix increment and decrement | ||
Function call | |||
Array subscripting | |||
Element selection by reference | |||
Element selection through pointer | |||
3 | Prefix increment and decrement | Right-to-left | |
Unary plus and minus | |||
Logical NOT and bitwise NOT | |||
) | Type cast | ||
Indirection (dereference) | |||
Address-of | |||
Size-of | |||
, | Dynamic memory allocation | ||
, | Dynamic memory deallocation | ||
4 | Pointer to member | Left-to-right | |
5 | Multiplication, division, and remainder | ||
6 | Addition and subtraction | ||
7 | Bitwise left shift and right shift | ||
8 | For relational operators < and ≤ respectively | ||
For relational operators > and ≥ respectively | |||
9 | For relational = and ≠ respectively | ||
10 | Bitwise AND | ||
11 | Bitwise XOR (exclusive or) | ||
12 | Bitwise OR (inclusive or) | ||
13 | Logical AND | ||
14 | Logical OR | ||
15 | Ternary conditional | Right-to-left | |
Direct assignment (provided by default for C++ classes) | |||
Assignment by sum and difference | |||
Assignment by product, quotient, and remainder | |||
Assignment by bitwise left shift and right shift | |||
Assignment by bitwise AND, XOR, and OR | |||
16 | Throw operator (for exceptions) | ||
17 | Comma | Left-to-right |
Operator precedence determines how operators are parsed concerning each other. Operators with higher precedence become the operands of operators with lower precedence.
Consider an expression describable by the representation below, where both OP1 and OP2 are fill-in-the-blanks for OPerators.
The combination above has two possible interpretations:
Which one the language decides to adopt depends on the identity of OP1 and OP2 .
If OP1 and OP2 have different precedence levels (see the table below), the operator with the higher precedence goes first and associativity does not matter. Observe how multiplication has higher precedence than addition and executed first, even though addition is written first in the code.
Within operators of the same precedence, the language groups them by associativity . Left-associativity (left-to-right) means that it is interpreted as (a OP1 b) OP2 c , while right-associativity (right-to-left) means it is interpreted as a OP1 (b OP2 c) . Assignment operators are right-associative, so you can write:
with the expected result that a and b get the value 5. This is because the assignment operator returns the value that is assigned. First, b is set to 5. Then the a is also set to 5 — the return value of b = 5 , a.k.a. right operand of the assignment.
As another example, the unique exponentiation operator has right-associativity, whereas other arithmetic operators have left-associativity.
Operators are first grouped by precedence, and then, for adjacent operators that have the same precedence, by associativity. So, when mixing division and exponentiation, the exponentiation always comes before the division. For example, 2 ** 3 / 3 ** 2 results in 0.8888888888888888 because it is the same as (2 ** 3) / (3 ** 2) .
For prefix unary operators, suppose we have the following pattern:
where OP1 is a prefix unary operator and OP2 is a binary operator. If OP1 has higher precedence than OP2 , then it would be grouped as (OP1 a) OP2 b ; otherwise, it would be OP1 (a OP2 b) .
If the unary operator is on the second operand:
Then the binary operator OP2 must have lower precedence than the unary operator OP1 for it to be grouped as a OP2 (OP1 b) . For example, the following is invalid:
Because + has higher precedence than yield , this would become (a + yield) 1 — but because yield is a reserved word in generator functions, this would be a syntax error. Luckily, most unary operators have higher precedence than binary operators and do not suffer from this pitfall.
If we have two prefix unary operators:
Then the unary operator closer to the operand, OP2 , must have higher precedence than OP1 for it to be grouped as OP1 (OP2 a) . It's possible to get it the other way and end up with (OP1 OP2) a :
Because await has higher precedence than yield , this would become (await yield) 1 , which is awaiting an identifier called yield , and a syntax error. Similarly, if you have new !A; , because ! has lower precedence than new , this would become (new !) A , which is obviously invalid. (This code looks nonsensical to write anyway, since !A always produces a boolean, not a constructor function.)
For postfix unary operators (namely, ++ and -- ), the same rules apply. Luckily, both operators have higher precedence than any binary operator, so the grouping is always what you would expect. Moreover, because ++ evaluates to a value , not a reference , you can't chain multiple increments together either, as you may do in C.
Operator precedence will be handled recursively . For example, consider this expression:
First, we group operators with different precedence by decreasing levels of precedence.
Within the * / / group, because they are both left-associative, the left operand would be grouped.
Note that operator precedence and associativity only affect the order of evaluation of operators (the implicit grouping), but not the order of evaluation of operands . The operands are always evaluated from left-to-right. The higher-precedence expressions are always evaluated first, and their results are then composed according to the order of operator precedence.
If you are familiar with binary trees, think about it as a post-order traversal .
After all operators have been properly grouped, the binary operators would form a binary tree. Evaluation starts from the outermost group — which is the operator with the lowest precedence ( / in this case). The left operand of this operator is first evaluated, which may be composed of higher-precedence operators (such as a call expression echo("left", 4) ). After the left operand has been evaluated, the right operand is evaluated in the same fashion. Therefore, all leaf nodes — the echo() calls — would be visited left-to-right, regardless of the precedence of operators joining them.
In the previous section, we said "the higher-precedence expressions are always evaluated first" — this is generally true, but it has to be amended with the acknowledgement of short-circuiting , in which case an operand may not be evaluated at all.
Short-circuiting is jargon for conditional evaluation. For example, in the expression a && (b + c) , if a is falsy , then the sub-expression (b + c) will not even get evaluated, even if it is grouped and therefore has higher precedence than && . We could say that the logical AND operator ( && ) is "short-circuited". Along with logical AND, other short-circuited operators include logical OR ( || ), nullish coalescing ( ?? ), and optional chaining ( ?. ).
When evaluating a short-circuited operator, the left operand is always evaluated. The right operand will only be evaluated if the left operand cannot determine the result of the operation.
Note: The behavior of short-circuiting is baked in these operators. Other operators would always evaluate both operands, regardless if that's actually useful — for example, NaN * foo() will always call foo , even when the result would never be something other than NaN .
The previous model of a post-order traversal still stands. However, after the left subtree of a short-circuiting operator has been visited, the language will decide if the right operand needs to be evaluated. If not (for example, because the left operand of || is already truthy), the result is directly returned without visiting the right subtree.
Consider this case:
Only C() is evaluated, despite && having higher precedence. This does not mean that || has higher precedence in this case — it's exactly because (B() && A()) has higher precedence that causes it to be neglected as a whole. If it's re-arranged as:
Then the short-circuiting effect of && would only prevent C() from being evaluated, but because A() && C() as a whole is false , B() would still be evaluated.
However, note that short-circuiting does not change the final evaluation outcome. It only affects the evaluation of operands , not how operators are grouped — if evaluation of operands doesn't have side effects (for example, logging to the console, assigning to variables, throwing an error), short-circuiting would not be observable at all.
The assignment counterparts of these operators ( &&= , ||= , ??= ) are short-circuited as well. They are short-circuited in a way that the assignment does not happen at all.
The following table lists operators in order from highest precedence (18) to lowest precedence (1).
Several general notes about the table:
Precedence | Associativity | Individual operators | Notes |
---|---|---|---|
18: grouping | n/a | | [1] |
17: access and call | left-to-right | | [2] |
| |||
n/a | | [3] | |
with argument list | [4] | ||
| |||
16: new | n/a | without argument list | |
15: postfix operators | n/a | | [5] |
| |||
14: prefix operators | n/a | | [6] |
| |||
| |||
| |||
| |||
| |||
[7] | |||
13: exponentiation | right-to-left | | [8] |
12: multiplicative operators | left-to-right | | |
| |||
| |||
11: additive operators | left-to-right | | |
| |||
10: bitwise shift | left-to-right | | |
| |||
| |||
9: relational operators | left-to-right | | |
| |||
| |||
| |||
8: equality operators | left-to-right | | |
| |||
| |||
| |||
7: bitwise AND | left-to-right | | |
6: bitwise XOR | left-to-right | | |
5: bitwise OR | left-to-right | | |
4: logical AND | left-to-right | | |
3: logical OR, nullish coalescing | left-to-right | | |
| [9] | ||
2: assignment and miscellaneous | right-to-left | | [10] |
| |||
| |||
| |||
| |||
| |||
| |||
| |||
| |||
| |||
| |||
| |||
| |||
| |||
| |||
| |||
right-to-left | | [11] | |
right-to-left | | [12] | |
n/a | |||
| [13] | ||
1: comma | left-to-right | |
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Consider the following Python3 program:
I expected the output to be:
But instead I got:
My question is: is there anything in the Python language specification about associativity of the assignment operator, or is the behavior for the above example undefined?
All I was able to find is that expressions are evaluated form left to right, except that r-value is evaluated first in case of assignment, but that doesn't help.
Short answer: the code is well defined; the order is left-to-right.
Long answer:
First of all, let's get the terminology right. Unlike in some other languages, assignment in Python is a statement , not an operator . This means that you can't use assignment as part of another expression: for example i = (j = 0) is not valid Python code.
The assignment statement is defined to explicitly permit multiple assignment targets (in your example, these are i and a[i] ). Each target can be a list, but let's leave that aside.
Where there are multiple assignment targets, the value is assigned from left to right. To quote the documentation :
An assignment statement evaluates the expression list (remember that this can be a single expression or a comma-separated list, the latter yielding a tuple) and assigns the single resulting object to each of the target lists, from left to right .
Just to make it clear, since I struggled myself to understand this. The statement:
is equivalent to
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Control statements, java object class, java inheritance, java polymorphism, java abstraction, java encapsulation, java oops misc.
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The associativity and precedence of an operator is a part of the definition of the programming language; different programming languages may have different associativity and precedence for the same type of operator. Consider the expression a ~ b ~ c. If the operator ~ has left associativity, this expression would be interpreted as (a ~ b) ~ c.
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Operator associative refers to the order in which operators of the same precedence are used in a word. In a programming language, it is important to understand the interactions between operators to properly define and test expressions. In this article, we will discuss operator associativity in programming. Table of Content.
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The precedence of operators determines which operator is executed first if there is more than one operator in an expression. Let us consider an example: In C, the precedence of * is higher than - and =. Hence, 17 * 6 is evaluated first. Then the expression involving - is evaluated as the precedence of - is higher than that of =.
Associativity in CPU caches. The Associative property in mathematics is a property of operators such as addition (+). This property allows you to rearrange parentheses without changing the value of a statement, i.e.: (a + b) + c = a + (b + c) In programming languages, the associativity (or fixity) of an operator is a property that determines ...
C++ operator precedence and associativity table. The following table shows the precedence and associativity of C++ operators (from highest to lowest precedence). Operators with the same precedence number have equal precedence unless another relationship is explicitly forced by parentheses. Expand table. Operator Description.
C++ Operators Associativity. Operator associativity is the direction from which an expression is evaluated. For example, int a = 1; int b = 4; // a will be 4 a = b; Take a look at a = 4; statement. The associativity of the = operator is from right to left. Hence, the value of b is assigned to a, and not in the other direction.. Also, multiple operators can have the same level of precedence (as ...
Assignment operators are right-associative, so you can write: a = b = 5; // same as writing a = (b = 5); with the expected result that a and b get the value 5. This is because the assignment operator returns the value that is assigned. First, b is set to 5. Then the a is also set to 5 — the return value of b = 5, a.k.a. right operand of the ...
Operators that have the same precedence are bound to their arguments in the direction of their associativity. For example, the expression a = b = c is parsed as a =(b = c), and not as (a = b)= c because of right-to-left associativity of assignment, but a + b - c is parsed (a + b)- c and not a +(b - c) because of left-to-right associativity of ...
The precedence of operators in C dictates the order in which the operators will be evolved in an expression. Associativity, on the other hand, defines the order in which the operators of the same precedence will be evaluated in an expression. Also, associativity can occur from either right to left or left to right.
An operation is a mathematical process involving zero or more input values (called operands) that produces a new value (called an output value). The specific operation to be performed is denoted by a construct (typically a symbol or pair of symbols) called an operator. For example, as children we all learn that 2 + 3 equals 5.
If there are multiple operators of the same precedence in the expression, the order of evaluation is defined by their associativity: either right-to-left or left-to-right. For example, a + b - c is equivalent to (a + b) - c as associativity of these particular operators is left to right. The following table lists the precedence and ...
To solve this problem there is the concept of operator precedence. Operator Precedence is a set of rules that defines the priority for all the operators present in a programming language. The operation which has an operator with the highest priority will be executed first. Example: a= 4+5/10; In the above given example if we solve the addition ...
When operators of the same precedence level appear in an expression, the order of evaluation is determined by the associativity. Except for the assignment operator, associativity of most binary operators is left to right; associativity of the assignment operator and most unary operators is right to left. Consider the following program fragment:
This is because the assignment operator returns the value that is assigned. First, b is set to 5. Then the a is also set to 5 — the return value of b = 5, a.k.a. right operand of the assignment. As another example, the unique exponentiation operator has right-associativity, whereas other arithmetic operators have left-associativity.
13. Short answer: the code is well defined; the order is left-to-right. Long answer: First of all, let's get the terminology right. Unlike in some other languages, assignment in Python is a statement, not an operator. This means that you can't use assignment as part of another expression: for example i = (j = 0) is not valid Python code.
Associativity specifies the order in which operators are executed, which can be left to right or right to left. For example, in the phrase a = b = c = 8, the assignment operator is used from right to left. It means that the value 8 is assigned to c, then c is assigned to b, and at last b is assigned to a. This phrase can be parenthesized as (a ...
Assignment operators. All assignment expressions exist in C and C++ and can be overloaded in C++. ... The following is a table that lists the precedence and associativity of all the operators in the C and C++ languages. Operators are listed top to bottom, in descending precedence. Descending precedence refers to the priority of the grouping of ...
Assignment operators are used in programming to assign values to variables. We use an assignment operator to store and update data within a program. They enable programmers to store data in variables and manipulate that data. The most common assignment operator is the equals sign (=), which assigns the value on the right side of the operator to ...
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Assignment Operators; Identity Operators and Membership Operators; ... The following code shows how Operator Associativity in Python works: Example: The code showcases various mathematical operations. It calculates and prints the results of division and multiplication, addition and subtraction, subtraction within parentheses, and exponentiation